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Fit a multiple linear regression model with total as the response variable and predictor variables of expending, ratio, salary, and takers.

INSTRUCTIONS TO CANDIDATES
ANSWER ALL QUESTIONS

Lab 5: Multiple Linear Regression

Lab Objectives: By the end of this lab, you should be able to:

. Fit a multiple linear regression model using R.
. Conduct a global test of hypothesis for a multiple linear regression model.
. Interpret the value of 2 for a multiple linear regression model.
. Determine if a reduced (nested) model is adequate.
. Create and interpret interaction plots for two categorical predictor variables.
. Determine if an interaction effect and the corresponding main effects are appropriate for the regression model.

Testing the Utility of a Model

You should already have the faraway package installed on your computer from last week’s lab.
However, if you do not, you will need to install this package to your computer. Once you have done this, load the faraway package, then load the sat data set that is included. View the help file to learn more about the variables in this data set. If you do not remember how to do anything of these things, review Lab 4.

1. (1 point) Fit a multiple linear regression model with total as the response variable and predictor variables of expending, ratio, salary, and takers. Entitle this model regress complete. What is the code to do this?

2. (2 points) Compute the quantities SS, and SSE for the model. Paste your code and numeric answers.

3. (5 points) Consider the hypothesis test H0: ßexpencz = ßratio = ßsaiary = ßtakers = O VS. Ha at least one ß * O

a. What is the numerical value of the F test statistic for this test? Round your answer to  two decimal places.

b. What are the numerator and denominator degrees of freedom for this F statistic?

c. What is the p-value for this test? Include your R code.

d. What are the decision and conclusion (in context) for this hypothesis test?

4. (2 points) You should have found an R2 value of 0.8246. Interpret this value in the context of the problem.

5. (1 point) Explain why the value of the Adjusted R2 is smaller than the value of the
Multiple R2.

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