Application and Reasoning Problems

9.3. Ms. Carrie Allover needs more information about the model we developed to predict the number of weekly riders on her commuter rail system. The model equation is in example 1. Recall that it predicts the number of weekly riders based on population, price per ride, parking rates, and disposable income. Ms. Allover wants more explanation of what the equation means. She has asked some very specific questions about the situation.

1. Based on the model equation, which of the following will have the largest impact on the number of weekly riders: an increase of 10,000 people in the region, a ten cent drop in the price per ticket, a ten cent raise in parking rates, or a $100 decrease in average disposable income? Explain your answer.
2. Demographics experts suggest that the population will drop by 10% next year. The model predicts that this will change the number of weekly riders. Ms. Allover wants to ensure that the revenue (=price per ticket * number of tickets sold) remains about the same for next year as it is for this year. In order to accomplish this, the price per ticket will have to change. Should the ticket price be raised or lowered? By how much? Use the regression model and your software to help answer this.

9.4. The data file C09 Homes.xls [.rda] contains data on 271 homes sold in a three-month period in 2001 in the greater Rochester, NY area. A realtor has enlisted your help to develop a regression model in order to explain which characteristics of a home influence its price. You are going to build the regression model by adding one variable at a time and removing variables that do not seem to be significant. At each stage of the model building process, record the equation of the model, the R², the adjusted R² and the standard error of estimate. You should record all of this information in a table like the one below in order to make it easier to compare the results.

1. Introduce a new variable for the age of the home. To do this, add a new column heading ”Age” in cell M3. In cell M4, enter the formula ”=2003 - H4” in order to calculate the age of the home based on the year in which it was built (H4). Copy this formula to all the cells in the column.
2. Develop a series of models to predict the price of the home by adding one variable at a time. Add them in this order: Size, Baths, Age, Acres, Rooms, and Taxes. Make sure that each model includes all of the previous variables. (The second model will include size and baths as explanatory variables; the third will include size, baths, and age.) Record the model equation and the summary measures indicated in the table below.
3. What do you expect to happen to each of the summary measures as you add more variables into the model? What actually happens each time? What do the differences tell you about some of the variables?
4. Based on your observations of the summary measures eliminate the variable or variables that you feel are not helpful in predicting the price of a home. Using the remaining variables, develop your ”best regression model” and compare it to the others you have developed.