The document provides an overview of correlation, regression, and other statistical methods. It defines correlation as measuring the association between two variables, while regression finds the best fitting line to predict a dependent variable from an independent variable. Simple linear regression uses one predictor variable, while multiple linear regression uses two or more. Logistic regression is used for nominal dependent variables. Nonlinear regression fits curved lines to nonlinear data. The document provides examples and guidelines for choosing the appropriate statistical test based on the type of variables.
This document provides an overview of various statistical tests for comparing variables, including t-tests, ANOVA, MANOVA, ANCOVA, and MANCOVA. It defines each test and provides examples of their proper usage. T-tests are used to compare two groups on a continuous variable, including paired and unpaired, parametric and non-parametric versions. ANOVA and MANOVA are used to compare three or more groups and two or more dependent variables, respectively. ANCOVA and MANCOVA control for covariates/confounding variables in one-way and two-way designs with single or multiple dependent variables. Examples and best practices are given for selecting and conducting each type of test.
This document discusses various statistical concepts including outliers, transforming data, normalizing data, weighting data, robustness, and homoscedasticity and heteroscedasticity. Outliers are values far from other data points and should be carefully examined before removing. Data can be transformed using logarithms, square roots, or other functions to better fit a normal distribution or equalize variances between groups. Normalizing data puts variables on comparable scales. Weighting data adjusts for under- or over-representation in samples. Robust tests are resistant to violations of assumptions. Homoscedasticity refers to equal variances between groups while heteroscedasticity refers to unequal variances.
1. The document discusses linear correlation and regression between plasma amphetamine levels and amphetamine-induced psychosis scores using data from 10 patients.
2. A positive correlation was found between the two variables, and a linear regression equation was established to predict psychosis scores from amphetamine levels.
3. However, further statistical tests were needed to determine if the correlation and regression model could be generalized to the overall patient population.
Correlation & Regression Analysis using SPSSParag Shah
Concept of Correlation, Simple Linear Regression & Multiple Linear Regression and its analysis using SPSS. How it check the validity of assumptions in Regression
This document discusses multiple linear regression analysis. It begins by defining a multiple regression equation that describes the relationship between a response variable and two or more explanatory variables. It notes that multiple regression allows prediction of a response using more than one predictor variable. The document outlines key elements of multiple regression including visualization of relationships, statistical significance testing, and evaluating model fit. It provides examples of interpreting multiple regression output and using the technique to predict outcomes.
Introduction to correlation and regression analysisFarzad Javidanrad
This document provides an introduction to correlation and regression analysis. It defines key concepts like variables, random variables, and probability distributions. It discusses how correlation measures the strength and direction of a linear relationship between two variables. Correlation coefficients range from -1 to 1, with values closer to these extremes indicating stronger correlation. The document also introduces determination coefficients, which measure the proportion of variance in one variable explained by the other. Regression analysis builds on correlation to study and predict the average value of one variable based on the values of other explanatory variables.
The document discusses multiple linear regression analysis to predict gasoline mileage using automobile data. It covers the basics of regression modeling, assessing model fit, and diagnostics. Key steps include fitting a linear regression model of miles per gallon as the response variable against predictors like vehicle weight, engine size, and more. The document also demonstrates how to perform the multiple regression analysis in R using the automobile data set.
Multiple Linear Regression II and ANOVA IJames Neill
Explains advanced use of multiple linear regression, including residuals, interactions and analysis of change, then introduces the principles of ANOVA starting with explanation of t-tests.
This document provides an overview of various statistical tests for comparing variables, including t-tests, ANOVA, MANOVA, ANCOVA, and MANCOVA. It defines each test and provides examples of their proper usage. T-tests are used to compare two groups on a continuous variable, including paired and unpaired, parametric and non-parametric versions. ANOVA and MANOVA are used to compare three or more groups and two or more dependent variables, respectively. ANCOVA and MANCOVA control for covariates/confounding variables in one-way and two-way designs with single or multiple dependent variables. Examples and best practices are given for selecting and conducting each type of test.
This document discusses various statistical concepts including outliers, transforming data, normalizing data, weighting data, robustness, and homoscedasticity and heteroscedasticity. Outliers are values far from other data points and should be carefully examined before removing. Data can be transformed using logarithms, square roots, or other functions to better fit a normal distribution or equalize variances between groups. Normalizing data puts variables on comparable scales. Weighting data adjusts for under- or over-representation in samples. Robust tests are resistant to violations of assumptions. Homoscedasticity refers to equal variances between groups while heteroscedasticity refers to unequal variances.
1. The document discusses linear correlation and regression between plasma amphetamine levels and amphetamine-induced psychosis scores using data from 10 patients.
2. A positive correlation was found between the two variables, and a linear regression equation was established to predict psychosis scores from amphetamine levels.
3. However, further statistical tests were needed to determine if the correlation and regression model could be generalized to the overall patient population.
Correlation & Regression Analysis using SPSSParag Shah
Concept of Correlation, Simple Linear Regression & Multiple Linear Regression and its analysis using SPSS. How it check the validity of assumptions in Regression
This document discusses multiple linear regression analysis. It begins by defining a multiple regression equation that describes the relationship between a response variable and two or more explanatory variables. It notes that multiple regression allows prediction of a response using more than one predictor variable. The document outlines key elements of multiple regression including visualization of relationships, statistical significance testing, and evaluating model fit. It provides examples of interpreting multiple regression output and using the technique to predict outcomes.
Introduction to correlation and regression analysisFarzad Javidanrad
This document provides an introduction to correlation and regression analysis. It defines key concepts like variables, random variables, and probability distributions. It discusses how correlation measures the strength and direction of a linear relationship between two variables. Correlation coefficients range from -1 to 1, with values closer to these extremes indicating stronger correlation. The document also introduces determination coefficients, which measure the proportion of variance in one variable explained by the other. Regression analysis builds on correlation to study and predict the average value of one variable based on the values of other explanatory variables.
The document discusses multiple linear regression analysis to predict gasoline mileage using automobile data. It covers the basics of regression modeling, assessing model fit, and diagnostics. Key steps include fitting a linear regression model of miles per gallon as the response variable against predictors like vehicle weight, engine size, and more. The document also demonstrates how to perform the multiple regression analysis in R using the automobile data set.
Multiple Linear Regression II and ANOVA IJames Neill
Explains advanced use of multiple linear regression, including residuals, interactions and analysis of change, then introduces the principles of ANOVA starting with explanation of t-tests.
