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
this ppt gives you adequate information about Karl Pearsonscoefficient correlation and its calculation. its the widely used to calculate a relationship between two variables. The correlation shows a specific value of the degree of a linear relationship between the X and Y variables. it is also called as The Karl Pearson‘s product-moment correlation coefficient. the value of r is alwys lies between -1 to +1. + 0.1 shows Lower degree of +ve correlation, +0.8 shows Higher degree of +ve correlation.-0.1 shows Lower degree of -ve correlation. -0.8 shows Higher degree of -ve correlation.
The document presents a presentation on coefficient correlation by Irshad Narejo. It defines correlation as a technique used to measure the relationship between two or more variables. A correlation coefficient measures the degree to which changes in one variable can predict changes in another, though correlation does not imply causation. Correlation coefficient formulas return a value between -1 and 1 to indicate the strength and direction of relationships between data. Positive correlation means high values in one variable are associated with high values in the other, while negative correlation means high values in one variable are associated with low values in the other. The document discusses Pearson's correlation coefficient formula and provides an example of calculating correlation by hand versus using SPSS.
Regression analysis is a statistical technique for modeling the relationship between variables. It can be used to predict the value of a dependent variable based on the value of one or more independent variables. The earliest and most common type of regression is linear regression, which finds the line of best fit to describe the relationship between two variables (e.g. y= a + bx). More advanced techniques allow for modeling nonlinear relationships and multiple independent variables. Regression analysis is widely used in fields like economics, sciences, and social sciences.
Multiple regression analysis allows researchers to examine the relationship between one dependent or outcome variable and two or more independent or predictor variables. It extends simple linear regression to model more complex relationships. Stepwise regression is a technique that automates the process of building regression models by sequentially adding or removing variables based on statistical criteria. It begins with no variables in the model and adds variables one at a time based on their contribution to the model until none improve it significantly.
Parametric tests make specific assumptions about the population parameter and use distributions to determine test statistics. They apply to interval/ratio variables where the population is completely known. Nonparametric tests do not make assumptions about the population or its distribution and use arbitrary test statistics. They apply to nominal/ordinal variables where the population is unknown. The key differences are in the basis of the test statistic, measurement level, measure of central tendency, population information known, and applicability to variables versus attributes.
This document discusses correlation and different aspects of studying correlation. It defines correlation as the association or relationship between two variables that do not cause each other. It describes different types of correlation including positive, negative, linear, non-linear, simple, multiple and partial correlation. It also discusses various methods of studying correlation including graphic methods like scattered diagrams and correlation graphs, and algebraic methods like Karl Pearson's correlation coefficient and Spearman's rank correlation coefficient. The document explains concepts like coefficient of determination and hypothesis testing in correlation. It emphasizes that correlation indicates association but does not necessarily imply causation between variables.
This document discusses correlation analysis and its various types. Correlation is the degree of relationship between two or more variables. There are three stages to solve correlation problems: determining the relationship, measuring significance, and establishing causation. Correlation can be positive, negative, simple, partial, or multiple depending on the direction and number of variables. It is used to understand relationships, reduce uncertainty in predictions, and present average relationships. Conditions like probable error and coefficient of determination help interpret correlation values.
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This document presents information about regression analysis. It defines regression as the dependence of one variable on another and lists the objectives as defining regression, describing its types (simple, multiple, linear), assumptions, models (deterministic, probabilistic), and the method of least squares. Examples are provided to illustrate simple regression of computer speed on processor speed. Formulas are given to calculate the regression coefficients and lines for predicting y from x and x from y.
Regression analysis is a statistical technique for investigating relationships between variables. Simple linear regression defines a relationship between two variables (X and Y) using a best-fit straight line. Multiple regression extends this to model relationships between a dependent variable Y and multiple independent variables (X1, X2, etc.). Regression coefficients are estimated to define the regression equation, and R-squared and the standard error can be used to assess the goodness of fit of the regression model to the data. Regression analysis has applications in pharmaceutical experimentation such as analyzing standard curves for drug analysis.
1. Correlation analysis measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 is a perfect negative correlation, 0 is no correlation, and 1 is a perfect positive correlation.
