The following table is copied from ‘Assign#4_MTB2304_SS17_V14.MTW’ or ‘Assign#4_

Question

The following table is copied from ‘Assign#4_MTB2304_SS17_V14.MTW’ or ‘Assign#4_MTB2304_SS17_V17.MTW’.

SPrice   SqFt   NumFlrs   BdRms   Baths
345.0   12   1   4   1.50
157.0   16   1   4   2.00
592.5   20   1   4   3.00
520.0   22   1   6   3.00
582.5   20   1   6   3.00
607.5   20   1   6   3.00
625.0   22   1   6   3.00
640.0   30   2   6   3.75
649.5   26   1   6   2.55
665.0   26   2   6   3.75
675.0   26   2   6   3.75
687.5   30   2   6   3.75
699.5   26   1   6   3.00
719.5   28   2   6   3.75
739.5   34   2   6   3.75
774.5   30   2   6   3.75
800.0   38   2   6   3.00
845.0   30   1   6   3.00
849.5   36   1   6   3.00
625.0   26   1   8   3.00
674.5   26   1   8   3.00
699.5   34   1   8   3.00
735.0   36   1   8   3.00
795.0   28   1   8   3.00
849.5   34   2   8   4.50
894.5   38   1   8   3.00
972.5   40   2   8   4.50
1099.5   42   1   8   3.75
1345.0   50   2   8   4.50

Variable Definitions: SPrice: Selling Price in SK (thousands of dollars) SqFt: Area in Square Feet x100 NumFlrs: Number of Floors BdRms: Number of Bedrooms (can be fractional) Baths: Number of Bathrooms (can also be fractional) In a red-hot real estate market, a real estate company wanted to establish some type of a linear relationship between the dependent /response variable of 'Selling Price' of houses in SK and the 4 independent / predictor variables given above. The data is given in the file: 'Assig4-MTB2304-SS17-V14.MTW, or Assign#4-MTB2304. SSI 7-V17.MTW'. Use each of the 4 independent variables, one at a time and obtain 4 Simple Linear Regression (SLR) Equations for the response variable, ‘Selling Price. Rank these 4 SLR equations in ‘Descending Order' from the Best' to the ‘worst'. Explain what specific criteria you use in this ranking. a. b. Now use all the 4 independent variables to obtain 1 Full Multiple Linear Regression c. Manually calculate the R2 and Rdi for this MLR equation and comment on the quality d. By simply observing the MiniTab printout and without doing any formal analysis, e. Now drop the worst performing independent variable and use the remaining three (MLR) equation for all the independent/explanatory variables. of the regression. Explain the significance of R2 comment on which of the parameters, °, , 2, 3, 4 are significant. What specific numerical criterion did you use? Explain briefly independent variables, to obtain the new 'Best' MLR equation.

Explanation / Answer

a)

Regression Analysis: SPrice versus SqFt

Analysis of Variance

Model Summary

Coefficients

Regression Equation

Fits and Diagnostics for Unusual Observations

R Large residual
X Unusual X

Regression Analysis: SPrice versus NumFlrs

Analysis of Variance

Model Summary

Coefficients

Regression Equation

Fits and Diagnostics for Unusual Observations

Regression Analysis: SPrice versus BdRms

Analysis of Variance

Model Summary

Coefficients

Regression Equation

Fits and Diagnostics for Unusual Observations

Regression Analysis: SPrice versus Baths

Analysis of Variance

Model Summary

Coefficients

Regression Equation

Fits and Diagnostics for Unusual Observations

model R^2_adj

1 0.8145

2 0.0712

3 0.4331

4 0.4815

1 > 4 > 3 > 2

b)

Regression Analysis: SPrice versus SqFt, NumFlrs, BdRms, Baths

Analysis of Variance

Model Summary

Coefficients

Regression Equation

Fits and Diagnostics for Unusual Observations

c)

R^2 = 0.876

R^2_adjusted = 0.8553

d)

if p-value is less than 0.05 ,the variacle is significant

b1, b2,b4 are significant   

b0 abd b3 are nor not significant

e)

we remove varible 3 that is bedroom (not significant)

Regression Analysis: SPrice versus SqFt, NumFlrs, Baths

Analysis of Variance

Model Summary

Coefficients

Regression Equation

Fits and Diagnostics for Unusual Observations

f) R^2 = 0.8735 , R^2_adj = 0.8583

since R^2_adj (new) > R^2_adj (old) { 0.8583 > 0.8533

new model is best (after removing variable 3)

Source DF Adj SS Adj MS F-Value P-Value Regression 1 1048996 1048996 123.97 0.000 SqFt 1 1048996 1048996 123.97 0.000 Error 27 228463 8462 Lack-of-Fit 11 168547 15322 4.09 0.006 Pure Error 16 59916 3745 Total 28 1277459

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