Discriminant analysis (DA) is a statistical technique used to predict group membership when the dependent variable is categorical and the independent variables are continuous. It identifies which variables discriminate between two or more naturally occurring groups. DA develops a linear equation to predict group membership based on weighted combinations of predictor variables. It aims to maximize the distance between group means to achieve strong discriminatory power. Like regression, DA assumes variables are normally distributed, cases are randomly sampled, and groups are mutually exclusive and collectively exhaustive. It requires at least two groups with minimal overlap and similar group sizes of at least five cases. DA can classify new cases into groups based on the discriminant functions derived from existing data.
T test, independant sample, paired sample and anovaQasim Raza
The document discusses various statistical analyses that can be performed in SPSS, including t-tests, ANOVA, and post-hoc tests. It provides details on one-sample t-tests, independent t-tests, paired t-tests, one-way ANOVA tests, and evaluating assumptions like normality. Examples are given on how to conduct these tests in SPSS and how to interpret the output. Guidance is provided on follow-up post-hoc tests that can be used after ANOVA to examine differences between specific groups.
The document describes how to conduct and interpret a paired samples t-test in SPSS. It explains that a paired samples t-test is used to compare the means of two related variables measured on the same subjects. It provides an example using reaction time data collected from participants before and after drinking a beer. It outlines the steps to check assumptions, run the t-test in SPSS, and interpret the output, finding that participants had significantly slower reaction times after consuming alcohol.
Correlation and regression are statistical techniques used to analyze relationships between variables. Correlation determines the strength and direction of a relationship, while regression describes the linear relationship to predict changes in one variable based on changes in another. There are different types of correlation including simple, multiple, and partial correlation. Regression analysis determines the regression line that best fits the data to estimate values of one variable based on the other. The correlation coefficient measures the strength of linear correlation from -1 to 1, while regression coefficients are used to predict changes in the variables.
Correlation analysis is a statistical technique used to determine the degree of relationship between two quantitative variables. Scatterplots are used to graphically depict the relationship and identify if it is positive, negative, or no correlation. The correlation coefficient measures the strength and direction of correlation, ranging from -1 to 1. A significance test determines if a correlation is likely to have occurred by chance or is statistically significant. Different types of correlation include simple, multiple, partial, and autocorrelation.
T-Test for Correlated Groups by STR Grp. 2Oj Acopiado
The t-test for two correlated groups is used to determine if there is a significant difference between the means of two groups that are correlated, such as samples tested before and after an intervention. In an example, students' sensory-motor coordination was tested with two types of music. A t-test found no significant difference between students' performance on the two music types, as the calculated t value of -3.0 was smaller than the critical value of ±2.145 for 14 degrees of freedom and a significance level of 0.05. Therefore, the null hypothesis that there is no difference between the music types was retained.
The document discusses analysis of variance (ANOVA) which is used to compare the means of three or more groups. It explains that ANOVA avoids the problems of multiple t-tests by providing an omnibus test of differences between groups. The key steps of ANOVA are outlined, including partitioning variation between and within groups to calculate an F-ratio. A large F value indicates more difference between groups than expected by chance alone.
The document provides an overview of two-factor ANOVA, including:
- Two-factor ANOVA involves more than one independent variable (IV) and evaluates three main hypotheses - the main effects of each IV and their interaction.
- It partitions the total variance into between-treatments variance and within-treatments variance. Between-treatments variance is further partitioned into portions attributable to each IV and their interaction.
- F-ratios are calculated to test the three hypotheses by comparing the between-treatments mean squares to the within-treatments mean squares. If an F-ratio exceeds the critical value, its hypothesis is supported.
SPSS does not have Z test for proportions, So, we use Chi-Square test for proportion tests. Test for single proportion and Test for proportions of two samples
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 10: Correlation and Regression
10.1: Correlation
The document discusses various parametric statistical tests including t-tests, ANOVA, ANCOVA, and MANOVA. It provides definitions and assumptions for parametric tests and explains how they can be used to analyze quantitative data that follows a normal distribution. Specific parametric tests covered in detail include the independent samples t-test, paired t-test, one-way ANOVA, two-way ANOVA, and ANCOVA. Examples are provided to illustrate how each test is conducted and how results are interpreted.
This document provides an overview of regression analysis, including linear regression, multiple regression, and assessing assumptions. It defines regression as a technique for investigating relationships between variables. Simple linear regression involves one predictor and one response variable, while multiple regression extends this to multiple predictors. Key steps are outlined such as assessing the fit of regression models using R-squared, testing the significance of individual predictors, and ensuring assumptions of normality, linearity and equal variance are met. Examples are provided demonstrating how to evaluate these assumptions and interpret regression results.
The document discusses regression and correlation analysis between BMI (Kg/m2) of pregnant mothers and birth weight (kg) of their newborns using data from 15 mothers. A scatter plot showed a positive linear relationship between BMI and birth weight. Linear regression was used to calculate the regression line as y=1.775351+0.0330817x, which can be used to predict birth weight based on a mother's BMI. The correlation coefficient (R) between BMI and birth weight was 0.94, indicating a strong positive correlation.
Chi-Square test for independence of attributes / Chi-Square test for checking association between two categorical variables, Chi-Square test for goodness of fit
Correlation is a statistical technique used to determine the degree of relationship between two variables. Correlational research aims to identify and describe relationships but does not imply causation. Positive correlation indicates high scores on one variable are associated with high scores on the other, while negative correlation means high scores on one variable are associated with low scores on the other. Correlational research can be used for explanatory or predictive purposes. More complex techniques like multiple regression allow prediction using combinations of variables. Threats to internal validity like subject characteristics must be controlled.
Data Science - Part IV - Regression Analysis & ANOVADerek Kane
This lecture provides an overview of linear regression analysis, interaction terms, ANOVA, optimization, log-level, and log-log transformations. The first practical example centers around the Boston housing market where the second example dives into business applications of regression analysis in a supermarket retailer.
This document provides an overview of one-way ANOVA, including its assumptions, steps, and an example. One-way ANOVA tests whether the means of three or more independent groups are significantly different. It compares the variance between sample means to the variance within samples using an F-statistic. If the F-statistic exceeds a critical value, then at least one group mean is significantly different from the others. Post-hoc tests may then be used to determine specifically which group means differ. The example calculates statistics to compare the analgesic effects of three drugs and finds no significant difference between the group means.
The document provides an overview of regression analysis techniques, including linear regression and logistic regression. It explains that regression analysis is used to understand relationships between variables and can be used for prediction. Linear regression finds relationships when the dependent variable is continuous, while logistic regression is used when the dependent variable is binary. The document also discusses selecting the appropriate regression model and highlights important considerations for linear and logistic regression.
This document provides an overview of correlation and linear regression analysis. It defines correlation as a statistical measure of the relationship between two variables. Pearson's correlation coefficient (r) ranges from -1 to 1, with values farther from 0 indicating a stronger linear relationship. Positive values indicate an increasing relationship, while negative values indicate a decreasing relationship. The coefficient of determination (r2) represents the proportion of shared variance between variables. While correlation indicates linear association, it does not imply causation. Multiple regression allows predicting a continuous dependent variable from two or more independent variables.
