252y0641s1 12/6/06
Computer Output for Question 1
Regression A
Data description
C1 Price - Price of property in $thousands
C2 Livsqft – Living area in thousands of square feet
C3 Lotsqft – Lot size in thousands of square feet.
C4 Loc1 – A dummy variable, 1 if property is in Area 1 of 3
C5 Loc2 – A dummy variable, 1 if property is in Area 2 of 3
C6 Baths – Number of baths in house.
C7 Lot 1 – An interaction variable, the product of Lotsqft and Loc1.
C8 Lot 2 - An interaction variable, the product of Lotsqft and Loc2.
C9 Liv 1 – An interaction variable, the product of Livsqft and Loc1.
C10 Liv 2 - An interaction variable, the product of Livsqft and Loc2.
C11 Libsqsq – The living area squared.
This is a regression suggested by Leonard J Kazmier.The dependent variable is the price of the property. The remainder of the variables listed above are candidates for explanatory variables. Since there are only 30 observations the number of independent variables needed to explain the values of the price variable should be relatively small. The data set and descriptive statistics appear at the end.
————— 12/4/2006 8:36:27 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\RBOVE\My Documents\Minitab\252x06041-021.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\RBOVE\My
Documents\Minitab\252x06041-021.MTW'
Worksheet was saved on Mon Dec 04 2006
Results for: 252x06041-021.MTW
MTB > regress c1 10 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11;
SUBC> vif.
1)Regression Analysis: price versus livsqft, lotsqft, ...
The regression equation is
price = - 783 + 705 livsqft - 2.90 lotsqft + 569 loc1 + 423 loc 2 + 18.1 baths
+ 5.78 lot1 - 1.07 lot2 - 349 liv1 - 197 liv2 - 125 livsqsq
Predictor Coef SE Coef T P VIF
Constant -782.8 265.1 -2.95 0.008
livsqft 704.6 213.8 3.30 0.004 8142.7
lotsqft -2.900 3.283 -0.88 0.388 76.1
loc1 569.4 190.3 2.99 0.007 5725.1
loc 2 423.3 139.0 3.05 0.007 3054.2
baths 18.121 4.392 4.13 0.001 2.3
lot1 5.775 4.709 1.23 0.235 520.6
lot2 -1.071 5.196 -0.21 0.839 997.7
liv1 -349.3 117.8 -2.96 0.008 4382.0
liv2 -196.54 79.91 -2.46 0.024 3414.8
livsqsq -125.48 39.56 -3.17 0.005 4606.9
S = 6.49288 R-Sq = 97.5% R-Sq(adj) = 96.2%
Analysis of Variance
Source DF SS MS F P
Regression 10 31197.6 3119.8 74.00 0.000
Residual Error 19 801.0 42.2
Total 29 31998.6
Source DF Seq SS
livsqft 1 29642.7
lotsqft 1 126.4
loc1 1 2.9
loc 2 1 492.5
baths 1 472.4
lot1 1 4.2
lot2 1 27.5
liv1 1 0.0
liv2 1 4.7
livsqsq 1 424.2
Unusual Observations
Obs livsqft price Fit SE Fit Residual St Resid
29 2.50 199.40 190.70 5.36 8.70 2.37R
R denotes an observation with a large standardized residual.
MTB > regress c1 9 c3 c4 c5 c6 c7 c8 c9 c10 c11;
SUBC> vif.
2)Regression Analysis: price versus lotsqft, loc1, ...
The regression equation is
price = 85.2 + 2.12 lotsqft - 48.5 loc1 - 20.4 loc 2 + 11.0 baths - 1.73 lot1
- 4.13 lot2 + 23.3 liv1 + 29.2 liv2 + 4.16 livsqsq
Predictor Coef SE Coef T P VIF
Constant 85.16 36.25 2.35 0.029
lotsqft 2.121 3.552 0.60 0.557 59.7
loc1 -48.47 39.41 -1.23 0.233 164.5
loc 2 -20.39 41.96 -0.49 0.632 186.5
baths 11.012 4.675 2.36 0.029 1.7
lot1 -1.728 5.036 -0.34 0.735 398.9
lot2 -4.127 6.247 -0.66 0.516 965.9
liv1 23.32 40.44 0.58 0.571 345.9
liv2 29.22 50.24 0.58 0.567 904.3
livsqsq 4.156 5.025 0.83 0.418 49.8
S = 7.93322 R-Sq = 96.1% R-Sq(adj) = 94.3%
Analysis of Variance
Source DF SS MS F P
Regression 9 30739.9 3415.5 54.27 0.000
Residual Error 20 1258.7 62.9
Total 29 31998.6
Source DF Seq SS
lotsqft 1 26347.5
loc1 1 61.3
loc 2 1 3609.1
baths 1 509.1
lot1 1 8.0
lot2 1 47.0
liv1 1 59.8
liv2 1 55.1
livsqsq 1 43.0
Unusual Observations
Obs lotsqft price Fit SE Fit Residual St Resid
29 20.0 199.40 186.60 6.37 12.80 2.71R
R denotes an observation with a large standardized residual.
