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.
This document contains slides from a presentation on simple linear regression and correlation. It introduces simple linear regression modeling, including estimating the regression line using the method of least squares. It discusses the assumptions of the simple linear regression model and defines key terms like the regression coefficients (intercept and slope), error variance, standard errors of the estimates, and how to perform hypothesis tests and construct confidence intervals for the regression parameters. Examples are provided to demonstrate calculating quantities like sums of squares, estimating the regression line, and evaluating the fit of the regression model.
Multiple regression analysis is a powerful technique used for predicting the unknown value of a variable from the known value of two or more variables.
Regression analysis is a statistical technique used to estimate the relationships between variables. It allows one to predict the value of a dependent variable based on the value of one or more independent variables. The document discusses simple linear regression, where there is one independent variable, as well as multiple linear regression which involves two or more independent variables. Examples of linear relationships that can be modeled using regression analysis include price vs. quantity, sales vs. advertising, and crop yield vs. fertilizer usage. The key methods for performing regression analysis covered in the document are least squares regression and regressions based on deviations from the mean.
The document discusses simple linear regression. It defines key terms like regression equation, regression line, slope, intercept, residuals, and residual plot. It provides examples of using sample data to generate a regression equation and evaluating that regression model. Specifically, it shows generating a regression equation from bivariate data, checking assumptions visually through scatter plots and residual plots, and interpreting the slope as the marginal change in the response variable from a one unit change in the explanatory variable.
The document presents the results of a simple linear regression analysis conducted by a black belt to predict the number of calls answered (dependent variable) based on staffing levels (independent variable) using data collected over 240 samples in a call center. The regression equation found 83.4% of the variation in calls answered was explained by staffing levels. Notable outliers and leverage points were identified that could impact the strength of the predicted relationship between calls answered and staffing.
This document provides an introduction to basic statistics and regression analysis. It defines regression as relating to or predicting one variable based on another. Regression analysis is useful for economics and business. The document outlines the objectives of understanding simple linear regression, regression coefficients, and merits and demerits of regression analysis. It describes types of regression including simple and multiple regression. Key concepts explained in more detail include regression lines, regression equations, regression coefficients, and the difference between correlation and regression. Examples are provided to demonstrate calculating regression equations using different methods.
- Regression analysis is a statistical tool used to examine relationships between variables and can help predict future outcomes. It allows one to assess how the value of a dependent variable changes as the value of an independent variable is varied.
- Simple linear regression involves one independent variable, while multiple regression can include any number of independent variables. Regression analysis outputs include coefficients, residuals, and measures of fit like the R-squared value.
- An example uses home size and price data from 10 houses to generate a linear regression equation predicting that price increases by around $110 for each additional square foot. This model explains 58% of the variation in home prices.
The document provides an introduction to regression analysis and performing regression using SPSS. It discusses key concepts like dependent and independent variables, assumptions of regression like linearity and homoscedasticity. It explains how to calculate regression coefficients using the method of least squares and how to perform regression analysis in SPSS, including selecting variables and interpreting the output.
Regression and correlation analysis allow researchers to assess relationships between variables. Regression fits a line to two variables that minimizes the sum of squared errors, representing how well the independent variable predicts the dependent variable. Correlation assesses the strength and direction of association, ranging from -1 to 1. R-squared indicates the proportion of variance in the dependent variable explained by the independent variable.
- The document discusses simple linear regression analysis and how to use it to predict a dependent variable (y) based on an independent variable (x).
- Key points covered include the simple linear regression model, estimating regression coefficients, evaluating assumptions, making predictions, and interpreting results.
- Examples are provided to demonstrate simple linear regression analysis using data on house prices and sizes.
Regression analysis is a statistical technique for predicting a dependent variable based on one or more independent variables. Simple linear regression fits a straight line to the data to predict a continuous dependent variable (y) from a single independent variable (x). The output is an equation of the form y= b0 + b1x + ε, where b0 is the y-intercept, b1 is the slope, and ε is the error. Multiple linear regression extends this to include more than one independent variable. Regression analysis calculates the "best fit" line that minimizes the residuals, or differences between predicted and observed y values.
The document provides an overview of regression analysis techniques including linear regression and logistic regression. It defines regression as a statistical technique to model relationships between variables, with the goal of prediction or forecasting. Linear regression finds the best fitting straight line to model relationships between a continuous dependent variable and one or more independent variables. Logistic regression is used for classification problems where the dependent variable is categorical. The document explains the key differences between linear and logistic regression techniques.