This document discusses correlation and regression analysis. It defines correlation as a statistical measure of how two variables are related. A correlation coefficient between -1 and 1 indicates the strength and direction of the linear relationship between variables. A scatterplot can show this graphically. Regression analysis involves using one variable to predict scores on another variable. Simple linear regression uses one independent variable to predict a dependent variable, while multiple regression uses two or more independent variables. The goal is to identify the regression line that best fits the data with the least error. The coefficient of determination, R2, indicates how much variance in the dependent variable is explained by the independent variables.
Assessment 2 ContextIn many data analyses, it is desirable.docxfestockton
Assessment 2 Context
In many data analyses, it is desirable to compute a coefficient of association. Coefficients of association are quantitative measures of the amount of relationship between two variables. Ultimately, most techniques can be reduced to a coefficient of association and expressed as the amount of relationship between the variables in the analysis. There are many types of coefficients of association. They express the mathematical association in different ways, usually based on assumptions about the data. The most common coefficient of association you will encounter is the Pearson product-moment correlation coefficient (symbolized as the italicized r), and it is the only coefficient of association that can safely be referred to as simply the "correlation coefficient". It is common enough so that if no other information is provided, it is reasonable to assume that is what is meant.
Correlation coefficients are numbers that give information about the strength of relationship between two variables, such as two different test scores from a sample of participants. The coefficient ranges from -1 through +1. Coefficients between 0 and +1 indicate a positive relationship between the two scores, such as high scores on one test tending to come from people with high scores on the second. The other possible relationship, which is every bit as useful, is a negative correlation between -1 and 0. A negative correlation possesses no less predictive power between the two scores. The difference is that high scores on one measure are associated with low scores on the other.
An example of the kinds of measures that might correlate negatively is absences and grades. People with higher absences will be expected to have lower grades. When a correlation is said to be significant, it can be shown that the correlation is significantly different form zero in the population. A correlation of zero means no relationship between variables. A correlation other than zero means the variables are related. As the coefficient gets further from zero (toward +1 or -1), the relationship becomes stronger.Interpreting Correlation: Magnitude and Sign
Interpreting a Pearson's correlation coefficient (rXY) requires an understanding of two concepts:
· Magnitude.
· Sign (+/-).
The magnitude refers to the strength of the linear relationship between Variable X and Variable
The rXY ranges in values from -1.00 to +1.00. To determine magnitude, ignore the sign of the correlation, and the absolute value of rXY indicates the extent to which Variable X and Variable Y are linearly related. For correlations close to 0, there is no linear relationship. As the correlation approaches either -1.00 or +1.00, the magnitude of the correlation increases. Therefore, for example, the magnitude of r = -.65 is greater than the magnitude of r = +.25 (|.65| > |.25|).
In contrast to magnitude, the sign of a non-zero correlation is either negative or positive.
These labels are not interpreted ...
Discriminant analysis (DA) is a statistical technique used to predict group membership when the dependent variable is categorical and the independent variables are continuous. It identifies which variables discriminate between two or more naturally occurring groups. DA develops a linear equation to predict group membership based on weighted combinations of predictor variables. It aims to maximize the distance between group means to achieve strong discriminatory power. Like regression, DA assumes variables are normally distributed, cases are randomly sampled, and groups are mutually exclusive and collectively exhaustive. It requires at least two groups with minimal overlap and similar group sizes of at least five cases. DA can classify new cases into groups based on the discriminant functions derived from existing data.
T test, independant sample, paired sample and anovaQasim Raza
The document discusses various statistical analyses that can be performed in SPSS, including t-tests, ANOVA, and post-hoc tests. It provides details on one-sample t-tests, independent t-tests, paired t-tests, one-way ANOVA tests, and evaluating assumptions like normality. Examples are given on how to conduct these tests in SPSS and how to interpret the output. Guidance is provided on follow-up post-hoc tests that can be used after ANOVA to examine differences between specific groups.
The document describes how to conduct and interpret a paired samples t-test in SPSS. It explains that a paired samples t-test is used to compare the means of two related variables measured on the same subjects. It provides an example using reaction time data collected from participants before and after drinking a beer. It outlines the steps to check assumptions, run the t-test in SPSS, and interpret the output, finding that participants had significantly slower reaction times after consuming alcohol.
Correlation and regression are statistical techniques used to analyze relationships between variables. Correlation determines the strength and direction of a relationship, while regression describes the linear relationship to predict changes in one variable based on changes in another. There are different types of correlation including simple, multiple, and partial correlation. Regression analysis determines the regression line that best fits the data to estimate values of one variable based on the other. The correlation coefficient measures the strength of linear correlation from -1 to 1, while regression coefficients are used to predict changes in the variables.
Correlation analysis is a statistical technique used to determine the degree of relationship between two quantitative variables. Scatterplots are used to graphically depict the relationship and identify if it is positive, negative, or no correlation. The correlation coefficient measures the strength and direction of correlation, ranging from -1 to 1. A significance test determines if a correlation is likely to have occurred by chance or is statistically significant. Different types of correlation include simple, multiple, partial, and autocorrelation.
T-Test for Correlated Groups by STR Grp. 2Oj Acopiado
The t-test for two correlated groups is used to determine if there is a significant difference between the means of two groups that are correlated, such as samples tested before and after an intervention. In an example, students' sensory-motor coordination was tested with two types of music. A t-test found no significant difference between students' performance on the two music types, as the calculated t value of -3.0 was smaller than the critical value of ±2.145 for 14 degrees of freedom and a significance level of 0.05. Therefore, the null hypothesis that there is no difference between the music types was retained.
The document discusses analysis of variance (ANOVA) which is used to compare the means of three or more groups. It explains that ANOVA avoids the problems of multiple t-tests by providing an omnibus test of differences between groups. The key steps of ANOVA are outlined, including partitioning variation between and within groups to calculate an F-ratio. A large F value indicates more difference between groups than expected by chance alone.
The document provides an overview of two-factor ANOVA, including:
- Two-factor ANOVA involves more than one independent variable (IV) and evaluates three main hypotheses - the main effects of each IV and their interaction.
- It partitions the total variance into between-treatments variance and within-treatments variance. Between-treatments variance is further partitioned into portions attributable to each IV and their interaction.
- F-ratios are calculated to test the three hypotheses by comparing the between-treatments mean squares to the within-treatments mean squares. If an F-ratio exceeds the critical value, its hypothesis is supported.