MTB > regress c1 7 c3 c4 c5 c6 c9 c10 c11;
SUBC> vif.
3)Regression Analysis: price versus lotsqft, loc1, ...
The regression equation is
price = 99.0 + 0.67 lotsqft - 58.7 loc1 - 28.3 loc 2 + 11.4 baths + 15.1 liv1
- 0.2 liv2 + 6.04 livsqsq
Predictor Coef SE Coef T P VIF
Constant 99.01 24.22 4.09 0.000
lotsqft 0.671 2.072 0.32 0.749 21.9
loc1 -58.68 33.91 -1.73 0.098 131.1
loc 2 -28.32 37.49 -0.76 0.458 160.2
baths 11.441 4.105 2.79 0.011 1.4
liv1 15.12 21.04 0.72 0.480 100.7
liv2 -0.22 19.15 -0.01 0.991 141.4
livsqsq 6.044 3.435 1.76 0.092 25.0
S = 7.64800 R-Sq = 96.0% R-Sq(adj) = 94.7%
Analysis of Variance
Source DF SS MS F P
Regression 7 30711.8 4387.4 75.01 0.000
Residual Error 22 1286.8 58.5
Total 29 31998.6
Source DF Seq SS
lotsqft 1 26347.5
loc1 1 61.3
loc 2 1 3609.1
baths 1 509.1
liv1 1 2.4
liv2 1 1.3
livsqsq 1 181.1
Unusual Observations
Obs lotsqft price Fit SE Fit Residual St Resid
29 20.0 199.40 184.53 5.16 14.87 2.63R
R denotes an observation with a large standardized residual.
MTB > regress c1 5 c3 c6 c9 c10 c11;
SUBC> vif.
4)Regression Analysis: price versus lotsqft, baths, liv1, liv2, livsqsq
The regression equation is
price = 68.4 + 2.73 lotsqft + 10.6 baths - 19.9 liv1 - 13.3 liv2 + 5.10 livsqsq
Predictor Coef SE Coef T P VIF
Constant 68.38 15.84 4.32 0.000
lotsqft 2.731 1.726 1.58 0.127 14.6
baths 10.568 4.157 2.54 0.018 1.4
liv1 -19.906 5.390 -3.69 0.001 6.3
liv2 -13.334 3.662 -3.64 0.001 5.0
livsqsq 5.105 3.425 1.49 0.149 23.9
S = 7.80489 R-Sq = 95.4% R-Sq(adj) = 94.5%
Analysis of Variance
Source DF SS MS F P
Regression 5 30536.6 6107.3 100.26 0.000
Residual Error 24 1462.0 60.9
Total 29 31998.6
Source DF Seq SS
lotsqft 1 26347.5
baths 1 168.4
liv1 1 123.9
liv2 1 3761.5
livsqsq 1 135.3
Unusual Observations
Obs lotsqft price Fit SE Fit Residual St Resid
29 20.0 199.40 186.61 5.12 12.79 2.17R
R denotes an observation with a large standardized residual.
MTB > regress c1 4 c6 c9 c10 c11;
SUBC> vif.
5)Regression Analysis: price versus baths, liv1, liv2, livsqsq
The regression equation is
price = 86.8 + 11.1 baths - 17.0 liv1 - 10.1 liv2 + 9.92 livsqsq
Predictor Coef SE Coef T P VIF
Constant 86.77 11.08 7.83 0.000
baths 11.090 4.267 2.60 0.015 1.4
liv1 -16.988 5.214 -3.26 0.003 5.6
liv2 -10.148 3.149 -3.22 0.004 3.5
livsqsq 9.915 1.622 6.11 0.000 5.1
S = 8.03608 R-Sq = 95.0% R-Sq(adj) = 94.1%
Analysis of Variance
Source DF SS MS F P
Regression 4 30384.2 7596.0 117.62 0.000
Residual Error 25 1614.5 64.6
Total 29 31998.6
Source DF Seq SS
baths 1 8914.5
liv1 1 8231.0
liv2 1 10825.9
livsqsq 1 2412.9
Unusual Observations
Obs baths price Fit SE Fit Residual St Resid
3 2.00 87.90 102.84 3.19 -14.94 -2.03R
27 3.00 195.85 209.28 5.08 -13.43 -2.16R
29 3.00 199.40 182.01 4.34 17.39 2.57R
R denotes an observation with a large standardized residual.
MTB > BReg c1 c6 c9 c10 c11 ;
SUBC> NVars 1 4;
SUBC> Best 2;
SUBC> Constant.
6)Best Subsets Regression: price versus baths, liv1, liv2, livsqsq
Response is price
l
i
b v
a l l s
t i i q
Mallows h v v s
Vars R-Sq R-Sq(adj) C-p S s 1 2 q
1 91.9 91.6 14.3 9.6448 X
1 45.3 43.3 245.3 25.013 X
2 92.6 92.1 12.5 9.3441 X X
2 92.2 91.6 14.7 9.6171 X X
3 93.6 92.9 9.8 8.8812 X X X
3 92.9 92.0 13.4 9.3746 X X X
4 95.0 94.1 5.0 8.0361 X X X X
MTB > regress c1 10 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11
7)Regression Analysis: price versus livsqft, lotsqft, ...