2. Scatter diagrams provide a visual representation of the relationship between two variables but do not provide a precise measure of correlation. Pearson's correlation coefficient (r) calculates the numerical strength of the linear relationship.
3. Correlation is widely used in fields like agriculture, genetics, and physiology to study relationships between variables like crop yield and fertilizer use, gene linkage, and organism growth and environmental factors.
The document discusses regression analysis and its key concepts. Regression analysis is used to understand the relationship between two or more variables and make predictions. There are two main types: simple linear regression, which involves two variables, and multiple regression, which involves more than two variables. Regression lines show the average relationship between the variables and can be used to predict outcomes. The regression coefficients measure the change in the dependent variable for a unit change in the independent variable. The standard error of the estimate indicates how close the data points are to the regression line.
This document discusses correlation and provides examples of its applications. It begins with an introduction that defines correlation as measuring the linear relationship between two variables. It then provides definitions of positive and negative correlation. The next sections discuss types of correlation based on degree, number of variables, and linearity. Correlation coefficient is introduced as a measure of the strength of the linear relationship between -1 and 1. Examples of its applications include the relationships between tree cutting and erosion, study time and test scores, clothing size and growth. Limitations of only considering linear relationships are also covered. Real-life examples of positive, negative, and no correlation between variables like temperature and sales, exercise and body fat, and weather and sales are presented.
The Spearman’s Rank Correlation Coefficient is the non-parametric statistical measure used to study the strength of association between the two ranked variables. This method is applied to the ordinal set of numbers, which can be arranged in order, i.e. one after the other so that ranks can be given to each. This presentation slides explains the procedure to find out the Rank Difference correlation and its applications.
This document discusses the meaning and types of correlation. It defines correlation as a statistical tool that measures the relationship between two variables. The degree of relationship is measured by the correlation coefficient, which ranges from -1 to 1. A positive correlation means the variables change in the same direction, while a negative correlation means they change in opposite directions. Common methods for studying correlation include scatter plots, Karl Pearson's coefficient, and Spearman's rank correlation coefficient. The coefficient of correlation, denoted by r, measures the strength and direction of the linear relationship between variables.
This document discusses correlation and regression. Correlation describes the strength and direction of a linear relationship between two variables, while regression allows predicting a dependent variable from an independent variable. It provides examples of calculating the correlation coefficient r to determine the strength and direction of relationships between variables like education and self-esteem or family income and number of children. The regression equation describes the linear regression line and can be used to predict values of the dependent variable from known values of the independent variable.
The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population.
There are two types of errors in hypothesis testing:
Type I errors occur when a null hypothesis is true but rejected. This is a false positive. Type I error rate is called alpha.
Type II errors occur when a null hypothesis is false but not rejected. This is a false negative. Type II error rate is called beta.
Reducing one type of error increases the other - more stringent criteria lower Type I errors but raise Type II errors, and vice versa. Both errors cannot be reduced simultaneously.
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.
This document discusses correlation coefficient and different types of correlation. It defines correlation coefficient as the measure of the degree of relationship between two variables. It explains different types of correlation such as perfect positive correlation, perfect negative correlation, moderately positive correlation, moderately negative correlation, and no correlation. It also discusses different methods to study correlation including scatter diagram method, graphic method, Karl Pearson's coefficient of correlation method, and Spearman's rank correlation method. It provides examples and steps to calculate correlation coefficient using these different methods.
This document discusses correlation analysis and different methods of studying correlation. It begins by defining correlation as the association between two or more variables. There are different types of correlation such as positive, negative, linear, and curvilinear correlation. The degree of correlation can be determined using the correlation coefficient, with values ranging from -1 to 1. Common methods for studying correlation discussed include scatter diagrams, Karl Pearson's coefficient, Spearman's rank correlation, and concurrent deviation method. The properties and interpretation of the correlation coefficient are also outlined.
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This document discusses correlation and regression analysis techniques used in physical geography to examine relationships between variables. Correlation determines the degree of relationship between two variables and is represented by the correlation coefficient r, which ranges from -1 to 1. Regression identifies relationships between a dependent variable and one or more independent variables by calculating a best-fit line that minimizes residuals. The document provides examples of calculating the correlation coefficient r and estimating the regression equation between variables.
