Correlation
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This document discusses correlation and regression. It defines correlation as measuring the degree of relationship between two variables. There are several methods to measure correlation including scatter diagrams, covariance, Karl Pearson's coefficient of correlation, and Spearman's rank correlation coefficient. Regression finds the functional relationship between two correlated variables by estimating the value of one variable based on the other. There are two regression equations: regression of y on x and regression of x on x, where y is the dependent variable and x is the independent variable in each case.
Correlation
- 1. Correlation And Regression Created By :- Shrayas.s Wesley.V Tahir hussain Qureshi
- 2. CORRELATION • When we have data on only one variable we can find arithmetic mean , median , mode or variance of the variable. • By saying that marks scored by students at s.s.c. and h.s.c. are related is not sufficient to measure degree of relationship.
- 3. CORRELATION To measure the degree of relationship we have following measure: 1. Scatter diagram method 2. Co-variance method 3. Karl-pearson’s coefficient of correlation 4. Spearman’s rank correlation coefficient.
- 4. Scatter Diagram • A scatter diagram is used for analyzing relationships between two variables graphically . One variable is plotted on the horizontal axis and the other is plotted on the vertical axis. • Types of Scatter diagram : 1. Perfect positive correlation 2. Positive correlation 3. Negative correlation 4. Perfect negative correlation
- 9. Covariance method • If(x1,y1),(x2,y2),........(xn,yn) are n observation on bivariate data then covariance between two variables is defined as Using covariance the realtion between x and y is interpreted as under.if cov(x,y)<0 then there is negative correlation between x and y. If cov(x,y)=0 then there is no linear relationship nbetween x and y. If cov(x,y)>0 then there is positive correlation between x and y.
- 10. KARL PEARSON’S COEFFICIENT • If (xi,yi),i=1,2,....n are n pairs of observations on bivariate data then Karl Pearson’s coefficient of correlation between x and y is given by:
- 11. Spearman’s rank correlation • If (xi,yi),i=1,2,....n are n observation in bivariate data and Rx denotes the rank of X observation and Ry denotes the rank of Y observations then define d=Rx-Ry. • Rank correlation coefficient between x and y is
- 12. Regression • Regression gives the functional relationship between two variables
- 13. Regression means estimate value of one variable when value of other correlated variable are known. Thus to estimate y, for given x, y is dependent and x is independent variable. whereas to estimate x for given y, x is dependent and y is independent variable.
- 14. Accordingly we have two regression equation : 1)Regression equation of y on x 2) Regression equation of x on y
- 15. Regression equation of y on x Here y is dependent variable and x is independent variable. And we denote By :-
- 16. Regression equation of x on y :- Here y is dependent variable and x is independent variable. And we denote By :-