The regression equation is
price = - 783 + 705 livsqft - 2.90 lotsqft + 569 loc1 + 423 loc 2 + 18.1 baths
+ 5.78 lot1 - 1.07 lot2 - 349 liv1 - 197 liv2 - 125 livsqsq
Predictor Coef SE Coef T P
Constant -782.8 265.1 -2.95 0.008
livsqft 704.6 213.8 3.30 0.004
lotsqft -2.900 3.283 -0.88 0.388
loc1 569.4 190.3 2.99 0.007
loc 2 423.3 139.0 3.05 0.007
baths 18.121 4.392 4.13 0.001
lot1 5.775 4.709 1.23 0.235
lot2 -1.071 5.196 -0.21 0.839
liv1 -349.3 117.8 -2.96 0.008
liv2 -196.54 79.91 -2.46 0.024
livsqsq -125.48 39.56 -3.17 0.005
S = 6.49288 R-Sq = 97.5% R-Sq(adj) = 96.2%
Analysis of Variance
Source DF SS MS F P
Regression 10 31197.6 3119.8 74.00 0.000
Residual Error 19 801.0 42.2
Total 29 31998.6
Source DF Seq SS
livsqft 1 29642.7
lotsqft 1 126.4
loc1 1 2.9
loc 2 1 492.5
baths 1 472.4
lot1 1 4.2
lot2 1 27.5
liv1 1 0.0
liv2 1 4.7
livsqsq 1 424.2
Unusual Observations
Obs livsqft price Fit SE Fit Residual St Resid
29 2.50 199.40 190.70 5.36 8.70 2.37R
R denotes an observation with a large standardized residual.
MTB > regress c1 8 c2 c3 c4 c5 c6 c9 c10 c11
8)Regression Analysis: price versus livsqft, lotsqft, ...
The regression equation is
price = - 637 + 574 livsqft - 0.24 lotsqft + 463 loc1 + 351 loc 2 + 14.9 baths
- 247 liv1 - 174 liv2 - 103 livsqsq
Predictor Coef SE Coef T P
Constant -636.8 241.4 -2.64 0.015
livsqft 573.8 187.6 3.06 0.006
lotsqft -0.241 1.789 -0.13 0.894
loc1 462.9 173.0 2.68 0.014
loc 2 350.9 128.0 2.74 0.012
baths 14.910 3.674 4.06 0.001
liv1 -247.23 87.63 -2.82 0.010
liv2 -173.97 59.10 -2.94 0.008
livsqsq -103.43 35.91 -2.88 0.009
S = 6.51098 R-Sq = 97.2% R-Sq(adj) = 96.2%
Analysis of Variance
Source DF SS MS F P
Regression 8 31108.4 3888.5 91.73 0.000
Residual Error 21 890.3 42.4
Total 29 31998.6
Source DF Seq SS
livsqft 1 29642.7
lotsqft 1 126.4
loc1 1 2.9
loc 2 1 492.5
baths 1 472.4
liv1 1 2.5
liv2 1 17.3
livsqsq 1 351.6
MTB > regress c1 7 c2 c4 c5 c6 c9 c10 c11
9)Regression Analysis: price versus livsqft, loc1, ...
The regression equation is
price = - 634 + 570 livsqft + 461 loc1 + 349 loc 2 + 14.8 baths - 247 liv1
- 173 liv2 - 103 livsqsq
Predictor Coef SE Coef T P
Constant -633.6 234.9 -2.70 0.013
livsqft 569.6 180.8 3.15 0.005
loc1 461.3 168.7 2.74 0.012
loc 2 349.5 124.7 2.80 0.010
baths 14.822 3.534 4.19 0.000
liv1 -246.77 85.58 -2.88 0.009
liv2 -173.49 57.66 -3.01 0.006
livsqsq -102.93 34.92 -2.95 0.007
S = 6.36403 R-Sq = 97.2% R-Sq(adj) = 96.3%
Analysis of Variance
Source DF SS MS F P
Regression 7 31107.6 4443.9 109.72 0.000
Residual Error 22 891.0 40.5
Total 29 31998.6
Source DF Seq SS
livsqft 1 29642.7
loc1 1 10.8
loc 2 1 597.7
baths 1 484.7
liv1 1 3.3
liv2 1 16.4
livsqsq 1 352.0
MTB > regress c1 7 c2 c4 c5 c6 c9 c10 c11;
SUBC> vif.
10)Regression Analysis: price versus livsqft, loc1, ...
