A Realtor is interested in modeling the selling price of houses based on the squ
ID: 3362577 • Letter: A
Question
A Realtor is interested in modeling the selling price of houses based on the square footage (X1), the age of the house (X2) and the number of bedrooms (X3). The data was collected in the two largest cities in Arkansas and is given in an excel file.
1. a) Write down your first order regression model.
b) Obtain the Minitab output for this model and fill in the ANOVA table below.
Source
Df
SS
MS
F
Regression
Error
Total
c) Test if this model is useful.
2. a) Write down your complete second order regression model with all interaction (there should be 4 interaction terms).
b) Obtain the Minitab output for this model and fill in the ANOVA table below.
Source
Df
SS
MS
F
Regression
Error
Total
c) Test if this model is useful.
d) Now test if the squared terms and interaction terms are significant to the regression model, when taken together, by conducting the partial F-test.
Note that the model in problem 1 is the reduced model and the model in problem 2 is the full model.
3. Now using the appropriate model, write down the prediction equation. Then predict the selling price of a house that has 720 square feet, 4 bedrooms and is 54 years old. What is the residual?
Source
Df
SS
MS
F
Regression
Error
Total
0040 7258212 4759889 7769000 83518335067 135560522884021298141 3224833120268851 1122 866555808066452582 491809883610822600 112113222623382047541 000000080006006008000 008250 188399 3224135653106611 01887205 610243 1552 212141232111 500800000006008806000 708652060 638976256 848121380828915878129 233326423833615459842 1208403 2102284 6665956 1112 16195 85262 1096 8061 21121 59646656164655 28525723 916951 601624 349322322331568 12211621 58122 10920 58516212 0 34417 60445408 008 6 2 8050503409902002 0 9 1 4 2 0 1 6 4 9 4 6 9 9 2 5 9 9542 6 4 5 7 4 6 8 6 2 7 2 2 2 1 7 3 8 5244 313182242121 444535684029613529034 3 794759857684454148455 345337431613279737534 2 00060004002802000 58010402885806005 777867988381846072526 111121121111 000000000000000200000 000000000000000185900 005905550050550173591 844901237992820367598 0123456789012 1234Explanation / Answer
Regression Analysis: y versus x1, x2, x3
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 3 4216454982 1405484994 13.54 0.000
x1 1 128129914 128129914 1.23 0.282
x2 1 208662048 208662048 2.01 0.174
x3 1 1267907850 1267907850 12.21 0.003
Error 17 1764831142 103813597
Total 20 5981286124
Model Summary
S R-sq R-sq(adj) R-sq(pred)
10188.9 70.49% 65.29% 58.65%
R-Sq is 70.49% therefore this model is useful.
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 21482 7865 2.73 0.014
x1 -10.86 9.78 -1.11 0.282 6.14
x2 152 107 1.42 0.174 1.02
x3 4741 1357 3.49 0.003 6.10
Regression Equation
y = 21482 - 10.86 x1 + 152 x2 + 4741 x3
Fits and Diagnostics for Unusual Observations
Obs y Fit Resid Std Resid
13 68500 69723 -1223 -0.21 X
19 85590 60832 24758 2.51 R
R Large residual
X Unusual X
___________________________________________________________________________________________
Regression Analysis: y versus x1-sq, x2-sq, x3-sq
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 3 3631589701 1210529900 8.76 0.001
x1-sq 1 219035860 219035860 1.58 0.225
x2-sq 1 161151138 161151138 1.17 0.295
x3-sq 1 1528646886 1528646886 11.06 0.004
Error 17 2349696423 138217437
Total 20 5981286124
From anova x1Sq ,X2Sq are significant but x3sq is not significant.
Model Summary
S R-sq R-sq(adj) R-sq(pred)
11756.6 60.72% 53.78% 43.93%
R-Sq = 60.72% therefore this model is useful
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 37799 5154 7.33 0.000
x1-sq -0.00382 0.00303 -1.26 0.225 4.58
x2-sq 1.24 1.14 1.08 0.295 1.04
x3-sq 244.8 73.6 3.33 0.004 4.57
Regression Equation
y = 37799 - 0.00382 x1-sq + 1.24 x2-sq + 244.8 x3-sq
Fits and Diagnostics for Unusual Observations
Obs y Fit Resid Std Resid
13 68500 69519 -1019 -0.21 X
19 85590 57295 28295 2.47 R
R Large residual
X Unusual X
___________________________________________________________________________________________
R-Sq for model 1 is 70.49% is more as compaire to model 2 i.e. R-Sq = 60.72% therefore model 1 is appropriatre to predict selling price.
Predicted Regression Equation is,
y = 21482 - 10.86 x1 + 152 x2 + 4741 x3
x1 square footage = 720
x2 age of house = 54
x3 number of bedrooms = 4
y^ = 21482 - 10.86 * 720 + 152 * 54 + 4741 * 4
y^ = 40834.8
Residul = y - y^
= 60832 - 40834.8 = 19997.2
Residual = 19997.2
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.