BUSSTAT 208
Multiple Regression Problem Set I
Using the Motor Trend Cars Data Set, you would like to determine if there is a relationship between MPG (miles per gallon) and specific variables included in the data set.
a. Develop a correlation matrix using MPG (miles per gallon), HP (horsepower), WT (weight). Is the correlation between the variables significant or not? Conduct a test for all correlations; that is for MPG v. HP; MPG v. WT; HP v. WT. Use a level of significance of 0.05
b. Fit a multiple regression model using MPG (miles per gallon) as the dependent variable and HP (horsepower), and WT (weight) as the independent variables.
c. Is the overall regression model significant? Conduct the appropriate hypothesis tests for the significance of the overall regression model. Use a 0.05 level of significance.
d. Are the individual independent variables significant? Conduct a hypothesis tests for the significance of each independent variable at the= 0.05 level of significance.
e. What proportion of the variation in MPG is explained by the independent variables HP and WT?
f. Graph the residuals from the regression you developed in part (a). Do the regression assumptions appear to be appropriate given the residual plots?