The regression equation is
price = - 634 + 570 livsqft + 461 loc1 + 349 loc 2 + 14.8 baths - 247 liv1
- 173 liv2 - 103 livsqsq
Predictor Coef SE Coef T P VIF
Constant -633.6 234.9 -2.70 0.013
livsqft 569.6 180.8 3.15 0.005 6060.8
loc1 461.3 168.7 2.74 0.012 4682.2
loc 2 349.5 124.7 2.80 0.010 2559.1
baths 14.822 3.534 4.19 0.000 1.5
liv1 -246.77 85.58 -2.88 0.009 2406.6
liv2 -173.49 57.66 -3.01 0.006 1851.0
livsqsq -102.93 34.92 -2.95 0.007 3736.4
S = 6.36403 R-Sq = 97.2% R-Sq(adj) = 96.3%
Analysis of Variance
Source DF SS MS F P
Regression 7 31107.6 4443.9 109.72 0.000
Residual Error 22 891.0 40.5
Total 29 31998.6
Source DF Seq SS
livsqft 1 29642.7
loc1 1 10.8
loc 2 1 597.7
baths 1 484.7
liv1 1 3.3
liv2 1 16.4
livsqsq 1 352.0
MTB > Stepwise c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11;
SUBC> AEnter 0.15;
SUBC> ARemove 0.15;
SUBC> Best 0;
SUBC> Constant.
11)Stepwise Regression: price versus livsqft, lotsqft, ...
Alpha-to-Enter: 0.15 Alpha-to-Remove: 0.15
Response is price on 10 predictors, with N = 30
Step 1 2 3 4
Constant 13.59 16.80 59.44 53.49
livsqft 62.8 62.2 45.9 38.0
T-Value 18.77 19.15 6.17 5.53
P-Value 0.000 0.000 0.000 0.000
lot2 -0.40 -1.22 -1.51
T-Value -1.76 -3.03 -4.21
P-Value 0.090 0.005 0.000
loc1 -21.6 -25.8
T-Value -2.39 -3.27
P-Value 0.024 0.003
baths 11.8
T-Value 3.18
P-Value 0.004
S 9.17 8.85 8.17 7.03
R-Sq 92.64 93.39 94.58 96.14
R-Sq(adj) 92.37 92.90 93.96 95.53
Mallows C-p 29.9 26.1 19.1 9.3
More? (Yes, No, Subcommand, or Help)
SUBC> y
No variables entered or removed
More? (Yes, No, Subcommand, or Help)
SUBC> n
Correlations: livsqft, lot2, loc1, baths
livsqft lot2 loc1
lot2 -0.109
0.565
loc1 -0.735 -0.497
0.000 0.005
baths 0.472 0.136 -0.405
0.009 0.475 0.026
Cell Contents: Pearson correlation
P-Value
MTB > Save "C:\Documents and Settings\RBOVE\My Documents\Minitab\252x06041-021.MTW";
SUBC> Replace.
Saving file as: 'C:\Documents and Settings\RBOVE\My
Documents\Minitab\252x06041-021.MTW'
Existing file replaced.
MTB> describe c1-c11
Descriptive Statistics: price, livsqft, lotsqft, loc1, loc 2, baths, lot1, ...
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
price 30 0 134.23 6.06 33.22 87.90 109.45 124.20 164.25
livsqft 30 0 1.9200 0.0929 0.5088 1.2000 1.5000 1.8500 2.4000
lotsqft 30 0 15.267 0.585 3.205 10.000 12.000 15.000 18.000
loc1 30 0 0.3333 0.0875 0.4795 0.0000 0.0000 0.0000 1.0000
loc 2 30 0 0.3333 0.0875 0.4795 0.0000 0.0000 0.0000 1.0000
baths 30 0 2.0333 0.0756 0.4138 1.0000 2.0000 2.0000 2.0000
lot1 30 0 4.00 1.07 5.84 0.00 0.00 0.00 10.50
lot2 30 0 5.07 1.34 7.33 0.00 0.00 0.00 15.00
liv1 30 0 0.467 0.124 0.677 0.000 0.000 0.000 1.225
liv2 30 0 0.610 0.161 0.882 0.000 0.000 0.000 1.725
livsqsq 30 0 3.937 0.378 2.069 1.440 2.250 3.425 5.760
Variable Maximum
price 199.40
livsqft 3.0000
lotsqft 22.000
loc1 1.0000
loc 2 1.0000
baths 3.0000
lot1 15.00
lot2 17.00
liv1 1.600
liv2 2.000
livsqsq 9.000
MTB > print c1 - c11
Data Display
Row price livsqft lotsqft loc1 loc 2 baths lot1 lot2 liv1 liv2
1 102.20 1.5 12 1 0 2 12 0 1.5 0.0
2 103.95 1.2 10 1 0 2 10 0 1.2 0.0
3 87.90 1.2 10 1 0 2 10 0 1.2 0.0
4 110.00 1.6 15 1 0 2 15 0 1.6 0.0
5 97.00 1.4 12 1 0 1 12 0 1.4 0.0
6 95.70 1.2 10 1 0 2 10 0 1.2 0.0
7 113.60 1.6 15 1 0 2 15 0 1.6 0.0
8 109.60 1.5 12 1 0 2 12 0 1.5 0.0
9 110.80 1.5 12 1 0 2 12 0 1.5 0.0
10 90.60 1.3 12 1 0 1 12 0 1.3 0.0
11 109.00 1.6 13 0 1 2 0 13 0.0 1.6
12 133.00 1.9 15 0 1 2 0 15 0.0 1.9
13 134.00 1.8 15 0 1 2 0 15 0.0 1.8
14 120.30 2.0 17 0 1 2 0 17 0.0 2.0
15 137.00 2.0 17 0 1 3 0 17 0.0 2.0