- 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 chapter discusses simple linear regression analysis. It introduces the simple linear regression model and how it is used to predict a dependent variable (Y) based on the value of an independent variable (X). It explains how the least squares method is used to calculate the regression coefficients (slope and intercept) that best fit a line to the data. It also discusses measures of variation like R-squared and the assumptions of the linear regression model. An example using data on house prices and sizes is presented to demonstrate how to perform simple linear regression using Excel and interpret the results.
Applications of regression analysis - Measurement of validity of relationshipRithish Kumar
This document provides a summary of regression analysis in 9 steps: 1) Specify dependent and independent variables, 2) Check for linearity with scatter plots, 3) Transform variables if nonlinear, 4) Estimate the regression model, 5) Test the model fit with R2, 6) Perform a joint hypothesis test of the coefficients, 7) Test individual coefficients, 8) Check for violations of assumptions like autocorrelation and heteroscedasticity, 9) Interpret the intercept and slope coefficients. Regression analysis is used to determine relationships between variables and estimate how changes in independents impact dependents.
This document provides an overview of simple linear regression analysis. It discusses estimating regression coefficients using the least squares method, interpreting the regression equation, assessing model fit using measures like the standard error of the estimate and coefficient of determination, testing hypotheses about regression coefficients, and using the regression model to make predictions.
Regression (Linear Regression and Logistic Regression) by Akanksha BaliAkanksha Bali
Regression analysis is a statistical technique used to examine relationships between variables. Linear regression finds the best fitting straight line through data points to model the relationship between a continuous dependent variable (Y) and one or more independent variables (X). Logistic regression produces results in a binary format to predict outcomes of categorical dependent variables. It transforms the linear equation using logarithms to restrict predicted Y values between 0 and 1.
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.
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).
This document provides an introduction to regression and correlation analysis. It discusses simple and multiple linear regression models, how to interpret regression coefficients, and how to check the assumptions and adequacy of regression models. Key aspects covered include computing the regression line using the least squares method, interpreting the slope and intercept, checking the normality of residuals, and examining residual plots to validate the model. The goal of regression analysis is to model the relationship between a dependent variable and one or more independent variables.
Regression analysis is a statistical technique used to describe relationships between variables. Simple linear regression examines the relationship between a dependent variable (Y) and a single independent variable (X). The goal is to find the best fit line that expresses this relationship. Multiple regression extends this to predict Y from multiple independent variables. Key outputs include the regression line, R-squared value (the proportion of variance in Y explained by X), and measures of explained and unexplained variance such as the sum of squares.
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.
Regression analysis is a statistical technique for predicting the value of a variable based on the value of one or more other variables. Linear regression involves using a linear equation to model the relationship between a dependent or criterion variable (Y) and one or more independent or predictor variables (X). Multiple regression expands this to model the relationship between a dependent variable and more than one independent variable. Key aspects of regression covered in the document include the regression equation, slope, intercept, correlation, prediction, and use of regression in research.
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.
This document provides an overview of simple linear regression. It defines regression as determining the statistical relationship between variables where changes in one variable depend on changes in another. Regression analysis is used for prediction and exploring relationships between dependent and independent variables. The key aspects covered include:
- Dependent variables change due to independent variables.
- Lines of regression show the relationship between the variables.
- The method of least squares is used to determine the line of best fit that minimizes the error between predicted and actual values.
- Linear regression models take the form of y = a + bx and are used for tasks like prediction and determining impact of 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.
This document provides an overview of supervised learning techniques, focusing on different types of regression algorithms. It begins with an introduction to regression and discusses simple linear regression, multiple linear regression, and the assumptions of regression analysis. It then covers common regression algorithms like polynomial regression and logistic regression. Key concepts explained include the slope and intercept of linear regression lines, residual errors, and ways to improve regression accuracy like regularization and dimensionality reduction. Logistic regression is highlighted as preferable to linear regression for qualitative response variables with more than two levels.
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.
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 discusses linear correlation and regression analysis. It defines correlation as the degree of linear association between two quantitative variables. Positive correlation means both variables increase together, while negative correlation means one variable increases as the other decreases. The correlation coefficient r quantifies the strength of linear correlation between -1 and 1, where -1 is perfect negative correlation, 1 is perfect positive correlation, and 0 is no correlation. The regression line represents the linear relationship that best predicts the response variable y from the predictor variable x.
