Question 1.1. (TCO E) A local realtor wishes to study the relationship between selling price (PRICE in $), house size (HOUSESIZE in square feet), lot size (LOTSIZE in acres), and number of bathrooms (BATHROOM). A sample of 10 homes is selected at random. The data is given below (in MINITAB).
PRICE

HOUSESIZE

LOTSIZE

BATHROOMS

Pred House Size

Pred Lot Size

Pred Bath

100000

1600

0.8

1.5

2500

1

2.5

107000

1750

0.8

2.0

2500

5

2.5

121000

1900

0.8

2.5




124000

2150

1.0

2.5




132000

2400

0.9

2.5




140000

2300

0.9

3.0




144000

2400

1.0

2.5




158000

2700

1.0

3.0




170000

3000

1.0

3.0




182000

2900

1.2

3.5




Correlations: PRICE, HOUSESIZE, LOTSIZE, BATHROOMS PRICE HOUSESIZE LOTSIZE HOUSESIZE 0.971 0.000 LOTSIZE 0.919 0.875 0.000 0.001 BATHROOMS 0.921 0.877 0.877 0.000 0.001 0.002 Cell Contents: Pearson correlation PValue Regression Analysis: PRICE versus HOUSESIZE, LOTSIZE, BATHROOMS The regression equation is PRICE = 5918 + 32.9 HOUSESIZE + 43646 LOTSIZE + 10394 BATHROOMS. Predictor Coef SE Coef T P Constant 5918 13612 0.43 0.679 HOUSESIZE 32.945 9.069 3.63 0.011 LOTSIZE 43646 29384 1.49 0.188 BATHROOMS 10394 6863 1.51 0.181 S = 5269.97 RSq = 97.4% RSq(adj) = 96.0% Analysis of Variance Source DF SS MS F P Regression 3 6158964520 2052988173 73.92 0.000 Residual Error 6 166635480 27772580 Total 9 6325600000 Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 146075 2998 (138738, 153412) (131239, 160912) 1 320659 118964 ( 29565, 611752) ( 29280, 612038)XX XX denotes a point that is an extreme outlier in the predictors. Values of Predictors for New Observations New Obs HOUSESIZE LOTSIZE BATHROOMS 1 2500 1.00 2.50 1 2500 5.00 2.50 a. Analyze the above output to determine the multiple regression equation. b. Find and interpret the multiple index of determination (RSq). c. Perform the ttests on , , (use two tailed test with (a = .05). Interpret your results. d. Predict the selling price for an individual home having house size of 2,500 sq. ft, lot size of 1 acre, and 2.5 bathrooms. Use both a point estimate and the appropriate interval estimate. (Points : 31)