16 122.40 1.7 15 0 1 2 0 15 0.0 1.7
17 121.70 1.8 15 0 1 2 0 15 0.0 1.8
18 126.00 1.9 16 0 1 2 0 16 0.0 1.9
19 128.00 2.0 16 0 1 2 0 16 0.0 2.0
20 117.50 1.6 13 0 1 2 0 13 0.0 1.6
21 158.70 2.4 18 0 0 2 0 0 0.0 0.0
22 186.80 2.6 18 0 0 2 0 0 0.0 0.0
23 172.40 2.3 16 0 0 2 0 0 0.0 0.0
24 151.20 2.2 16 0 0 2 0 0 0.0 0.0
25 179.10 2.8 20 0 0 2 0 0 0.0 0.0
26 182.30 2.7 20 0 0 2 0 0 0.0 0.0
27 195.85 3.0 22 0 0 3 0 0 0.0 0.0
28 168.00 2.4 18 0 0 2 0 0 0.0 0.0
29 199.40 2.5 20 0 0 3 0 0 0.0 0.0
30 163.00 2.4 18 0 0 2 0 0 0.0 0.0
Row livsqsq
1 2.25
2 1.44
3 1.44
4 2.56
5 1.96
6 1.44
7 2.56
8 2.25
9 2.25
10 1.69
11 2.56
12 3.61
13 3.24
14 4.00
15 4.00
16 2.89
17 3.24
18 3.61
19 4.00
20 2.56
21 5.76
22 6.76
23 5.29
24 4.84
25 7.84
26 7.29
27 9.00
28 5.76
29 6.25
30 5.76
Regression B
Data description
C1 Sq.ft – Number of square feet
C2 Sqftsq – The square of the previous variable.
C3 Assessed – Assessed value in $1000s
C4 Market – Market value in $1000s – The dependent variable.
C5 Low – A dummy variable; indicates an inferior property.
C6 Med - A dummy variable; indicates a normal property.
C7 High - A dummy variable; indicates a superior property.
C9 AL – An interaction variable; the product of Assessed and Low.
C10 AM – An interaction variable; the product of Assessed and Med.
C11 AH – An interaction variable; the product of Assessed and High.
This is a regression mentioned in the Minitab handbook and the data comes from the Minitab website maintained by the publisher. The dependent variable is the market price of the property. The remainder of the variables listed above are candidates for explanatory variables. Since there are only 60 observations the number of independent variables needed to explain the values of the price variable should be relatively small. The data and some descriptive statistics appear at the end.
————— 12/4/2006 10:28:02 PM ————————————————————
Welcome to Minitab, press F1 for help.
MTB > WOpen "C:\Documents and Settings\RBOVE\My Documents\Minitab\252x06041-022.MTW".
Retrieving worksheet from file: 'C:\Documents and Settings\RBOVE\My
Documents\Minitab\252x06041-022.MTW'
Worksheet was saved on Mon Dec 04 2006
Results for: 252x06041-022.MTW
MTB > regress c4 7 c1 c2 c3 c5 c6 c9 c10;
SUBC> vif.
12)Regression Analysis: Market versus Sq.ft, Sqftsq, ...
The regression equation is
Market = 9.9 + 0.0438 Sq.ft - 0.000015 Sqftsq + 0.129 Assessed - 6.2 Low
- 5.9 Med - 0.012 AL + 0.176 AM
Predictor Coef SE Coef T P VIF
Constant 9.87 15.05 0.66 0.515
Sq.ft 0.043807 0.008169 5.36 0.000 31.3
Sqftsq -0.00001476 0.00000370 -3.99 0.000 29.6
Assessed 0.1289 0.4909 0.26 0.794 64.9
Low -6.16 14.12 -0.44 0.664 257.6
Med -5.87 14.11 -0.42 0.679 314.7
AL -0.0122 0.5023 -0.02 0.981 133.8
AM 0.1762 0.4985 0.35 0.725 265.9
S = 2.72518 R-Sq = 81.5% R-Sq(adj) = 79.1%
Analysis of Variance
Source DF SS MS F P
Regression 7 1706.22 243.75 32.82 0.000
Residual Error 52 386.18 7.43
Total 59 2092.40
Source DF Seq SS
Sq.ft 1 1173.10
Sqftsq 1 231.97
Assessed 1 177.38
Low 1 107.14
Med 1 3.57
AL 1 12.13
AM 1 0.93
Unusual Observations
Obs Sq.ft Market Fit SE Fit Residual St Resid
2 538 19.400 26.297 1.433 -6.897 -2.98R
3 544 25.200 30.544 1.188 -5.344 -2.18R
10 712 42.400 34.179 0.696 8.221 3.12R
30 923 30.000 32.106 1.752 -2.106 -1.01 X
57 1298 45.200 44.904 2.670 0.296 0.54 X
59 1602 47.400 46.162 2.032 1.238 0.68 X
60 1804 45.400 44.330 2.309 1.070 0.74 X
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
MTB > regress c4 5 c1 c2 c3 c9 c10;
SUBC> vif.