SPSS does not have Z test for proportions, So, we use Chi-Square test for proportion tests. Test for single proportion and Test for proportions of two samples
Please Subscribe to this Channel for more solutions and lectures
http://www.youtube.com/onlineteaching
Chapter 10: Correlation and Regression
10.1: Correlation
The document discusses various parametric statistical tests including t-tests, ANOVA, ANCOVA, and MANOVA. It provides definitions and assumptions for parametric tests and explains how they can be used to analyze quantitative data that follows a normal distribution. Specific parametric tests covered in detail include the independent samples t-test, paired t-test, one-way ANOVA, two-way ANOVA, and ANCOVA. Examples are provided to illustrate how each test is conducted and how results are interpreted.
This document provides an overview of regression analysis, including linear regression, multiple regression, and assessing assumptions. It defines regression as a technique for investigating relationships between variables. Simple linear regression involves one predictor and one response variable, while multiple regression extends this to multiple predictors. Key steps are outlined such as assessing the fit of regression models using R-squared, testing the significance of individual predictors, and ensuring assumptions of normality, linearity and equal variance are met. Examples are provided demonstrating how to evaluate these assumptions and interpret regression results.
The document discusses regression and correlation analysis between BMI (Kg/m2) of pregnant mothers and birth weight (kg) of their newborns using data from 15 mothers. A scatter plot showed a positive linear relationship between BMI and birth weight. Linear regression was used to calculate the regression line as y=1.775351+0.0330817x, which can be used to predict birth weight based on a mother's BMI. The correlation coefficient (R) between BMI and birth weight was 0.94, indicating a strong positive correlation.
Chi-Square test for independence of attributes / Chi-Square test for checking association between two categorical variables, Chi-Square test for goodness of fit
Correlation is a statistical technique used to determine the degree of relationship between two variables. Correlational research aims to identify and describe relationships but does not imply causation. Positive correlation indicates high scores on one variable are associated with high scores on the other, while negative correlation means high scores on one variable are associated with low scores on the other. Correlational research can be used for explanatory or predictive purposes. More complex techniques like multiple regression allow prediction using combinations of variables. Threats to internal validity like subject characteristics must be controlled.
Data Science - Part IV - Regression Analysis & ANOVADerek Kane
This lecture provides an overview of linear regression analysis, interaction terms, ANOVA, optimization, log-level, and log-log transformations. The first practical example centers around the Boston housing market where the second example dives into business applications of regression analysis in a supermarket retailer.
This document provides an overview of one-way ANOVA, including its assumptions, steps, and an example. One-way ANOVA tests whether the means of three or more independent groups are significantly different. It compares the variance between sample means to the variance within samples using an F-statistic. If the F-statistic exceeds a critical value, then at least one group mean is significantly different from the others. Post-hoc tests may then be used to determine specifically which group means differ. The example calculates statistics to compare the analgesic effects of three drugs and finds no significant difference between the group means.
The document provides an overview of regression analysis techniques, including linear regression and logistic regression. It explains that regression analysis is used to understand relationships between variables and can be used for prediction. Linear regression finds relationships when the dependent variable is continuous, while logistic regression is used when the dependent variable is binary. The document also discusses selecting the appropriate regression model and highlights important considerations for linear and logistic regression.
This document provides an overview of correlation and linear regression analysis. It defines correlation as a statistical measure of the relationship between two variables. Pearson's correlation coefficient (r) ranges from -1 to 1, with values farther from 0 indicating a stronger linear relationship. Positive values indicate an increasing relationship, while negative values indicate a decreasing relationship. The coefficient of determination (r2) represents the proportion of shared variance between variables. While correlation indicates linear association, it does not imply causation. Multiple regression allows predicting a continuous dependent variable from two or more independent variables.
This document discusses correlation and regression analysis. It defines correlation as a statistical measure of how two variables are related. A correlation coefficient between -1 and 1 indicates the strength and direction of the linear relationship between variables. A scatterplot can show this graphically. Regression analysis involves using one variable to predict scores on another variable. Simple linear regression uses one independent variable to predict a dependent variable, while multiple regression uses two or more independent variables. The goal is to identify the regression line that best fits the data with the least error. The coefficient of determination, R2, indicates how much variance in the dependent variable is explained by the independent variables.
Assessment 2 ContextIn many data analyses, it is desirable.docxfestockton
Assessment 2 Context
In many data analyses, it is desirable to compute a coefficient of association. Coefficients of association are quantitative measures of the amount of relationship between two variables. Ultimately, most techniques can be reduced to a coefficient of association and expressed as the amount of relationship between the variables in the analysis. There are many types of coefficients of association. They express the mathematical association in different ways, usually based on assumptions about the data. The most common coefficient of association you will encounter is the Pearson product-moment correlation coefficient (symbolized as the italicized r), and it is the only coefficient of association that can safely be referred to as simply the "correlation coefficient". It is common enough so that if no other information is provided, it is reasonable to assume that is what is meant.
Correlation coefficients are numbers that give information about the strength of relationship between two variables, such as two different test scores from a sample of participants. The coefficient ranges from -1 through +1. Coefficients between 0 and +1 indicate a positive relationship between the two scores, such as high scores on one test tending to come from people with high scores on the second. The other possible relationship, which is every bit as useful, is a negative correlation between -1 and 0. A negative correlation possesses no less predictive power between the two scores. The difference is that high scores on one measure are associated with low scores on the other.
An example of the kinds of measures that might correlate negatively is absences and grades. People with higher absences will be expected to have lower grades. When a correlation is said to be significant, it can be shown that the correlation is significantly different form zero in the population. A correlation of zero means no relationship between variables. A correlation other than zero means the variables are related. As the coefficient gets further from zero (toward +1 or -1), the relationship becomes stronger.Interpreting Correlation: Magnitude and Sign
Interpreting a Pearson's correlation coefficient (rXY) requires an understanding of two concepts:
· Magnitude.
· Sign (+/-).
The magnitude refers to the strength of the linear relationship between Variable X and Variable
The rXY ranges in values from -1.00 to +1.00. To determine magnitude, ignore the sign of the correlation, and the absolute value of rXY indicates the extent to which Variable X and Variable Y are linearly related. For correlations close to 0, there is no linear relationship. As the correlation approaches either -1.00 or +1.00, the magnitude of the correlation increases. Therefore, for example, the magnitude of r = -.65 is greater than the magnitude of r = +.25 (|.65| > |.25|).
In contrast to magnitude, the sign of a non-zero correlation is either negative or positive.
These labels are not interpreted ...
