Multiple Regression and Correlation Analysis
NB: PLEASE DO EVERYTHING IN EXCEL: Refer to the Real Estate data, at:
which reports information on homes sold in the Denver, Colorado, area during the last year. Use the selling price of the home as the dependent variable and determine the regression equation with number of bedrooms, size of the house, whether there is a pool, whether there is an attached garage, distance from the center of the city, and the number of bathrooms as independent variables.
a. Write out the regression equation. Discuss each of the variables. For example, are you surprised that the regression coefficient for distance from the center of the city is negative? How much does a garage or a swimming pool add to the selling price of a home?
b. Determine the value of R2(R squared)–and interpret.
c. Develop a correlation matrix. Which independent variables have strong or weak correlations with the dependent variable? Do you see any problems with multicollinearity?
d. Conduct the global test on the set of independent variables and interpret.
e. Conduct a test of hypothesis on each of the independent variables. Would you consider deleting any of the variables? If so–which ones?
f. Rerun the analysis until only significant regression coefficients remain in the analysis. Identify these variables.
G. Develop a Histogram or a Stem and-Leaf display of the residuals from the final regression equation developed in part (f). Is it reasonable to conclude that the normality assumption has been met?
h. Plot the residuals against the fitted values from the final regression equation developed in part(f) against the fitted values of Y. Plot the residuals on the vertical axis and the fitted values on the horizontal axis.