13)Regression Analysis: Market versus Sq.ft, Sqftsq, Assessed, AL, AM
The regression equation is
Market = 3.69 + 0.0443 Sq.ft - 0.000015 Sqftsq + 0.337 Assessed - 0.230 AL
- 0.0289 AM
Predictor Coef SE Coef T P VIF
Constant 3.691 4.390 0.84 0.404
Sq.ft 0.044273 0.007962 5.56 0.000 30.7
Sqftsq -0.00001498 0.00000360 -4.16 0.000 29.1
Assessed 0.33686 0.07850 4.29 0.000 1.7
AL -0.22961 0.07316 -3.14 0.003 2.9
AM -0.02893 0.05321 -0.54 0.589 3.1
S = 2.67918 R-Sq = 81.5% R-Sq(adj) = 79.8%
Analysis of Variance
Source DF SS MS F P
Regression 5 1704.79 340.96 47.50 0.000
Residual Error 54 387.61 7.18
Total 59 2092.40
Source DF Seq SS
Sq.ft 1 1173.10
Sqftsq 1 231.97
Assessed 1 177.38
AL 1 120.21
AM 1 2.12
Unusual Observations
Obs Sq.ft Market Fit SE Fit Residual St Resid
2 538 19.400 26.200 1.322 -6.800 -2.92R
3 544 25.200 30.488 1.156 -5.288 -2.19R
10 712 42.400 34.150 0.636 8.250 3.17R
45 1060 44.800 43.631 1.471 1.169 0.52 X
59 1602 47.400 46.627 1.681 0.773 0.37 X
60 1804 45.400 44.247 2.253 1.153 0.80 X
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
MTB > BReg c4 5 c1 c2 c3 c9 c10;
SUBC> NVars 1 4;
SUBC> Best 2;
SUBC> Constant.
14)Best Subsets Regression: Market versus Sq.ft, Sqftsq, Assessed, AL, AM
Response is Market
A
s
S s
S q e
q f s
. t s
Mallows f s e A A
Vars R-Sq R-Sq(adj) C-p S t q d L M
1 56.1 55.3 72.1 3.9812 X
1 44.9 44.0 104.6 4.4582 X
2 67.9 66.7 39.7 3.4347 X X
2 67.2 66.0 41.8 3.4725 X X
3 75.6 74.3 19.0 3.0176 X X X
3 75.5 74.2 19.4 3.0242 X X X
4 81.4 80.0 4.3 2.6620 X X X X
4 78.1 76.5 13.9 2.8867 X X X X
5 81.5 79.8 6.0 2.6792 X X X X X
MTB > regress c4 7 c1 c2 c3 c5 c6 c9 c10
15)Regression Analysis: Market versus Sq.ft, Sqftsq, ...
The regression equation is
Market = 9.9 + 0.0438 Sq.ft - 0.000015 Sqftsq + 0.129 Assessed - 6.2 Low
- 5.9 Med - 0.012 AL + 0.176 AM
Predictor Coef SE Coef T P
Constant 9.87 15.05 0.66 0.515
Sq.ft 0.043807 0.008169 5.36 0.000
Sqftsq -0.00001476 0.00000370 -3.99 0.000
Assessed 0.1289 0.4909 0.26 0.794
Low -6.16 14.12 -0.44 0.664
Med -5.87 14.11 -0.42 0.679
AL -0.0122 0.5023 -0.02 0.981
AM 0.1762 0.4985 0.35 0.725
S = 2.72518 R-Sq = 81.5% R-Sq(adj) = 79.1%
Analysis of Variance
Source DF SS MS F P
Regression 7 1706.22 243.75 32.82 0.000
Residual Error 52 386.18 7.43
Total 59 2092.40
Source DF Seq SS
Sq.ft 1 1173.10
Sqftsq 1 231.97
Assessed 1 177.38
Low 1 107.14
Med 1 3.57
AL 1 12.13
AM 1 0.93
Unusual Observations
Obs Sq.ft Market Fit SE Fit Residual St Resid
2 538 19.400 26.297 1.433 -6.897 -2.98R
3 544 25.200 30.544 1.188 -5.344 -2.18R
10 712 42.400 34.179 0.696 8.221 3.12R
30 923 30.000 32.106 1.752 -2.106 -1.01 X
57 1298 45.200 44.904 2.670 0.296 0.54 X
59 1602 47.400 46.162 2.032 1.238 0.68 X
60 1804 45.400 44.330 2.309 1.070 0.74 X
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
MTB > let c11 = c3 - c9 -c10
MTB > regress c4 7 c1 c2 c5 c6 c9 c10 c11
16)Regression Analysis: Market versus Sq.ft, Sqftsq, Low, Med, AL, AM, AH
The regression equation is
Market = 9.9 + 0.0438 Sq.ft - 0.000015 Sqftsq - 6.2 Low - 5.9 Med + 0.117 AL
+ 0.305 AM + 0.129 AH
Predictor Coef SE Coef T P
Constant 9.87 15.05 0.66 0.515
Sq.ft 0.043807 0.008169 5.36 0.000
