In Chapter 15, we are learning about multiple regression. Consider the following scenario:

A real estate agent is interested in building a regression model to predict the selling price of a home. She hopes this model will assist with determining appropriate list prices. The agent collected the following variables from 100 homes recently sold in her town:

Age (in years), Square feet, List Price (in $1000 units) and Sale Price (in $1000 units)

The agent has hired you to select the best regression model to predict the sale price (SP) using one or more of the predictor variables, Age (AGE), Square feet (SQFT), List Price (LP).

The table below lists seven (7) possible regression models that you have calculated.

1. If the agent wants a regression model with one predictor variable, which model is best? Explain your answer.

2. Considering all of the models shown in the table above, which regression equation is best for predicting sale price? Explain your answer.

3. Using the model you selected in question 2, predict the sale prices for ONE of the following houses listed by this agent last month:

Smith House: 16 years old, 2000 square feet, list price is $640,000

Gomez House: 3 years old, 2450 square feet, list price is $855,000

Singh House: 8 years old, 1475 square feet, list price is $575,000

NOTE: If your model includes the list price, you must change the list price to $1000s to use in the regression equation: Smith is 640, Gomez 855, Singh 575

4. Suppose the house you selected in question 3 was sold for the price shown here:

Smith House: $595,000 Gomez House: $790,000 Singh House: $550,000

Calculate the residual for your prediction. Remember to convert the sale prices to $1000s, before calculating the residual.

5. For the house you selected, did the regression model you used predict a better outcome for the seller or the buyer? Explain your answer using information from your previous answers.

Predictor (x) variables MSE R2 Adjusted R2 Regression Equation Age 25,275.43 0.581 0.577 y =1130.5-21.9331(age) Square feet 13,826.34 0.771 0.769 y = 31.665 +0.2601(square feet) List Price 1,811.61 0.970 0.970 y =12.029 +0.8773(list price) Age, Square feet 10,434.21 0.829 0.825 y = 386.55-9.253(age) + 0.197(square feet) Age, List price 1,811.75 0.970 0.970 y = 42.493-0.775(age) + 0.859(list price) Square feet, List price 1,764.10 0.971 0.970 y = 2.869 + 0.0202(square feet) + 0.824(list price) Age, Square feet, List 1,762.71 0.971 0.970 y = 34.104-0.797(age) + 0.0203(square feet)+0.805(list price) Price