This document discusses correlation and linear regression. It defines correlation as the degree of linear association between two quantitative variables. Positive correlation means that as one variable increases, the other also increases. Negative correlation means that as one variable increases, the other decreases. The correlation coefficient r quantifies the strength of linear correlation between -1 and 1. A regression line represents the best fit linear relationship between an independent variable x and dependent variable y. The slope and y-intercept of the regression line are used to predict y-hat values based on x values.
This document discusses analyzing and summarizing relationships between two quantitative variables (bivariate data) using scatterplots. It covers key topics like correlation, linear regression lines, residuals, outliers and influential points. Scatterplots display the relationship between two variables and can show positive or negative linear associations or no relationship. Correlation coefficients measure the strength and direction of linear relationships, while regression lines predict variable relationships. Residual plots assess linearity and outliers.
FSE 200AdkinsPage 1 of 10Simple Linear Regression Corr.docxbudbarber38650
FSE 200
Adkins Page 1 of 10
Simple Linear Regression
Correlation only measures the strength and direction of the linear relationship between two quantitative variables. If the relationship is linear, then we would like to try to model that relationship with the equation of a line. We will use a regression line to describe the relationship between an explanatory variable and a response variable.
A regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression line to predict the value of y for a given value of x.
Ex. It has been suggested that there is a relationship between sleep deprivation of employees and the ability to complete simple tasks. To evaluate this hypothesis, 12 people were asked to solve simple tasks after having been without sleep for 15, 18, 21, and 24 hours. The sample data are shown below.
Subject
Hours without sleep, x
Tasks completed, y
1
15
13
2
15
9
3
15
15
4
18
8
5
18
12
6
18
10
7
21
5
8
21
8
9
21
7
10
24
3
11
24
5
12
24
4
Draw a scatterplot and describe the relationship. Lay a straight-edge on top of the plot and move it around until you find what you think might be a “line of best fit.” Then try to predict the number of tasks completed for someone having been without sleep 16 hours.
Was your line the same as that of the classmate sitting next to you? Probably not. We need a method that we can use to find the “best” regression line to use for prediction. The method we will use is called least-squares. No line will pass exactly through all the points in the scatterplot. When we use the line to predict a y for a given x value, if there is a data point with that same x value, we can compute the error (residual):
Our goal is going to be to make the vertical distances from the line as small as possible. The most commonly used method for doing this is the least-squares method.
The least-squares regression line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible.
Equation of the Least-Squares Regression Line
· Least-Squares Regression Line:
· Slope of the Regression Line:
· Intercept of the Regression Line:
Generally, regression is performed using statistical software. Clearly, given the appropriate information, the above formulas are simple to use.
Once we have the regression line, how do we interpret it, and what can we do with it?
The slope of a regression line is the rate of change, that amount of change in when x increases by 1.
The intercept of the regression line is the value of when x = 0. It is statistically meaningful only when x can take on values that are close to zero.
To make a prediction, just substitute an x-value into the equation and find .
To plot the line on a scatterplot, just find a couple of points on the regression line, one near each end of the range of x in the data. Plot the points and connect them with a line. .
This presentation discusses correlation, rank correlation, bivariate analysis, and the chi-square test. Correlation measures the strength and direction of association between two variables. Rank correlation analyzes relationships between different rankings using Spearman's correlation coefficient. Bivariate analysis examines the empirical relationship between two variables. The chi-square test statistically tests if an observed distribution differs from an expected distribution using a chi-square distributed test statistic.
This document discusses correlation, regression, and the general linear model. It defines correlation as assessing the relationship between two variables, while regression describes how well one variable can predict another. Pearson's r standardizes the covariance between variables. Linear regression finds the best-fitting line that minimizes the residuals through the least squares method. The coefficient of determination, r-squared, indicates how much variance in the dependent variable is explained by the independent variable. Multiple regression extends this to include multiple independent variables. The general linear model encompasses linear regression and can analyze effects across multiple dependent variables.
This document discusses correlation, regression, and the general linear model. It defines correlation as assessing the relationship between two variables, while regression describes how well one variable can predict another. Pearson's r standardizes the covariance between variables. Linear regression finds the best-fitting line that minimizes the residuals through the least squares method. The coefficient of determination, r2, indicates how much variance in the dependent variable is explained by the independent variable. Multiple regression extends this to include multiple independent variables. The general linear model encompasses both linear regression and multiple regression.
