Male(0) Female College GPA Job Income (in 000s) SAT Score 1300 1700 1400 2000 24

Question

Male(0) Female College GPA Job Income (in 000s) SAT Score 1300 1700 1400 2000 2400 2200 2300 1700 1200 1500 2300 1500 60 69 62 4 3.9 2.2 160 120 125 120 110 130 120 160 110 100 4 85 0 0 0 0 0 0 89 95 93 4 3.7 1. Take the above data table and copy it into MSExcel 2. "Review of Multiple Regression" 2.1. Calculate the Correlation Matrix in Excel. Do you see any independent variables that are "closely related" or redundant? If so which variables? 2.2. From the correlation matrix which variables would you think are candidates to be removed? (none, x1,x2,x3 or x4?) Why? Run the initial regression. Is the Regression Model worth keeping (Global Assessment)? Explain Write the initial regression equation: True or False: If the Pvalue is larger than ? (i.e. 0.05) for a specific coefficient then I would eliminate the coefficient from the regression model Which individual coefficient would I remove from the model first? Run the regression until you have removed the "non-significant" B coefficients. regression model? What percent of the initial variability in Job Income is explained by the regression equation? From the final regression model what is my expected income if I am a female with a 3.0 GPA with SAT score of 2000 and an IQ-130? 3. 4. 5. 6. 7. What is the final 8. 9. 10. How much more money would I make if I had a 150 IQ?

Explanation / Answer

2.1 The correlation matrix is shown below:

The variables X3 and X1 are closely related because their correlation is 0.598.

2.2 We don't remove any variables after looking at the correlation matrix.

3. The intiial regression is worth keeping because the p-value from the anova output (Shown below) of the regression is highly significant(less than 5%):

4. Initial regression equation: Y=56.38506+6.304294*x1+0.003766*x2+0.035404*x3-24.4308*x4

5. False, We don't eliminate the coefficient from the regression model if P-value is larger than alpha.

Y x1 x2 x3 x4 Y 1 x1 0.401275 1 x2 -0.04287 -0.15292 1 x3 0.0529 0.597931 -0.22504 1 x4 -0.89962 -0.03257 0.101326 0.203549 1

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