CHAPTER 13 INTRODUCTION TO MULTIPLE CORRELATION MULTIPLE
to differentiate it from the multiple predictor case, where we use captial R for multiple correlation The subscripts Y 12 simply mean (in this case) that Y is the criterion variable that is being predicted by a best weighted combination of predictors 1 and 2 Again, note that this multiple correlation value is 477
Chapter 5 Multiple correlation and multiple regression
130 5 Multiple correlation and multiple regression 5 2 1 Direct and indirect effects, suppression and other surprises If the predictor set x i,x j are uncorrelated, then each separate variable makes a unique con-tribution to the dependent variable, y, and R2,the amount of variance accounted for in y,is the sum of the individual r2 In that
Correlation & Regression Chapter 5
Multiple Correlation & Regression Using several measures to predict a measure or future measure Y-hat = a + b1X1 + b2X2 + b3X3 + b4X4 •Y-hat is the Dependent Variable •X1, X2, X3, & X4 are the Predictor (Independent) Variables College GPA-hat = a + b1H S GPA + b2SAT + b3ACT + b4HoursWork R = Multiple Correlation (Range: -1 - 0 - +1)
Multiple, Partial, and Multiple Partial Correlations
Multiple R 2 •Multiple R 2: a measure of the amount of variability in the response that is explained collectively by the combination of predictors ",#, ,$ &' (,'), ,'* # = 33 −335 33 •Taking the positive square root yields the multiple correlation coefficient Example: Multiple R 2 •Scenario: Examine how patient satisfaction (1
Multiple R2 and Partial Correlation/Regression Coefficients
A demonstration of the partial nature of multiple correlation and regression coefficients Run the program Partial sas from my SAS programs page The data are from an earlier
Multiple Correlation - Western University
We can use this data to illustrate multiple correlation and regression, by evaluating how the “Big Five” personalityfactors( Openness to Experience, Conscientiousness, Extraversion, Agreeableness, and Neuroticism )
Linear Regression and Correlation in R Commander 1
Thus, the regression line is U The correlation coefficient is the square root of “Multiple R-squared ” So, N L L3 1749 E0 4488 √0 1533 L0 3915 6 Important caution: Correlation does NOT imply cause and effect Consider data x = number of TV’s per household, y = life expectancy for 100 countries which has r = 0 80 (so the more TV’s
Example of Interpreting and Applying a Multiple Regression Model
Example of Interpreting and Applying a Multiple Regression Model We'll use the same data set as for the bivariate correlation example -- the criterion is 1 st year graduate grade point average and the predictors are the program they are in and the three GRE scores
Chapter 4 Covariance, Regression, and Correlation
(multiple correlation and multiple regression) are left to Chapter 5 In the mid 19th century, the British polymath, Sir Francis Galton, became interested in the intergenerational similarity of physical and psychological traits In his original study developing the correlation coefficient Galton (1877) examined how the size of a sweet pea
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