This document discusses correlation, regression, and the general linear model. It defines correlation as assessing the relationship between two variables, while regression describes how well one variable can predict another. Pearson's r standardizes the covariance between variables. Linear regression finds the best-fitting line that minimizes the residuals through the least squares method. The coefficient of determination, r-squared, indicates how much variance in the dependent variable is explained by the independent variable. Multiple regression extends this to include multiple independent variables. The general linear model encompasses linear regression and can analyze effects across multiple dependent variables.
Correlation & Regression for Statistics Social Sciencessuser71ac73
This document discusses correlation, regression, and the general linear model. It defines correlation as assessing the relationship between two variables, while regression describes how well one variable can predict another. Pearson's r standardizes the covariance between variables. Linear regression finds the best-fitting line that minimizes the residuals through the least squares method. The coefficient of determination, r-squared, indicates how much variance in the dependent variable is explained by the independent variable. Multiple regression extends this to include multiple independent variables. The general linear model encompasses both simple and multiple regression.
1) This chapter provides an overview of issues in criminal psychology and policing, including the roles and responsibilities of police officers, how the police image has changed over time, and sources of stress for officers.
2) Police officers perform diverse social and law enforcement duties and interact with many groups, exposing them to potentially traumatic situations that can cause stress disorders like PTSD.
3) Increasing diversity within police forces helps them better serve the community, but minority officers may face additional stressors of discrimination. Psychological support for managing job stress is important.
This document provides an overview of offender profiling and linking crimes. It discusses key topics such as:
- The definition and goals of offender profiling versus linking crimes. Offender profiling involves inferring a criminal's characteristics from their crime scene behavior, while linking crimes analyzes similarities between crimes to identify serial offenders.
- The two main types of offender profiling: geographical profiling to identify an offender's home location, and profiling personal characteristics like age, gender, and occupation.
- The empirical evidence supporting some profiling assumptions like cross-situational consistency but not others like the homology assumption. More research is still needed to demonstrate profiling's effectiveness.
- Who conducts profiling like criminal psychologists, police officers,
Criminal psychologists fulfill a variety of roles including assisting police with investigations, interviewing suspects and witnesses, providing expert testimony in court, assessing and rehabilitating offenders, and conducting research. They may help profile offenders, analyze crime data, improve interview techniques, and assess police recruits and address officer stress. Criminal psychologists also assess and treat offenders to reduce recidivism and address psychological needs. Many also work in academia conducting research and teaching criminal psychology.
The zero state theorem of medical science states that if an infectious disease is spreading in different regions, there must have been a point in time when the disease was in a "zero state" and was transmitted by a "patient zero". This point can be proven using Bolzano's theorem and the intermediate value theorem from mathematical analysis, which state that if a continuous function is sometimes positive and sometimes negative over an interval, it must be 0 at some point within that interval. The zero state theorem is important as it reminds researchers to search for patient zero to understand the initial spread and treatment of a disease.
This document proposes modernizing Ghana's farming sector by having farmers register their farms as companies and regularly report production statistics and financial information to generate a national database. This would allow farmers to access loans, insurance, and be recognized as valid income earners. The government would pass laws supporting this and an income insurance program for all Ghanaians aged 18-59. The goals are to raise farmers' incomes, boost agricultural production, facilitate wealth distribution, and move farmers into the middle class.
1. The document discusses fundamental theorems of medical diagnosis, including three formulations of the theorems.
2. The first theorem states that no disorder exists without symptoms and no symptoms exist without a disorder. The second theorem states that a disorder can be transmitted between individuals.
3. Koch's postulates and an extended version by Fredericks and Relman are used to prove the second theorem by demonstrating disease transmission from one individual to another.
1. The document discusses fundamental theorems of medical diagnosis and outlines three formulations of the theorems.
2. The first theorem states that no disorder exists without symptoms and no symptoms exist without an underlying disorder. The second theorem states that a disorder can be transmitted between individuals. The third theorem discusses the practitioner-patient relationship.
3. Koch's postulates and an extended version by Fredericks and Relman are presented as ways to prove the second theorem regarding disorder transmission between individuals.