Sqftsq -0.00001476 0.00000370 -3.99 0.000
Low -6.16 14.12 -0.44 0.664
Med -5.87 14.11 -0.42 0.679
AL 0.1167 0.1085 1.08 0.287
AM 0.30502 0.09290 3.28 0.002
AH 0.1289 0.4909 0.26 0.794
S = 2.72518 R-Sq = 81.5% R-Sq(adj) = 79.1%
Analysis of Variance
Source DF SS MS F P
Regression 7 1706.22 243.75 32.82 0.000
Residual Error 52 386.18 7.43
Total 59 2092.40
Source DF Seq SS
Sq.ft 1 1173.10
Sqftsq 1 231.97
Low 1 202.81
Med 1 8.68
AL 1 9.22
AM 1 79.92
AH 1 0.51
Unusual Observations
Obs Sq.ft Market Fit SE Fit Residual St Resid
2 538 19.400 26.297 1.433 -6.897 -2.98R
3 544 25.200 30.544 1.188 -5.344 -2.18R
10 712 42.400 34.179 0.696 8.221 3.12R
30 923 30.000 32.106 1.752 -2.106 -1.01 X
57 1298 45.200 44.904 2.670 0.296 0.54 X
59 1602 47.400 46.162 2.032 1.238 0.68 X
60 1804 45.400 44.330 2.309 1.070 0.74 X
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
MTB > regress c4 6 c1 c2 c5 c6 c9 c10
17)Regression Analysis: Market versus Sq.ft, Sqftsq, Low, Med, AL, AM
The regression equation is
Market = 13.6 + 0.0436 Sq.ft - 0.000015 Sqftsq - 9.80 Low - 9.49 Med + 0.117 AL
+ 0.305 AM
Predictor Coef SE Coef T P
Constant 13.615 4.740 2.87 0.006
Sq.ft 0.043570 0.008047 5.41 0.000
Sqftsq -0.00001464 0.00000364 -4.03 0.000
Low -9.796 2.671 -3.67 0.001
Med -9.494 2.818 -3.37 0.001
AL 0.1166 0.1075 1.08 0.283
AM 0.30473 0.09207 3.31 0.002
S = 2.70113 R-Sq = 81.5% R-Sq(adj) = 79.4%
Analysis of Variance
Source DF SS MS F P
Regression 6 1705.71 284.28 38.96 0.000
Residual Error 53 386.69 7.30
Total 59 2092.40
Source DF Seq SS
Sq.ft 1 1173.10
Sqftsq 1 231.97
Low 1 202.81
Med 1 8.68
AL 1 9.22
AM 1 79.92
Unusual Observations
Obs Sq.ft Market Fit SE Fit Residual St Resid
1 521 26.000 23.454 1.617 2.546 1.18 X
2 538 19.400 26.309 1.419 -6.909 -3.01R
3 544 25.200 30.561 1.176 -5.361 -2.20R
10 712 42.400 34.182 0.690 8.218 3.15R
30 923 30.000 32.099 1.737 -2.099 -1.01 X
59 1602 47.400 45.846 1.621 1.554 0.72 X
60 1804 45.400 44.406 2.271 0.994 0.68 X
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
MTB > regress c4 5 c1 c2 c5 c6 c10
18)Regression Analysis: Market versus Sq.ft, Sqftsq, Low, Med, AM
The regression equation is
Market = 14.0 + 0.0430 Sq.ft - 0.000014 Sqftsq - 7.70 Low - 9.55 Med + 0.306 AM
Predictor Coef SE Coef T P
Constant 13.997 4.735 2.96 0.005
Sq.ft 0.042970 0.008041 5.34 0.000
Sqftsq -0.00001441 0.00000364 -3.96 0.000
Low -7.704 1.849 -4.17 0.000
Med -9.551 2.823 -3.38 0.001
AM 0.30594 0.09221 3.32 0.002
S = 2.70550 R-Sq = 81.1% R-Sq(adj) = 79.4%
Analysis of Variance
Source DF SS MS F P
Regression 5 1697.14 339.43 46.37 0.000
Residual Error 54 395.26 7.32
Total 59 2092.40
Source DF Seq SS
Sq.ft 1 1173.10
Sqftsq 1 231.97
Low 1 202.81
Med 1 8.68
AM 1 80.57
Unusual Observations
Obs Sq.ft Market Fit SE Fit Residual St Resid
2 538 19.400 25.240 1.022 -5.840 -2.33R
3 544 25.200 30.655 1.175 -5.455 -2.24R
10 712 42.400 34.222 0.690 8.178 3.13R
59 1602 47.400 45.856 1.623 1.544 0.71 X
60 1804 45.400 44.434 2.274 0.966 0.66 X
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
MTB > Stepwise c4 c1 c2 c3 c5 c6 c9 c10;
SUBC> AEnter 0.15;
SUBC> ARemove 0.15;
SUBC> Best 0;
SUBC> Constant.
17)Stepwise Regression: Market versus Sq.ft, Sqftsq, ...