Assessment 2 ContextIn many data analyses, it is desirable.docxgalerussel59292
Assessment 2 Context
In many data analyses, it is desirable to compute a coefficient of association. Coefficients of association are quantitative measures of the amount of relationship between two variables. Ultimately, most techniques can be reduced to a coefficient of association and expressed as the amount of relationship between the variables in the analysis. There are many types of coefficients of association. They express the mathematical association in different ways, usually based on assumptions about the data. The most common coefficient of association you will encounter is the Pearson product-moment correlation coefficient (symbolized as the italicized r), and it is the only coefficient of association that can safely be referred to as simply the "correlation coefficient". It is common enough so that if no other information is provided, it is reasonable to assume that is what is meant.
Correlation coefficients are numbers that give information about the strength of relationship between two variables, such as two different test scores from a sample of participants. The coefficient ranges from -1 through +1. Coefficients between 0 and +1 indicate a positive relationship between the two scores, such as high scores on one test tending to come from people with high scores on the second. The other possible relationship, which is every bit as useful, is a negative correlation between -1 and 0. A negative correlation possesses no less predictive power between the two scores. The difference is that high scores on one measure are associated with low scores on the other.
An example of the kinds of measures that might correlate negatively is absences and grades. People with higher absences will be expected to have lower grades. When a correlation is said to be significant, it can be shown that the correlation is significantly different form zero in the population. A correlation of zero means no relationship between variables. A correlation other than zero means the variables are related. As the coefficient gets further from zero (toward +1 or -1), the relationship becomes stronger.Interpreting Correlation: Magnitude and Sign
Interpreting a Pearson's correlation coefficient (rXY) requires an understanding of two concepts:
· Magnitude.
· Sign (+/-).
The magnitude refers to the strength of the linear relationship between Variable X and Variable
The rXY ranges in values from -1.00 to +1.00. To determine magnitude, ignore the sign of the correlation, and the absolute value of rXY indicates the extent to which Variable X and Variable Y are linearly related. For correlations close to 0, there is no linear relationship. As the correlation approaches either -1.00 or +1.00, the magnitude of the correlation increases. Therefore, for example, the magnitude of r = -.65 is greater than the magnitude of r = +.25 (|.65| > |.25|).
In contrast to magnitude, the sign of a non-zero correlation is either negative or positive.
These labels are not interpreted .
This document discusses correlation and regression analysis. It defines correlation as a statistical measure of how strongly two variables are related. A correlation coefficient between -1 and 1 indicates the strength and direction of the linear relationship between variables. Regression analysis allows us to predict the value of a dependent variable based on the value of one or more independent variables. Simple linear regression involves one independent variable, while multiple regression involves two or more independent variables to predict the dependent variable. The document provides examples and formulas for calculating correlation, regression lines, explained and unexplained variance, and the coefficient of determination.
This document discusses linear regression analysis. Regression analysis measures the relationship between two quantitative variables and can be used to make causal inferences. A regression model shows how dependent and independent variables are related. A bivariate model has one independent variable, while a multivariate model has two or more. Scatterplots graph the relationship between variables. The regression equation specifies the linear relationship between a dependent variable Y and independent variable X. The goal of regression is to find the line that best fits the data by minimizing distances between data points and the line. R-squared indicates how well the regression model predicts observed values, with higher R-squared indicating more of the variance is explained.
- Regression analysis is a statistical technique used to measure the relationship between two quantitative variables and make causal inferences.
- A regression model graphs the relationship between a dependent variable (Y axis) and one or more independent variables (X axis). The goal is to find the linear equation that best fits the data.
- The regression equation takes the form Y = a + bX, where a is the intercept, b is the slope coefficient, and X and Y are the variables. The coefficient b indicates the strength and direction of the relationship.
This document discusses correlation and defines it as the statistical relationship between two variables, where a change in one variable results in a corresponding change in the other. It describes different types of correlation including positive, negative, simple, partial and multiple. Methods for studying correlation are also outlined, including scatter diagrams and Karl Pearson's coefficient of correlation (represented by r), which quantifies the strength and direction of the linear relationship between two variables from -1 to 1. The coefficient of determination (r2) is also introduced, which expresses the proportion of variance in one variable that is predictable from the other.
Linear regression (1). spss analiisa statistikJuandaSatriyo1
This document discusses linear regression analysis, a statistical method used to analyze relationships between variables. It can be used to describe, estimate, and predict relationships. The document provides an overview of linear regression, including how it models relationships between dependent and independent variables using equations. It also discusses important considerations for performing and interpreting linear regression analyses correctly. Examples are provided to illustrate key points.
It is most useful for the students of BBA for the subject of "Data Analysis and Modeling"/
It has covered the content of chapter- Data regression Model
Visit for more on www.ramkumarshah.com.np/
This document discusses correlation and linear regression analysis. It begins by outlining the learning objectives which are to describe relationships between variables using correlation, estimate effects of independent variables on dependents with regression, and perform and interpret different types of regression analyses. It then provides examples of how correlation calculates the strength and direction of relationships between interval variables and how regression finds the best fitting linear equation to estimate relationships between variables. It emphasizes that regression minimizes the sum of squared errors to find the line of best fit for the data.
HOW IS IT USEFUL IN FIELD OF FORENSIC SCIENCE AND IN THIS I HAVE SHOWN THE TYPES OF CORRELATION, SIGNIFICANCE , METHODS AND KARL PEARSON'S METHOD OF CORRELATION
2. If you have a nonlinear relationship between an independent varia.pdfsuresh640714
2. If you have a nonlinear relationship between an independent variable x and a dependent
variable y, how can you apply the least -squares fit method? Does this work for all nonlinear
relationships? if not please give an example of a nonlinear equation where the fit method cannot
be used.(No need to use Matlab on this question).
Solution
A)The assumptions of linearity and additivity are both implicit in this specification. • Additivity
= assumption that for each IV X, the amount of change in E(Y) associated with a unit increase in
X (holding all other variables constant) is the same regardless of the values of the other IVs in
the model. That is, the effect of X1 does not depend on X2; increasing X1 from 10 to 11 will
have the same effect regardless of whether X2 = 0 or X2 = 1. • With non-additivity, the effect of
X on Y depends on the value of a third variable, e.g. gender. As we’ve just discussed, we use
models with multiplicative interaction effects when relationships are non-additive.
Linearity = assumption that for each IV, the amount of change in the mean value of Y associated
with a unit increase in the IV, holding all other variables constant, is the same regardless of the
level of X, e.g. increasing X from 10 to 11 will produce the same amount of increase in E(Y) as
increasing X from 20 to 21. Put another way, the effect of a 1 unit increase in X does not depend
on the value of X. • With nonlinearity, the effect of X on Y depends on the value of X; in effect,
X somehow interacts with itself. This is sometimes refered to as a self interaction. The
interaction may be multiplicative but it can take on other forms as well, e.g. you may need to
take logs of variables.