This document discusses evidence that ancient Iranians (Persians) and Ghanaians (Ancient Egyptians) were closely related tribes. It provides linguistic and historical evidence that Persian and Akan (the language of Ghana) share many similar words and names. The document traces the lineage of Ezer, father of Akan, and Dishan, father of Aran (Iran/Persia) as brothers descended from Esau in Genesis. It argues this supports the Persians and Egyptians having a shared ancestral civilization, with notable early kings and cities listed for both peoples. Overall it aims to show compelling evidence that ancient Persians and Egyptians were cousin tribes originating from the same African people before migrating and establishing major emp
Desmond Ayim-Aboagye is a psychology of religion scholar, educationist, and philosopher. He received his education from the University of Uppsala and Andrews University. His research focuses on areas such as psychology of religion, transcultural psychiatry, behavioral economics, social psychiatry, and pain psychology. He has developed several theories relating to war and mental disorders. Currently, he works as a Professor and Dean at Regent University College of Science and Technology in Ghana.
Desmond Ayim-Aboagye is a Ghanaian psychologist of religion, educationist, and philosopher known for developing numerous theories related to war, mental disorders, and evolution. He received his PhD from the University of Uppsala in Sweden and currently works as a professor in Ghana. His research focuses on areas like psychology of religion, pain psychology, social psychiatry, and behavioral economics. He has published extensively and developed theories on topics like the relationship between war and mental illness.
Desmond Ayim-Aboagye is a Ghanaian psychologist of religion, educationist, and philosopher known for his research in psychology of religion, transcultural psychiatry, behavioral economics, social psychiatry, and pain psychology. He has developed numerous scientific theories and discovered several psychiatric disorders related to war. He received his B.A. and M.A. from Andrews University and PhD from the University of Uppsala. Currently he is a professor and dean at Regent University College of Science and Technology in Ghana.
Desmond Ayim-Aboagye is a Ghanaian psychologist of religion, educationist, and philosopher. He received his PhD from the University of Uppsala in Sweden. His research focuses on psychology of religion, transcultural psychiatry, behavioral economics, social psychiatry, and pain psychology. Through his research on the relationship between war and mental disorders, he developed theories to explain conditions such as Hannibal Odyssey Complex and Stealing-covet Disorders of War. He has also studied indigenous healing practices in Ghana and their treatment of mental illness. Currently he is a professor and dean at Regent University College of Science and Technology in Ghana.
Desmond Ayim-Aboagye is a Ghanaian psychologist of religion, educator, and philosopher. He received his PhD from the University of Uppsala in Sweden and currently works as a professor and dean at Regent University College of Science and Technology in Ghana. His research focuses on psychology of religion, transcultural psychiatry, behavioral economics, social psychiatry, and pain psychology. Through his research, he has developed theories on disorders related to war such as Hannibal Odyssey Complex and theories on the role of traditional healers in treating mental illness in West Africa. He has published extensively on indigenous psychiatry, psychology of religion, and pain psychology.
Professor Desmond Ayim-Aboagye is an Associate Professor at Åbo Akademi University in Finland and Uppsala University in Sweden. He holds multiple degrees including a BA in Theology, BA in Elementary Education, MA in Religion, and a PhD in Psychology of Religion from Uppsala University. His research focuses on areas like philosophy, psychiatry, medical anthropology, healing, and religion. He has published numerous books and articles on these topics. Currently he is a research fellow at Uppsala University investigating immigrants' responses to drug treatments for substance abuse.
Desmond Ayim-Aboagye is a Ghanaian psychologist of religion, educationist, and philosopher known for his research on psychology of religion, transcultural psychiatry, behavioral economics, social psychiatry, and pain psychology. He received his PhD from the University of Uppsala in Sweden and currently works as a professor and dean at Regent University College of Science and Technology in Ghana. Some of his influential works include identifying psychiatric disorders related to war such as Hannibal Odyssey Complex and researching the contributions of indigenous practitioners to mental healthcare in Africa.
Still I Rise by Maya Angelou
-Table of Contents
● Questions to be Addressed
● Introduction
● About the Author
● Analysis
● Key Literary Devices Used in the Poem
1. Simile
2. Metaphor
3. Repetition
4. Rhetorical Question
5. Structure and Form
6. Imagery
7. Symbolism
● Conclusion
● References
-Questions to be Addressed
1. How does the meaning of the poem evolve as we progress through each stanza?
2. How do similes and metaphors enhance the imagery in "Still I Rise"?
3. What effect does the repetition of certain phrases have on the overall tone of the poem?
4. How does Maya Angelou use symbolism to convey her message of resilience and empowerment?
The membership Module in the Odoo 17 ERPCeline George
Some business organizations give membership to their customers to ensure the long term relationship with those customers. If the customer is a member of the business then they get special offers and other benefits. The membership module in odoo 17 is helpful to manage everything related to the membership of multiple customers.
