Sale prices of apartments. A Minneapolis, Minnesota, real estate appraiser used regression analysis to explore the relationship between the sale prices of apartment buildings and various characteristics of the buildings. The file contains data for a random sample of 25 apartment buildings. Note: Physical condition of each apartment building is coded E (excellent), G (good), or F (fair). Data for selected observations are shown in the table below.

a. Write a model that describes the relationship between sale price and number of apartment units as three parallel lines, one for each level of physical condition. Be sure to specify the dummy variable coding scheme you use.

b. Plot y against x1 (number of apartment units) for all buildings in excellent condition. On the same graph, plot y against x1 for all buildings in good condition. Do this again for all buildings in fair condition. Does it appear that the model you specified in part a is appropriate? Explain.

c. Fit the model from part a to the data. Report the least squares prediction equation for each of the three building condition levels.

d. Plot the three prediction equations of part c on a scatterplot of the data.

e. Do the data provide sufficient evidence to conclude that the relationship between sale price and number of units differs depending on the physical condition of the apartments? Test using a = .05.

f. Check the data set for multicollinearity. How does this impact your choice of independent variables to use in a model for sale price? g. Conduct a complete residual analysis for the model to check the assumptions on e.