Dealing with Nonlinearity in variables. We will see that many nonlinear specifications can be
converted to linear form by performing transformations on the variables in the model. For
example, if Y is related to X by the equation E Yi Xi ( ) = + 2 and the relationship between the
variables is therefore nonlinear, we can define a new variable Z = X2 . The new variable Z is
then linearly related to Y, and OLS regression can be used to estimate the coefficients of the
model. There are numerous other cases where, given appropriate transformations of the
variables, nonlinear relationships can be converted into models for which coefficients can be
estimated using OLS. We’ll cover a few of the most important and common ones here, but there
are many others. Detecting nonlinearity and nonadditivity. The key question is whether the slope
of the relationship between an IV and a DV can be expected to vary depending on the context. •
The first step in detecting nonlinearity or nonadditivity is theoretical rather than technical. Once
the nature of the expected relationship is understood well enough to make a rough graph of it, the
technical work should begin. Hence, ask such questions as, can the slope of the relationship
between Xi and E(Y) be expected to have the same sign for all value.
Correlation measures the strength and direction of association between two variables. Positive correlation means both variables increase or decrease together, while negative correlation means one variable increases as the other decreases. Correlation does not imply causation. The correlation coefficient r ranges from -1 to 1, where -1 is total negative correlation, 0 is no correlation, and 1 is total positive correlation. Common types of correlation coefficients include Pearson's correlation coefficient, used with normally distributed interval or ratio data, and Spearman's rank correlation coefficient, used with ordinal or non-normally distributed data. Regression analysis can be used to predict the value of a dependent variable from the value of an independent variable when they are linearly correlated.
Introduction to simple linear regression and correlation in spssAmjad Afridi
1. The document discusses simple linear regression and correlation. It defines simple correlation and describes positive, negative, and no correlation between two variables.
2. It explains that the correlation coefficient shows the degree of relation between two variables and can range from -1 to 1.
3. Simple linear regression predicts an outcome variable (y) as a function of a predictor variable (x) using the linear regression formula y = B0 + B1x, where B0 is the intercept and B1 is the regression coefficient.
1. Regression analysis is a statistical technique used to model relationships between variables and make predictions. It can be used to describe relationships, estimate coefficients, make predictions, and control systems.
2. Linear regression models describe straight-line relationships between variables, while non-linear models describe curved relationships. The goodness of fit of a model can be evaluated using the coefficient of determination.
3. The least squares method is used to fit regression lines by minimizing the sum of the squared vertical distances between observed and estimated y-values for a regression of y on x, or minimizing the sum of squared horizontal distances for a regression of x on y.
This document discusses correlation analysis and different types of correlation. It defines correlation as a statistical analysis of the relationship between two or more variables. There are three main types of correlation discussed:
1. Positive correlation means that as one variable increases, the other also tends to increase. Negative correlation means that as one variable increases, the other tends to decrease.
2. Simple correlation analyzes the relationship between two variables, while multiple correlation analyzes three or more variables simultaneously. Partial correlation holds the effect of other variables constant.
3. Methods for measuring correlation include scatter diagrams, which graphically show the relationship, and algebraic formulas that calculate a correlation coefficient to quantify the strength and direction of the relationship.
This document provides an introduction to linear regression analysis. It discusses how regression finds the best fitting straight line to describe the relationship between two variables. The regression line minimizes the residuals, or errors, between the predicted Y values from the line and the actual data points. The accuracy of predictions from the regression model can be evaluated using the correlation coefficient (r) and the standard error of estimate. Multiple linear regression extends this process to model relationships between a dependent variable Y and two or more independent variables (X1, X2, etc).
Linear regression analysis allows researchers to predict scores on a dependent or criterion variable (Y) based on knowledge of an independent or predictor variable (X). Simple linear regression involves using one predictor variable to predict scores on the dependent variable. Multiple regression expands this to use multiple predictor variables. Key aspects of regression analysis covered in the document include the correlation between variables, using the least squares method to determine the best fitting regression line, computing predicted Y scores, explaining and unexplained variance, and the importance of multiple regression in understanding how well predictor variables predict the criterion variable.
Correlation analysis measures the strength and direction of association between two or more variables. It is represented by the coefficient of correlation (r), which ranges from -1 to 1. A value of 0 indicates no association, 1 indicates perfect positive association, and -1 indicates perfect negative association. The scatter diagram is a graphical method to visualize the association between variables by plotting their values. Karl Pearson's coefficient is a commonly used algebraic method to calculate the coefficient of correlation from sample data.
This document discusses key concepts in applied statistics including hypothesis testing, p-values, types of errors, sensitivity and specificity. It provides examples and explanations of these topics using scenarios about testing if feeding chickens chocolate changes the gender ratio of offspring. Hypothesis testing involves defining the null and alternative hypotheses and using a statistical test to either reject or fail to reject the null hypothesis based on the p-value. Type I and type II errors in hypothesis testing are explained. Sensitivity and specificity in diagnostic tests are introduced using an example about detecting if a car is being stolen.
This document provides an introduction to applied statistics and various statistical concepts. It discusses the normal (Gaussian) distribution, standard deviation, standard error of the mean, and confidence intervals. Examples and explanations are provided for each concept. Hands-on examples for calculating these statistics in Excel, SPSS, and Prism are also presented. The document aims to explain key statistical terms and how they are applied in data analysis.
a clinically oriented discussion of blood coagulation and related diseases and treatment. also discussing DIC, plasma fractions and anti-platelet drugs.
HMG-CoA reductase inhibitors, commonly known as statins, are the primary drugs used to treat dyslipidemia. They work by inhibiting cholesterol production in the liver, leading to increased clearance of LDL cholesterol from the bloodstream. Fibrates also effectively lower triglyceride levels by increasing fatty acid metabolism. Bile acid sequestrants function by binding bile acids in the gut, enhancing their excretion and increasing LDL receptor activity in the liver. Combination drug therapies that target multiple lipid abnormalities can provide improved treatment outcomes over single agents alone.
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This document discusses drug use during pregnancy and lactation. It covers the effects of non-therapeutic drugs like alcohol, caffeine, cigarettes, cocaine and marijuana on the fetus. It also discusses the management of selected medical conditions in pregnancy like AIDS, UTI, asthma, diabetes, hypertension and epilepsy. The final sections discuss neonatal therapeutics including vitamin K administration and treatment of ophthalmia neonatorum. It concludes with guidance on drug use during lactation, identifying drugs that are generally safe and those that require caution.
This document discusses methemoglobinemia, which is a condition caused by elevated levels of methemoglobin in the blood. Methemoglobin cannot carry oxygen, so symptoms range from cyanosis to death depending on levels. It may be congenital or acquired through medications, chemicals, and certain foods. Diagnosis involves blood tests showing abnormal hemoglobin color. Treatment focuses on reducing methemoglobin back to hemoglobin, primarily using methylene blue or ascorbic acid. The document also briefly covers cyanide poisoning, which causes tissue anoxia and can be fatal within minutes of inhalation.