Beyond the Advance Presentation for By the Book 9John Rodzvilla
In June 2020, L.L. McKinney, a Black author of young adult novels, began the #publishingpaidme hashtag to create a discussion on how the publishing industry treats Black authors: “what they’re paid. What the marketing is. How the books are treated. How one Black book not reaching its parameters casts a shadow on all Black books and all Black authors, and that’s not the same for our white counterparts.” (Grady 2020) McKinney’s call resulted in an online discussion across 65,000 tweets between authors of all races and the creation of a Google spreadsheet that collected information on over 2,000 titles.
While the conversation was originally meant to discuss the ethical value of book publishing, it became an economic assessment by authors of how publishers treated authors of color and women authors without a full analysis of the data collected. This paper would present the data collected from relevant tweets and the Google database to show not only the range of advances among participating authors split out by their race, gender, sexual orientation and the genre of their work, but also the publishers’ treatment of their titles in terms of deal announcements and pre-pub attention in industry publications. The paper is based on a multi-year project of cleaning and evaluating the collected data to assess what it reveals about the habits and strategies of American publishers in acquiring and promoting titles from a diverse group of authors across the literary, non-fiction, children’s, mystery, romance, and SFF genres.
The Value of Time ~ A Story to Ponder On (Eng. & Chi.).pptxOH TEIK BIN
A PowerPoint presentation on the importance of time management based on a meaningful story to ponder on. The texts are in English and Chinese.
For the Video (texts in English and Chinese) with audio narration and explanation in English, please check out the Link:
https://www.youtube.com/watch?v=lUtjLnxEBKo
Split Shifts From Gantt View in the Odoo 17Celine George
Odoo allows users to split long shifts into multiple segments directly from the Gantt view.Each segment retains details of the original shift, such as employee assignment, start time, end time, and specific tasks or descriptions.
Slide Presentation from a Doctoral Virtual Open House presented on June 30, 2024 by staff and faculty of Capitol Technology University
Covers degrees offered, program details, tuition, financial aid and the application process.
Credit limit improvement system in odoo 17Celine George
In Odoo 17, confirmed and uninvoiced sales orders are now factored into a partner's total receivables. As a result, the credit limit warning system now considers this updated calculation, leading to more accurate and effective credit management.
Integrated Marketing Communications (IMC)- Concept, Features, Elements, Role of advertising in IMC
Advertising: Concept, Features, Evolution of Advertising, Active Participants, Benefits of advertising to Business firms and consumers.
Classification of advertising: Geographic, Media, Target audience and Functions.
Tales of Two States: A Comparative Study of Language and Literature in Kerala...
Linear regression
2. WHAT IS IT?
• LINEAR REGRESSION IS INTIMATELY RELATED TO CORRELATION
• IT IS A TECHNIQUE FOR PREDICTING A SCORE ON VARIABLE Y BASED ON WHAT WE KNOW TO BE TRUE
ABOUT THE VALUE OF SOME VARIABLE X.
• UNLESS ONE VARIABLE IS SUBSTANTIALLY CORRELATED WITH THE OTHER, THERE IS NO REASON TO USE
REGRESSION TO PREDICT A SCORE ON Y FROM A SCORE ON X.
3. EXAMPLES:
If I know that you studied 10 hours (X) for the exam, then, can I predict your
actual score on the exam (Y)?
Regression analysis helps in this regard by essentially searching for a
pattern in the data, usually a scatter plot of points representing hours studied
(x) by exam scores (Y).
It is a statistical technique that seeks to find the best fit for a straight line
projected among a points on the scatter plot.
5. SIMPLE LINEAR REGRESSION
• THE MOST BASIC FORM OF REGRESSION ANALYSIS IS CALLED SIMPLE LINEAR OR BIVARIATE (“TWO
VARIABLE”) REGRESSION.
6. DEFINITION:
Regression analysis is based on correlational analysis,
and it involves examining changes in the level of Y
relative to changes in the level of X.
Variable Y is the dependent measure and is called criterion measure
The independent or predictor variable is represented by variable X
8. THE Z-SCORE APPROACH TO REGRESSION
A variable Y can be predicted from X using the z score regression equation:
ZÝ = RxyZx
(please note it ^ which stands on Y and it is called “caret”)
ZÝ is predicted score for variable Y.
Rxy is the correlation between variables X and Y.