This document defines and explains different types of correlation. It begins by defining correlation as a statistical tool to measure the relationship between two variables. There are three main types of correlation discussed: positive correlation where both variables move in the same direction, negative correlation where the variables move in opposite directions, and zero correlation where a change in one variable does not affect the other. The document also discusses linear and non-linear correlation, as well as simple, partial, and multiple correlation. Different methods for measuring correlation are presented, including graphical methods like scatter diagrams and algebraic methods like Pearson's correlation coefficient.
This presentation covered the following topics:
1. Definition of Correlation and Regression
2. Meaning of Correlation and Regression
3. Types of Correlation and Regression
4. Karl Pearson's methods of correlation
5. Bivariate Grouped data method
6. Spearman's Rank correlation Method
7. Scattered diagram method
8. Interpretation of correlation coefficient
9. Lines of Regression
10. regression Equations
11. Difference between correlation and regression
12. Related examples
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 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.
This document discusses correlation analysis in agriculture. It begins by defining correlation as the relationship between two or more variables. Some key points:
- Correlation can be positive (variables move in the same direction), negative (variables move in opposite directions), linear, nonlinear, simple, multiple, partial or total.
- Common types analyzed in agriculture include the relationship between yield and rainfall, price and supply, height and weight.
- Methods for measuring correlation are discussed, including Karl Pearson's coefficient of correlation (denoted by r), Spearman's rank correlation, and scatter diagrams.
- The value of r ranges from -1 to 1, with higher positive or negative values indicating a stronger linear relationship between 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 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 analysis and different types of correlation. It begins by defining correlation as the association between two or more variables. Correlation can be positive, negative, linear, or curvilinear depending on how the variables move in relation to each other. The degree of correlation is determined by calculating the coefficient of correlation, with values ranging from +1 to -1. Several methods are described for studying correlation including scatter diagrams, Karl Pearson's coefficient, Spearman's rank correlation, and concurrent deviation method. The document also outlines how to interpret the coefficient of correlation and test its significance.
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 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.
Correlation and linear regression are fundamental statistical concepts used to explore relationships between variables and make predictions. Correlation measures the strength and direction of association between variables, while linear regression models relationships to enable predictions. Understanding these concepts equips analysts to draw meaningful conclusions from data and make informed recommendations. Mastery of correlation and linear regression techniques allows for discoveries of patterns within datasets across various domains like finance, economics, psychology, and more.
This document discusses correlation and regression analysis. It defines correlation as a relationship between two variables where a change in one variable is accompanied by a change in the other. There are three types of correlation: positive, negative, and no correlation. It also discusses various methods to calculate the coefficient of correlation, including Pearson's correlation coefficient, Spearman's rank correlation coefficient, and concurrent deviation method. Regression is defined as a functional relationship between two or more related variables that is represented by a curve or line of best fit called the regression line.
The document discusses various statistical techniques for analyzing the relationship between two variables, including scatter plots, covariance, correlation coefficients, linear regression, and curvilinear regression. It provides formulas and assumptions for each method, and explains how to interpret the results to determine if variables are related and the strength and direction of their relationship.
Power point presentationCORRELATION.pptxSimran Kaur
This document discusses different types of correlation and methods for determining correlation between variables. It defines correlation as the relationship between two or more variables, and describes positive correlation as variables changing in the same direction and negative correlation as changing in opposite directions. It also distinguishes between simple correlation of two variables and multiple correlation of more than two variables. Additionally, it introduces several methods for measuring correlation, including scatter plots, Karl Pearson's coefficient of correlation, and Spearman's rank correlation coefficient.
Regression analysis allows researchers to identify an equation that best fits paired data and predict the relationship between two quantitative variables. Linear regression assumes a linear relationship and finds the line that best describes how the dependent variable changes with the independent variable. The regression line equation takes the form Y = bX + a, where b is the slope and a is the intercept. Researchers can use linear regression to predict new Y values based on X and assess how well the linear model fits the data.
