CHAPTER 13 INTRODUCTION TO MULTIPLE CORRELATION MULTIPLE
CORRELATION The main purpose of multiple correlation, and also MULTIPLE REGRESSION, is to be able to predict some criterion variable better Thus, while the focus in partial and semi-partial correlation was to better understand the relationship between variables, the focus of multiple correlation and regression is to be able to better predict
A full analysis example Multiple correlations Partial
Multiple correlation is useful as a first-look search for connections between variables, and to see broad trends between data If there were only a few variables connected to each other, it would help us identify which ones without having to look at all 6 pairs individually
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 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 edition of Howell (6th edition, page 496) Students at a large university completed a survey about their classes
CORRELATION & REGRESSION MULTIPLE CHOICE QUESTIONS
CORRELATION & REGRESSION MULTIPLE CHOICE QUESTIONS In the following multiple-choice questions, select the best answer 1 The correlation coefficient is used to determine: a A specific value of the y-variable given a specific value of the x-variable b A specific value of the x-variable given a specific value of the y-variable c
Correlation and Regression - James Madison University
that there is no correlation (1 11803 falls between the two critical values of –2 042 and +2 042) Problem Suppose the correlation coefficient is 0 80 and the number of observations is 62 What is the calculated test statistic? Is this significant correlation using a 1 level of significance? Solution Hypotheses: H 0: = 0 H a:
Example of Interpreting and Applying a Multiple Regression Model
Correlation and multiple regression analyses were conducted to examine the relationship between first year graduate GPA and various potential predictors Table 1 summarizes the descriptive statistics and analysis results As can be seen each of the GRE scores is positively and significantly correlated with the criterion, indicating that those
Using SPSS for Multiple Regression
Pearson Correlation Sig (1-tailed) N BMI calorie exercise income education Check multicollinearity of independent variables If the absolute value of Pearson correlation is greater than 0 8, collinearity is very likely to exist If the absolute value of Pearson correlation is close to 0 8 (such as 0 7±0 1), collinearity is likely to exist
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