Zx actual z score based on variable X
9. IMPORTANCE
Two reasons:
1. When Rxy is positive in value, Zx will be multiplied by a positive number– thus, ZÝ will be positive when Zx is positive and
it will be negative when Zx is negative. [The importance of this characteristic is that when Rxy is positive, then ZÝ will
have the same sign as Zx, so that a high score will covary with high scores and low scores will do so with low scores (see
book 7.1.1). When Rxy is negative, however, the sign of ZÝ will be opposite of Zx; low scores will be associatedwith high
scores and high scores with low scores (see book7.1.1)
2. The second point is when z score equation for regression is that Rxy = ± 1.00, ZÝ will have the same score as Zx. As we
know, of course, such perfectcorrelation is rare in behavioral data. Thus, when Rxy <± 1.00, ZÝ will be closer to 0.0 than
Zx. Any Z score that approaches 0.0 is based on a raw score that is close to a distribution’s mean. When Zx is multiplied by
0.0 and ZÝ becomes equal to 0.0, the mean of the Z distribution.
10. THE MEAN, Z SCORE AND REGRESSION
When two variables are uncorrelated with one another,
the best predictor of any individual score on one of the
variables is the mean. The mean is the predicted value
of X or Y when the correlation between these variables is
0.
11. COMPUTATIONAL APPROACHES TO
REGRESSION
Computational equation: Y = a + b (X)
Y is criterion variable
a and b are constants with fixed values
X variable is the predictor variable
This is the formula for a straight line
12. SLOPE OF LINE
B =
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑌
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑋
B is called the slope of the line, the purpose of which is to link Y values to X values.
In regression equation, a is called the intercept of the line or y- intercept.
The intercept is the point in a regression of Y or X where the line crosses the Y axis.
13. 60
50
40
30
20
10
0
1 2 3 4 5 6 X
Y
Procra
stinati
on.
score
s
Minutes Spent on Behavioral Task
Fig. 7.1 Procrastination Scores as a Function of time Spent Performing Behavioral Task
(minutes)
Y = 20 + 5
(X)
14. A REGRESSION LINE
A regression line is a straight line projecting through a given set of
data, one designed to represent the best fitting linear relationship
between variables X and Y.
15. THE METHOD OF LEAST SQUARES FOR
REGRESSION
When the least squares method is used in the context of regression, the best fitting line
is the one drawn (out of an infinite number of possible lines) so that the sum of the
squared distances between the actual Y values and the predicted Y values is
minimized.
Y actual or observed value of Y
Ý (^) predicted or estimated value for Y
A regression line will minimize the distance between Y and Ý (^)
Sum of squares terms = ∑ (Y-Ý)²
Formula for a straight line =
Ý= a + b (X)
16. RAW SCORE METHOD FOR REGRESSION
Ý (^) = Ῡ + r (
𝑺𝒚
𝑺𝒙
) (X -X‾)
A rule of thumb for selecting r(Sx/Sy) or r(Sy/Sx) for the raw score regression
formula: The standard deviation for the variable you wish to predict is the
numerator and the standard deviation for the predictor variable is in the
denominator.
17. RESIDUAL VARIATION AND THE STANDARD
ERROR OF ESTIMATE
• OUR BEST FIT, OR COURSE, DEPENDENT ON HOW WELL PREDICTED VALUES MATCH UP TO ACTUAL VALUES,
OR THE RELATIVE AMOUNT OF ERROR IN OUR REGRESSION ANALYSIS.
• WE CAN CHARACTERIZE THE ACCURACY OF PREDICTION BY CONSIDERING ERROR IN REGRESSION AKIN
TO THE WAY SCORES DEVIATE FROM SOME AVERAGE (MEAN)
18. RESIDUAL VARIATION
Think about how the observations fall on or near the regression line in the same way that observations
cluster closer or farther away from the mean of a distribution– minor deviation entails low error and a better
fit of the line to the data, greater deviation indicates more error and a poorer fit.
The information leftover from any such deviation– the distance between a predicted and actual Y value– is
called a residual.
Residual variance refers to the variance of the observations around a regression line.
19. RESIDUAL VARIANCE
Symbol for residual variance:
S² estY =
(𝑌 − Ý)²
𝑁 − 2
It is known as error variance.
And is based on the sum of the squared deviations between the actual Y scores
and the predicted or Ý (^) scores divided by the number of pairs of X and Y
scores minus two (i.e., N – 2).
20. STANDARD ERROR OF ESTIMATE
The standard error of estimate is a numerical index describing the standard distance
between actual data points and the predicted points on a regression line. The
standard error of estimate characterizes the standard deviation around a regression
line.
