Mechanics and Techniques Problems

8.1. Suppose you know statistics for X and Y shown below. You also know that the correlation of X to Y is 0.56. Use these to determine the equations of the least-squares best fit regression model to predict Y as a function of X. Produce a graph of this regression equation. Show all work.

8.2. The regression output below was developed from data relating the monthly usage of electricity (MonthlyUsage, measured in kilowatt-hours) to the size of homes (HomeSize, measured in square feet). One-variable statistics for each of these variables is also given below.

1. Use this information to write down the equation of the regression model. Explain what each part of the regression model means, paying particular attention to the unit of the coefficients in the regression equation.
2. Analyze the quality of the regression model you wrote down, based on the summary statistics in the regression output and the statistics on the X and Y variables.
3. Based on your regression model, what is the relationship between home size and monthly usage? Does this seem realistic? (Hint: What does the model predict for bigger and bigger homes? What about smaller homes? Are there any homes for which the model predicts a monthly usage of zero?)

8.3. Pie in the Sky, Inc. runs a chain of pizza eateries (See data file C08 Pizza.xls [.rda].) The manager has collected data from each of the stores in the chain regarding the number of pizzas sold in one month, the average price of the pizzas, the amount the store spent on advertising that month, and the average disposable income of families in the area near the store.

1. The manager wants to know how these variables are related. Specifically, he wants to know which variable is the best to use for predicting the number of pizzas that a given store will sell in a month. Develop regression models to predict the quantity sold based on each variable in the data. Use the three models you develop to determine which variable is the most influential.
2. Use your best model to determine how many pizzas will be sold if a store has an average pizza cost of $11.00, spends $51,000 on advertising, and is in a region with an average disposable income of $40,000.
3. Based on the models that you developed, if a store wanted to sell 80,000 pizzas, what should the store do?