Question: Refer to the scenario described in Problem and the file Housing Bubble.

a. Consider the Pre-Crisis worksheet data. Partition the data into training (50 percent), validation (30 percent), and test (20 percent) sets. Predict the sale price using multiple linear regression. Use Price as the output variable and all the other variables as input variables. To generate a pool of models to consider, execute the following steps. In Step 2 of XLMiner's Multiple Linear Regression procedure, click the Best subset option. In the Best Subset dialog box, check the box next to Perform best subset selection, enter 16 in the box next to Maximum size of best subset:, enter 1 in the box next to Number of best subsets:, and check the box next to Exhaustive search. Once you have identified an acceptable model, rerun the Multiple Linear Regression procedure and in Step 2, check the box next to In worksheet in the Score new data area. In the Match variable in the new range dialog box,

(1) specify the NewDataToPredict worksheet in the Worksheet: field,

(2) enter the cell range A1:P2001 in the Data range: field, and

(3) click Match variable(s) with same name(s).

i. From the generated set of multiple linear regression models, select one that you believe is a good fit. Express the model as a mathematical equation relating the output variable to the input variables.

ii. For your model, what is the RMSE on the validation data and test data?

iii. What is the average error on the validation data and test data? What does this suggest?

b. Repeat part a with the Post-Crisis worksheet data.

c. The MLR_NewScore worksheets generated in parts a and b contain the sales price predictions for the 2000 homes in the New Data To Predict using the pre-crisis and postcrisis data, respectively. For each of these 2000 homes, compare the two predictionsby computing the percentage change in predicted price between the pre-crisis and postcrisis models. Let percentage change 5 (postcrisis predicted price 2 pre-crisis predicted price)/pre-crisis predicted price. Summarize these percentage changes with a histogram. What is the average percentage change in predicted price between the pre-crisis and postcrisis model?

Problem: As an intern with the local home builder's association, you have been asked to analyze the state of the local housing market that has suffered during a recent economic crisis. you have been provided three data sets in the file Housing Bubble. The Pre-Crisis worksheet contains information on 1978 single-family homes sold during the one-year period before the burst of the housing bubble. The Post-Crisis worksheet contains information on 1657 single-family homes sold during the one-year period after the burst of the housing bubble. The New Data To Predict worksheet contains information on homes currently for sale.

a. Consider the Pre-Crisis worksheet data. Partition the data into training (50 percent), validation (30 percent), and test (20 percent) sets. Predict the sale price using k-nearest neighbors with up to k = 20 Use Price as the output variable and all the other variables as input variables. In Step 2 of XLMiner's k-Nearest Neighbors Prediction procedure, be sure to Normalize input data and to Score on best k between 1 and specified value. Check the box next to In worksheet in the Score new data area. In the Match variables in the new range dialog box, (1) specify the New Data To Predict worksheet in the Worksheet: field, (2) enter the cell range A1:P2001 in the Data range: field, and (3) click Match variable(s) with same name(s). Completing the procedure will result in a KNNP_New Score worksheet that will contain the predicted sales price for each home in New Data To Predict.

i. What value of k minimizes the root mean squared error (RMSE) on the validation data?

ii. What is the RMSE on the validation data and test data?

iii. What is the average error on the validation data and test data? What does this suggest?

b. Repeat part a with the Post-Crisis worksheet data.

c. The KNNP_NewScore1 and KNNP_NewScore2 worksheets contain the sales price predictions for the 2000 homes in the New Data To Predict using the precrisis and postcrisis data, respectively. For each of these 2000 homes, compare the two predictions by computing the percentage change in predicted price between the precrisis and postcrisis models. Let percentage change 5 (postcrisis predicted price 2 precrisis predicted price)/precrisis predicted price. Summarize these percentage changes with a histogram. What is the average percentage change in predicted price between the precrisis and postcrisis model?