It is similar to the standard deviation, as both measures provide a standardized
indication of how close or far away observations lie from a certain point.
Mean- Standard deviation
Regression line – Standard error of estimate
21. TERMINOLOGIES
• HOMOSCEDASTICITY
• THE VARIABILITY ASSOCIATED WITH ONE
VARIABLE (Y) REMAINS CONSTANT AT ALL OF THE
LEVELS OF THE OTHER VARIABLE (X).
• HETEROSCEDASTICITY
• IT IS THE OPPOSITE OF HOMOSCEDASTICITY. IT
REFERS TO THE CONDITION WHERE (Y)
OBSERVATIONS VARY IN DIFFERING AMOUNTS AT
DIFFERENT LEVELS OF (X)
22. Y
X
- S est Y
+ S
est Y
Fig. 7.8 Standard Error of Estimate with Assumptions of Homoscedasticityand Normal Distribution
of Y at Every level of X being met.
Approx 68.3%
of Y scores fall
within + S est Y
23. EXPLAINED AND UNEXPLAINED VARIANCE
SUM OF SQUARES FOR
EXPLAINED VARIANCE IN
(Y)
∑ (Ý - Ῡ) 2
REGRESSION SUM OF
SQUARES
SUM OF SQUARES FOR THE
UNEXPLAINED VARIANCE IN
(Y)
∑ (Y - Ý) 2
ERROR SUM OF SQUARES
∑ (Y - Ῡ) 2
TOTAL SUM OF SQUARES
24. TOTAL SUM OF SQUARES
Total sum of squares = Unexplained variation in Y (i.e., error
sum of squares + Explained variation in Y (i.e., explained sum of
squares)
∑ (Y - Ῡ) 2
= ∑ (Ý - Ῡ) 2
+ ∑ (Y - Ý) 2
OR
SStot = SSunexplained + SSexplained
25. REGRESSION TOWARD THE MEAN
• REGRESSION TOWARD THE MEAN REFERS TO SITUATIONS WHERE INITIALLY HIGH OR LOW
OBSERVATIONS ARE FOUND TO MOVE CLOSER TO OR “REGRESS TOWARD” THEIR MEAN AFTER
SUBSEQUENT MEASUREMENT.
26. To begin, we know observations in any distribution tend to cluster around a
mean. If variables X and Y are more or less independent of one another (i.e.,
Rxy ≅ 0.0), then some outlying score on one variable is likely to be
associated with either a high or low score on the other variable (recall the
earlier review of the z score formula for regression). More to the point, though,
if we obtain an extreme score on X, the corresponding Y score is likely to
regress toward the mean of Y. If, however, X and Y are highly correlated with
one another (i.e., Rxy ≅ ±1.00), then an extreme score on X is likely to be
associated with an extreme score on Y, and regression to the mean will
probably not occur. Regression to the mean, then, can explain why an
unexpected or aberrant performance on one exam does mean subsequent
performance will be equally outstanding or disastrous.
Regression toward the mean
27. Multiple Regression Analysis
Multiple regression is a statistical technique for
exploring the relationship between one dependent
variable (Y) and more than one independent variable
(X1, X2, …, XN).
Multiple Regression equation for two independent variables:
Y = a + b1 (X1) + b2 (X2).
a is the intercept, b1 and b2 are the two slopes
X1 and X2 are the predictor variables
28. MULTIPLE REGRESSION: IMPORTANCE
Multiple regression is used to learn how well some predictor variables (X)
actually do predict the criterion variable (Y).
Any multiple regression analysis yields what is called a multiple correlation
coefficient, which is symbolized by the letter R (capital) and range in value from
.00 to +1.00. The multiple R, or simply R, indicates the degree of relationship
between a given criterion variable (Y) and a set of predictor variables (X).
As R increases in magnitude, the multiple regression equation is said to perform
a better job of predicting the dependent measure from the independent variables
(read further Dana S Dunn, 2001).
29. RequiredReadings:
1. Dunn, D. S. 2001.
Statistics and Data
Analysis for the
Behavioural
Sciences.Toronto:
McGraw Hill.
1. Babbie, E. 2007. The
Practiceof Social
Research. Eleventh
Edition. Thomsom:
Wadsworth.
1. Creswell, J. W. 2003.
Research Design:
Qualitative,
Quantitative, and
MixedMethods.
Second Edition.
Thousand Oaks: Sage
Publications.
1. Healey J. F. 2009.
Statistics: A Tool for
Social Research.