This document provides guidance on proper academic writing style and conventions. It discusses things to avoid such as adjectives, negatives, long sentences, and colloquial language. It also covers proper use of punctuation like commas, semicolons, and apostrophes. Connectors are addressed to link ideas clearly. The document aims to improve clarity, precision and formality of academic writing.
This document provides an overview of the key elements of academic writing, including:
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Objective
To identify the impact of speed limit restrictions in different constituencies over the years with the help of DID technique to conclude whether having strict speed limit restrictions can help to reduce the increasing number of road accidents on weekends.
Context*
Generally, on weekends people tend to spend time with their family and friends and go for outings, parties, shopping, etc. which results in an increased number of vehicles and crowds on the roads.
Over the years a rapid increase in road casualties was observed on weekends by the Government.
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Applied statistics part 4
1. Applied Statistics
Part 4
By
M. H. Farjoo MD, PhD, Bioanimator
Shahid Beheshti University of Medical Sciences
Instagram: @bio_animation
2. Applied Statistics
Part 4
Introduction of Correlation and regression
Difference Between Correlation & Regression
Correlation
Regression
Simple Linear regression
Multiple linear Regression
Simple Logistic Regression
Multiple Logistic Regression
Non linear (Curvilinear) Regression
Choosing Test
3. Introduction
Correlation and regression are not the same.
Use correlation to know:
Whether two measurement variables are associated.
Whether as one variable increases, the other increases
or decreases.
Use regression to know:
The strength of the association or relation.
The equation of a line that fits the cloud of data,
describes the relationship, and predicts unknown
values.
4. Difference Between Correlation & Regression
Goal:
Correlation quantifies the degree to which two variables are
related, and does not fit a line through the data points.
Linear regression finds the best line (equation) that fits data
points.
kind of data and sampling:
Correlation is used when you measure both variables and
sample both variables randomly from a population.
In regression, X is a variable we manipulate and choose its
values (time, concentration, etc.) and predict Y from X.
5. Difference Between Correlation & Regression
Relationship between results:
Correlation computes correlation coefficient, r.
Linear regression quantifies goodness of fit, r2 (or R2).
Which variable is which?
In correlation we get the same coefficient (r) if swap
the two variables.
Regression gets a different best-fit line and different
coefficient (r2) if we swap the two variables.
6. Correlation
When two variables vary together, there is
covariation or correlation.
The null hypothesis implies:
There is no relationship between the variables
As the X variable changes, the Y variable does not
change.
Correlation coefficient is not significantly different
form zero (or statistically: r = 0)
Correlation does not imply causation.
But a significant correlation may suggest further
research to test for a cause and effect relation.
11. Guidelines for Judging Causality
1. Is there a temporal relationship?
2. What is the strength of association?
3. Is there a dose/response relationship?
4. Were the findings replicated?
5. Is there biological plausibility?
6. What happens with cessation of exposure?
7. Is this explanation consistent with other knowledge?
12. Correlation
Causal inferences are licensed primarily by the design
of your study, not by the statistical techniques you
use.
Correlation only quantifies linear (straight line)
covariation.
A correlation analysis is not helpful if Y changes to a
point, and then continues to opposite direction.
In this case we obtain a low value of r, even though
the two variables are strongly related.
13. Correlation
The value of correlation may be:
-1 (perfect inverse relationship; X goes up, Y goes down)
1 (perfect positive relationship; X goes up so does Y).
0 (no correlation at all).
Pearson correlation (r) is parametric and assumes
both X and Y are from a Gaussian distribution.
Spearman correlation [rs or ρ (rho)] does not make
this assumption and is non-parametric.
Correlation is not sensitive to non-normality
So use Pearson method any time you have 2
measurement variables, even if they look non-normal.
14. Value of r (or rs) Interpretation
1.0 Perfect correlation
> 0 to 1
The two variables tend to
increase or decrease together.
0.0
The two variables do not vary
together at all.
-1 to < 0
One variable increases as the
other decreases.
-1.0
Perfect negative or inverse
correlation.
15. Correlation
If r or rs is far from zero, there are four possible
explanations:
1. Changes in the X variable causes a change in the value of
the Y variable.
2. Changes in the Y variable causes a change in the value of
the X variable.
3. Changes in another variable influences both X and Y.
4. X and Y don’t really correlate at all, and correlation is by
chance.
16. Regression
In regression we fit a line through the data and use its
equation to predict Y from X.
We predict scores on one variable (Y axis) from the
scores on a second variable (X axis).
The variable we are basing our predictions is the
independent or predictor variable (X axis).
The variable we are predicting is the criterion or
dependent variable (Y axis).
Only the dependent variable (Y axis) determines the type
of regression NOT the independent variable (X axis).
17. Regression
The null hypothesis implies: the slope of the best-fit
line is equal to zero.
Try to use the line equation for prediction within the
X values found in the data set (interpolation).
Predicting Y values outside the range of X values
(extrapolation) can yield ridiculous results if you go
too far!
The expansion of an iron rod is related to heat, but it
will not expand at 2000 °C, it will melt!!
18. Regression
r2 (in the output window of the results) is called the
coefficient of determination, or "r squared".
It is a value that ranges from 0 to 1, and is the fraction
of the variation in the two variables that is “shared”.
Regressions can have a small r2 (no relationship), yet
have a slope that is significantly different from zero.
The null hypothesis has nothing to do with r2.
19. Simulated data showing the effect of the range of X values on the
r2. For the exact same data, measuring Y over a smaller range of X
values yields a smaller r2.
20. Simple Linear regression
When Y is a continuous variable and there is only one
predictor variable, it is called: simple linear regression.
An example is: weight of the infant at birth (Y),
predicted by gestational age (X).
In simple linear regression, the predictions of Y from X
form a straight line.
Regression line can predict Y from X and is the best-
fitting straight line through the points with slope and
intercept.
The line minimizes the sum of the squares of the
vertical distances of the points (errors) from the line.
21. • The slope quantifies the steepness of the line. It equals the change in
Y for each unit change in X.
• The Y intercept is the Y value of the line when X equals zero. It
defines the elevation of the line.
24. in Graph A, the points are closer to the line than they are in Graph B.
Therefore, the predictions in Graph A are more accurate than in Graph B.
25. Simple Linear regression
The Frank Anscombe's quartet demonstrate the
importance of looking at your data.
They all have 11 points and are very different.
Surprisingly when analyzed by linear regression, all
these values are identical for all four graphs:
The mean values of X and Y
The slopes and intercepts
r2
The SE and CI of the slope and intercept
26. Frank Anscombe, (1918–2001) He was brother-in-law to
another well-known statistician, John Tukey; their wives were
sisters.
