College GPA Male(0) Q Female (1 in 000s) AT x2 1300 1700 16 60 69 59 2000 I2 400
ID: 3055231 • Letter: C
Question
College GPA Male(0) Q Female (1 in 000s) AT x2 1300 1700 16 60 69 59 2000 I2 400 2200 73 85 3.8 1700 13 1200 1500 16 89 95 1. Take the above data table and copy it into MSExcel. 2. Refer to "Review of Multiple Regression" on page 521 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? 3. Run the initial regression. Is the Regression Model worth keeping (Global Assessment)? Explain . Write the initial regression equation: 5. True or False. If the Pvalue is larger than ? (ie, 0.05) for a specific coefficient then I would eliminate the coefficient from the regression model. first? significant" ? coefficients. What is the final regression 6. Which individual coefficient would I remove from the model 7. Run the regression until you have removed the "non- model? explained by the regression equation? if I am a female with a 3.0 GPA with SAT score of 2000 and 8. What percent of the initial variability in Job Income is 9. From the final regression model what is my expected income an IQ 130? 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