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Answered: - A computer database in a small community contains the listed


A computer database in a small community contains the listed selling price (y, in thousands of dollars), the amount of living area (x1, in hundreds of square feet), and the number of floors (x2), bedrooms (x3), and bathrooms (x4) for 15 randomly selected condominiums currently on the market.?

(a) State the first-order multiple regression model for predicting listed selling price based on amount of living area, and the number of floors, bedrooms, and bathrooms. For the duration of this question, you may assume that the usual regression model assumptions are met.

(b) Use MINITAB to compute the correlation between each pair of independent variables. Do you have any concerns about potential multicollinearity in the model? Explain.

(c) Use MINITAB to fit the model you stated in part (a).

(d) Based on the output you generated in part (c), identify at least two indications that this fitted model may suffer from multicollinearity.

(e) Remove the variable that you believe is contributing the most to the multicollinearity in the model and use MINITAB to refit the model.

(f) Instead of doing what you did in part (e), remove the variable you would remove if performing backward elimination. Use MINITAB to refit the model.

(g) Based on your answers to (e) and (f), do you think multicollinearity was severe in the model? Which model do you think provided the best fit to the data set? Explain.




MINITAB ANSWER?

1

b. Correlation: List Price, y, Living Area, x1, Floors, x2, Bedrooms, x3, Baths, x4

?????????????????? List Price, y? Living Area, x1?????? Floors, x2???? Bedrooms, x3

Living Area, x1??????????? 0.951

?????????????????????????? 0.000

Floors, x2???????????????? 0.605??????????? 0.630

?????????????????????????? 0.017??????????? 0.012

Bedrooms, x3?????????????? 0.746??????????? 0.711??????????? 0.375

?????????????????????????? 0.001??????????? 0.003??????????? 0.168

Baths, x4????????????????? 0.837??????????? 0.724??????????? 0.747??????????? 0.681

?????????????????????????? 0.000??????????? 0.002??????????? 0.001??????????? 0.005

Cell Contents: Pearson correlation

?????????????? P-Value

?

c. Regression Analysis: List Price,? versus Living Area,, Floors, x2, Bedrooms, x3, Baths, x4

Analysis of Variance

Source???????????? DF?? Adj SS?? Adj MS? F-Value? P-Value

Regression????????? 4? 15883.5? 3970.88??? 79.63??? 0.000

? Living Area, x1?? 1?? 3434.3? 3434.33??? 68.87??? 0.000

? Floors, x2??????? 1??? 282.4?? 282.42???? 5.66??? 0.039

? Bedrooms, x3????? 1???? 13.4??? 13.43???? 0.27??? 0.615

? Baths, x4???????? 1?? ?887.0?? 886.95??? 17.79??? 0.002

Error????????????? 10??? 498.6??? 49.86

? Lack-of-Fit?????? 9??? 448.6??? 49.85???? 1.00??? 0.657

? Pure Error??????? 1???? 50.0??? 50.00

Total????????????? 14? 16382.2

Model Summary

????? S??? R-sq? R-sq(adj)? R-sq(pred)

7.06149? 96.96%???? 95.74%????? 93.26%

Coefficients

Term?????????????? Coef? SE Coef? T-Value? P-Value?? VIF

Constant???????? 116.70???? 9.56??? 12.20??? 0.000

Living Area, x1?? 6.216??? 0.749???? 8.30??? 0.000? 2.97

Floors, x2?????? -14.86???? 6.24 ???-2.38??? 0.039? 2.81

Bedrooms, x3????? -2.40???? 4.62??? -0.52??? 0.615? 2.74

Baths, x4???????? 30.03???? 7.12???? 4.22??? 0.002? 3.97

Regression Equation

List Price, y = 116.70 + 6.216 Living Area, x1 - 14.86 Floors, x2 - 2.40 Bedrooms, x3

??????????????? + 30.03 Baths, x4

Fits and Diagnostics for Unusual Observations

???????? List

Obs? Price, y???? Fit?? Resid? Std Resid

? 8??? 247.90? 260.55? -12.65????? -2.03? R

R? Large residual

e. Regression Analysis: List Price, y versus Living Area, x1, Floors, x2, Bedrooms, x3

Analysis of Variance

Source???????????? DF?? Adj SS?? Adj MS? F-Value? P-Value

Regression????????? 3? 14996.6? 4998.86??? 39.68??? 0.000

? Living Area, x1?? 1?? 3866.1? 3866.13??? 30.69??? 0.000

? Floors, x2??????? 1??? ??7.0???? 6.96???? 0.06??? 0.818

? Bedrooms, x3????? 1??? 166.4?? 166.41???? 1.32??? 0.275

Error????????????? 11?? 1385.6?? 125.96

? Lack-of-Fit????? 10?? 1335.6?? 133.56???? 2.67??? 0.446

? Pure Error??????? 1???? 50.0??? 50.00

Total????????????? 14? 16382.2

Model Summary

????? S??? R-sq? R-sq(adj)? R-sq(pred)

11.2234? 91.54%???? 89.24%????? 83.05%

Coefficients

Term????????????? Coef? SE Coef? T-Value? P-Value?? VIF

Constant???????? 123.4???? 15.0???? 8.23??? 0.000

Living Area, x1?? 6.56???? 1.18???? 5.54??? 0.000? 2.93

Floors, x2??????? 1.81???? 7.68???? 0.24??? 0.818? 1.69

Bedrooms, x3????? 7.32???? 6.36???? 1.15??? 0.275? 2.06

Regression Equation

List Price, y = 123.4 + 6.56 Living Area, x1 + 1.81 Floors, x2 + 7.32 Bedrooms, x3

f. Regression Analysis: List Price, y versus Living Area, x1, Floors, x2, Baths, x4

Analysis of Variance

Source???????????? DF?? Adj SS?? Adj MS? F-Value? P-Value

Regression????????? 3? 15870.1? 5290.03?? 113.64??? 0.000

? Living Area, x1?? 1?? 4374.6? 4374.61??? 93.97??? 0.000

? Floors, x2??????? 1??? 280.8?? 280.78???? 6.03??? 0.032

? Baths, x4???????? 1?? 1039.9? 1039.94??? 22.34??? 0.001

Error????????????? 11??? 512.1??? 46.55

? Lack-of-Fit?????? 7??? 349.1??? 49.87???? 1.22??? 0.447

? Pure Error??????? 4? ??163.0??? 40.75

Total????????????? 14? 16382.2

Model Summary

????? S??? R-sq? R-sq(adj)? R-sq(pred)

6.82291? 96.87%???? 96.02%????? 93.87%

Coefficients

Term?????????????? Coef? SE Coef? T-Value? P-Value?? VIF

Constant???????? 114.16???? 7.94??? 14.37??? 0.000

Living Area, x1?? 6.016??? 0.621???? 9.69??? 0.000? 2.18

Floors, x2?????? -13.55???? 5.52??? -2.46??? 0.032? 2.35

Baths, x4???????? 28.19???? 5.96???? 4.73??? 0.001? 2.98

Regression Equation

List Price, y = 114.16 + 6.016 Living Area, x1 - 13.55 Floors, x2 + 28.19 Baths, x4

Fits and Diagnostics for Unusual Observations

???????? List?????????????????? Std

Obs? Price, y???? Fit? Resid? Resid

?15??? 309.90? 297.98? 11.92?? 2.02? R

R? Large residual

 


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