29. Multiple Linear Regression
In multiple regression, Y is predicted by two or more
variables in X axis.
We can use it for:
Predicting the values of the dependent variable.
To decide which independent variable (X) has a major
effect on the dependent variable (Y).
An example is: weight of the infant at birth (Y), predicted
by gestational age, Weight of mother, and whether the
mother smokes or not ( all on X).
Not all the predictors (X) are worth of including in a
multiple linear regression model.
30. Multiple Linear Regression
Another example: to predict a student's university score
based on their high school scores and their total SAT
score.
The basic idea is to find a linear combination of high
school scores that best predicts University score.
Be very careful in using multiple regression to understand
cause-and-effect relationships.
It is very easy to get misled by the results of a fancy
multiple regression analysis.
The results should be used as a suggestion, rather than for
hypothesis testing.
32. Simple Logistic Regression
Simple logistic regression is used when there is one
measurement independent variable (X) and the Y variable
is nominal.
The goal is:
To check the probability of getting a particular condition of
Y is associated with X.
To predict a particular condition of Y, given the X.
If Y has only two values, the regression is called: “binary
logistic regression” (male/female, dead/alive).
If Y has more than two values, the regression is called:
"multinomial logistic regression”.
33. Simple Logistic Regression
Example of binary logistic regression: the effect of
study time (X), on exam outcome (Y).
The model can be used to predict the occurrence of
heart attack based on the plasma cholesterol.
An example of multinomial logistic regression: the
effect of the grade of a tumor (X), on the treatment
method (radiotherapy, chemotherapy, surgery) (Y).
The model can be used to choose how to treat the
patient based on the severity of the cancer.
34. Simple Logistic Regression
Pass:Y = 1
Fail: Y= 0
Y is only 0 or 1 because the result is only pass/fail and
there is nothing in between.
35. Multiple Logistic Regression
The dependent variable (Y) is nominal and there are 2
or more independent variables (X).
Example: the effect of cholesterol, age, and weight on
the probability of heart attack in the next year.
We can measure the risk factors on new individuals
and estimate the probability of heart attack.
This is done by comparing their odds ratios in the out
put window of the software.
36. Multiple Logistic Regression
We can try to guess what is the main risk factor that
changes the probability of the dependent variable.
The null hypothesis implies:
There is no relationship between the X variables and
the Y variable
Adding each X variable does not really improve the fit
of the equation.
37. Nonlinear (Curvilinear) Regression
If we have to transform nonlinear data to create a
linear relationship, nonlinear regression should be
used.
Avoid transformations such as Scatchard or
Lineweaver-Burk whose only goal is to linearize your
data.
These methods are outdated, and should not be used
to analyze data.
You might analyze the data by nonlinear regression
but show the results by linear transformation.
The human brain and eye is keen for straight lines!
38. The Scatchard equation is an equation for calculating the affinity
constant of a ligand with a protein.
39. In biochemistry, the Lineweaver–Burk plot is a representation
of enzyme kinetics.
40. Nonlinear (Curvilinear) Regression
Fitting a straight line to transformed data gives different
results than fitting a curved line to untransformed data.
The equation for a curve is a polynomial equation.
In polynomial equations X is raised to integer powers
such as X2 and X3.
A quadratic equation, is Y=aX1+bX2+d, and produces a
parabola.
A cubic equation is Y= aX1+bX2+cX3+d and produces
a S-shaped (sigmoid) curve.
43. Nonlinear (Curvilinear) Regression
Nonlinear regression is used for three purposes:
To fit a model to data for obtaining the best-fit values
of the parameters.
To compare the fits of alternative models.
To simply fit a smooth curve in order to interpolate
values from the curve.
The goal is not to describe the system perfectly, but to
fit a curve which comes close to knowing the system.
In this way we can understand the system, and reach
valid scientific conclusions.
44. Nonlinear (Curvilinear) Regression
The nonlinear method may yield results that are weird.
This happens with noisy or incomplete data, and include:
A rate constant that is negative.
A best-fit fraction that is greater than 1.
A best-fit Kd value that is negative.
Top of a sigmoid curve is far larger than the highest data.
An EC50 not within the range of your X values.
If the results make no sense, they are unacceptable, even
if the curve comes close to the points and R2 is close to 1.
45. Correlation & Regression
Hands-on practice
To calculate correlation & regression in SPSS:
For Correlation: Analyze => Correlate
For Regression: Analyze => Regression
To calculate correlation & regression in Prism:
XY (from welcome screen) => choose appropriate option
46. Choosing Test of Association
Dependent
Variable
Independen
t
Variable
Parametric
test
Non-
parametric test
Relationship
between 2
continuous
variables
Scale Scale
Pearson’s
Correlation
Coefficient
Spearman’s
Correlation
Coefficient
Predicting the value
of one variable from
the value of a
predictor variable or
looking
for significant
relationships
Scale Any
Simple Linear
Regression
Transform the
data
Nominal
(Binary)
Any
Logistic
regression
---------
Assessing the
relationship between
two categorical
variables
Categorical Categorical ---------
Chi-squared
test
47. Is your Dependent Variable (DV) continuous?
YES
NO
Is your Independent
Variable (IV) continuous?
Is your Independent
Variable (IV) continuous?
YES
YES
YES
Do you have
only two
groups?
NO
NO
NO
48. Type of Data
Goal
Measurement (from
Gaussian Population)
Rank, Score, or
Measurement (from Non-
Gaussian Population)
Binomial
(Two Possible
Outcomes)
Survival Time
Describe one group Mean, SD Median, interquartile range Proportion
Kaplan Meier survival
curve
Compare one group to a
hypothetical value
One-sample ttest Wilcoxon test
Chi-square
or
Binomial test **
Compare two
unpaired groups
Unpaired t test Mann-Whitney test
Fisher's test
(chi-square for large
samples)
Log-rank test or Mantel-
Haenszel*
Compare two paired
groups
Paired t test Wilcoxon test McNemar's test
Conditional proportional
hazards regression*
Compare three or more
unmatched groups
One-way ANOVA Kruskal-Wallis test Chi-square test
Cox proportional hazard
regression**
Compare three or more
matched groups
Repeated-measures
ANOVA
Friedman test Cochrane Q**
Conditional proportional
hazards regression**
Quantify association
between two variables
Pearson correlation Spearman correlation Contingency coefficients**
Predict value from another
measured variable
Simple linear regression
or
Nonlinear regression
Nonparametric
regression**
Simple logistic regression*
Cox proportional hazard
regression*
Predict value from several
measured or binomial
variables
Multiple linear regression*
or
Multiple nonlinear
regression**
Multiple logistic
regression*
Cox proportional hazard
regression*