Correlational research describes the linear relationship between two or more variables without attributing cause and effect. The correlation coefficient is used to measure the strength of this relationship on a scale from -1 to 1. Positive correlations indicate variables increase or decrease together, while negative correlations mean they change in opposite directions. Scatterplots visually depict the correlation by showing how paired values of different variables relate on a graph. The Pearson's r formula is commonly used to calculate correlation coefficients from sample data.
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2. CORRELATION
Correlation is an analysis used to determine the relationship between two or
more variables.
The measure of correlation is called coefficient of correlation and is denoted
by the symbol ‘r’.
It helps us in finding the degree or extent of quantitative relationship between
two variables.
It does not say anything about the cause and effect relationship between the
two variables.
3. SIGNIFICANCE OF CORRELATION
It is used to determine the relationship between two variables.
It reduces the range of uncertainty. The predictions based on correlation analysis
are more precise and reliable.
It helps us to estimate the value of dependent variable for the given value of
independent variable.
4. TYPES OF CORRELATION
Correlation is described or classified in several different ways such as:
1. Positive and Negative Correlation: Whether correlation is positive (direct) or negative
(inverse) would depend upon the direction of change of the variables. If both the variables
are varying in the same direction i.e., if as one variable is increasing the other, on an
average is also increasing or, if as one variable is decreasing the other, on an average, is
also decreasing, correlation is said to be positive.
If on the other hand, the variable are varying in positive direction, i.e. as one variable is
increasing the other is decreasing or vise versa, and correlation is said to be negative.
5. 2. Liner and Curvilinear (Non-Linear) Correlation.
Linear Correlation: Correlation is said to be linear when the amount of change in one
variable tends to bear a constant ratio to the amount of change in the other.
Non-Linear Correlation: The correlation would be non-linear if the amount of change in one
variable does not bear a constant ratio to the amount of change in the other variable.
6. METHODS OF STUDYING CORRELATION
Correlation can be studied by any of the following method.
1. Scatter diagram method.
2. Karl Pearson’s coefficient of correlation.
3. Spearman’s coefficient of rank correlation and
4. Concurrent deviation method.
7. Scatter diagram method
Scatter diagram or dot diagram is the simplest graphical device of showing the correlation
between the two variables (x and y). Such diagrammatic representation of bivariate data is
known as scatter diagram.
Observations:
Positive Correlation: When the x and y values increases together there will be a
positive correlation. (r= +1)
Negative Correlation: When the x value gets bigger and the y value gets smaller there
will be a negative correlation. (r= -1)
No Correlation: When the points do not show a pattern there is no correlation. (r= 0)
8. It is simple and non-
mathematical method
of studying
correlation
It is easy to
understand
Merit of
Scatter
Diagram
Method It gives only a rough
idea of how the two
variable are related.
Exact degree of
correlation between
the two variables can
not be established
by applying this
method.
Demerit
of Scatter
Diagram
Method
9. Karl Pearson’s Coefficient of Correlation
It is used universally for describing the degree of correlation between two series .
Formula of computing Pearson’s r is:
Here, x = ( X- X ) ; y= ( Y- Y )
Sx = Standard deviation of x series
Sy = Standard deviation of y series
N = Number of pairs of observation
Modified version:
Where, x = ( X- X ) ; y= ( Y- Y )
10. Procedure for computing the correlation coefficient
Calculate the mean of the two series ‘x’ &’y’
Calculate the deviations ‘x’ &’y’ in two series from their respective mean.
Square each deviation of ‘x’ &’y’ then obtain the sum of the squared deviation
i.e.
Multiply each deviation under x with each deviation under y & obtain the product of ‘xy’.
Then obtain the sum of the product of x , y i.e. Σxy
Substitute the value in the formula.
12. It is most
important and
precise
method of
measuring the
relationship of
two variables.
It measures the
direction as
well as the
relationship
between the
two variables.
Merit of
Karl
Pearson’s
Method
The computational
procedure of this
method is difficult
as compared to
other method.
The value of the
coefficient is
affected by
extreme items.
Demerit
of Karl
Pearson’s
Method