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# Multiple Regression example

Reggie is really excited because he managed to bust out enough manners to convince a lady to go to prom with him (take that, R^2 of .025!). Reggie realizes that manners alone will not be enough to woo his lady friend and guarantee a happy night out, and so he decides to research the style choices of 15 of his most idolized fashion icons, from Milli Vanilli to the Fonz. He tabulates the following data:

(See attached file.)

Please perform the following analyses:

a) Show the correlation matrix for the four predictors and date satisfaction; flag any significant correlations.
b) Run the multiple linear regression analysis on this data and show the important output.
c) Write out the regression equation using all four predictors.
d) What are the beta's?
e) Which variable has the largest semipartial (part) correlation with date satisfaction, partialling out the other variables?
f) What is the difference between partial and semipartial (part) correlation? Why is one less than the other?
g) How can having a sweet suit be significantly correlated with date satisfaction but not have a significant T or produce a significant F overall?
h) How could you create a significant F?
i) Run an analysis of multivariate normality. Are there variables you would want to discard? Why?
j) Show the calculations for converting R^2 into adjusted R^2.
k) Based on these analyses, what would you recommend that Reggie devote his time on in preparing for his date?

#### Solution Preview

a. The correlation coefficients between four predictor variables and satisfaction are provided below.
Satisfaction Smooth Talk Corsage Sweet Suit Hair Grease
Satisfaction 1.000
Smooth Talk 0.563 1.000
Corsage 0.522 0.835 1.000
Sweet Suit 0.580 0.402 0.604 1.000
Hair Grease -0.011 -0.138 0.019 0.036 1.000
Significant correlations are marked with blue color.
b.
Results of multiple regression for Satisfaction
Summary measures
Multiple R 0.6974
R-Square 0.4864
Adj R-Square 0.2809
StErr of Est 2.0572
ANOVA Table
Source df SS MS F p-value
Explained 4 40.0782 10.0195 2.3675 0.1227
Unexplained 10 42.3218 4.2322

Regression coefficients
Coefficient Std Err t-value p-value Lower limit Upper limit
Constant 1.6693 2.0316 0.8217 0.4304 -2.8573 6.1958
Smooth Talk 0.6052 0.4278 1.4145 0.1876 -0.3481 1.5584
Corsage -0.3340 0.5367 -0.6223 0.5477 -1.5299 0.8619
Sweet Suit 0.4855 0.2761 1.7585 0.1092 -0.1297 1.1007
Hair Grease 0.0702 0.2622 0.2678 0.7943 -0.5141 0.6545
c.
The Regression Equation using the four predictors is as follows:
Satisfaction = 1.6693 + 0.6052 * Smooth Talk - 0.3340 * Corsage + 0.4855 * Sweet Suit + 0.0702 * Hair Grease

d.
The betas for the four predictors are the coefficients displayed in the ...

#### Solution Summary

This posting provides a solution to a multiple regression example wherein Reggie wants to identify how to woo a lady using different parameters like smooth talk, Corsage, Sweet Suit, Hair Grease etc.

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