Alpha-to-Enter: 0.15 Alpha-to-Remove: 0.15
Response is Market on 7 predictors, with N = 60
Step 1 2 3 4
Constant 20.508 26.164 10.370 4.939
Sq.ft 0.0184 0.0137 0.0445 0.0450
T-Value 8.60 7.13 5.10 5.61
P-Value 0.000 0.000 0.000 0.000
Low -6.4 -5.3 -4.1
T-Value -5.55 -4.84 -3.82
P-Value 0.000 0.000 0.000
Sqftsq -0.00001 -0.00001
T-Value -3.60 -4.11
P-Value 0.001 0.000
Assessed 0.229
T-Value 3.34
P-Value 0.002
S 3.98 3.24 2.94 2.71
R-Sq 56.06 71.48 76.84 80.75
R-Sq(adj) 55.31 70.48 75.60 79.35
Mallows C-p 67.8 26.3 13.2 4.2
More? (Yes, No, Subcommand, or Help)
SUBC> y
No variables entered or removed
More? (Yes, No, Subcommand, or Help)
SUBC> n
MTB > corr c1 c2 c3
Correlations: Sq.ft, Sqftsq, Assessed
Sq.ft Sqftsq
Sqftsq 0.981
0.000
Assessed 0.347 0.333
0.007 0.009
Cell Contents: Pearson correlation
P-Value
MTB > print c1 c2 c3 c4 c5 c6 c7 c9 c10
Data Display
Row Sq.ft Sqftsq Assessed Market Low Med High AL AM
1 521 271441 7.8 26.0 1 0 0 7.8 0.0
2 538 289444 28.2 19.4 1 0 0 28.2 0.0
3 544 295936 23.2 25.2 0 1 0 0.0 23.2
4 577 332929 22.2 26.2 1 0 0 22.2 0.0
5 661 436921 23.8 31.0 1 0 0 23.8 0.0
6 662 438244 19.6 34.6 0 1 0 0.0 19.6
7 677 458329 22.8 36.4 0 1 0 0.0 22.8
8 691 477481 22.6 33.0 1 0 0 22.6 0.0
9 694 481636 28.0 37.4 0 1 0 0.0 28.0
10 712 506944 21.2 42.4 0 1 0 0.0 21.2
11 721 519841 21.6 32.8 0 1 0 0.0 21.6
12 722 521284 7.4 25.6 1 0 0 7.4 0.0
13 743 552049 26.2 34.8 0 1 0 0.0 26.2
14 760 577600 26.6 35.8 0 1 0 0.0 26.6
15 767 588289 22.2 33.6 1 0 0 22.2 0.0
16 780 608400 22.6 31.0 1 0 0 22.6 0.0
17 787 619369 22.4 39.2 0 1 0 0.0 22.4
18 802 643204 25.4 36.0 0 1 0 0.0 25.4
19 814 662596 14.8 34.8 0 1 0 0.0 14.8
20 815 664225 14.4 34.4 0 1 0 0.0 14.4
21 825 680625 28.2 38.0 0 1 0 0.0 28.2
22 834 695556 18.0 34.6 1 0 0 18.0 0.0
23 838 702244 25.6 35.6 0 1 0 0.0 25.6
24 858 736164 22.4 35.8 1 0 0 22.4 0.0
25 883 779689 25.8 39.6 0 1 0 0.0 25.8
26 890 792100 20.2 35.0 0 1 0 0.0 20.2
27 899 808201 23.2 37.6 0 1 0 0.0 23.2
28 918 842724 32.2 41.2 0 1 0 0.0 32.2
29 920 846400 20.8 31.2 1 0 0 20.8 0.0
30 923 851929 4.6 30.0 1 0 0 4.6 0.0
31 926 857476 18.2 37.4 0 1 0 0.0 18.2
32 931 866761 24.6 38.0 0 1 0 0.0 24.6
33 965 931225 14.6 37.2 0 1 0 0.0 14.6
34 966 933156 30.2 44.0 0 1 0 0.0 30.2
35 967 935089 26.0 44.2 0 1 0 0.0 26.0
36 1011 1022121 28.0 43.6 0 1 0 0.0 28.0
37 1011 1022121 26.0 38.4 0 1 0 0.0 26.0
38 1024 1048576 27.0 42.2 0 1 0 0.0 27.0
39 1033 1067089 25.2 40.4 0 1 0 0.0 25.2
40 1040 1081600 22.4 40.4 0 1 0 0.0 22.4
41 1047 1096209 30.0 43.6 0 1 0 0.0 30.0
42 1051 1104601 26.4 41.4 0 1 0 0.0 26.4
43 1052 1106704 20.2 39.6 0 1 0 0.0 20.2
44 1056 1115136 25.8 41.8 0 1 0 0.0 25.8
45 1060 1123600 29.2 44.8 0 0 1 0.0 0.0
46 1060 1123600 24.0 38.4 0 1 0 0.0 24.0
47 1070 1144900 22.8 43.6 0 1 0 0.0 22.8
48 1075 1155625 30.4 42.8 0 1 0 0.0 30.4
49 1079 1164241 24.2 40.6 0 1 0 0.0 24.2
50 1100 1210000 30.0 41.6 0 1 0 0.0 30.0
51 1106 1223236 31.6 42.8 0 1 0 0.0 31.6
52 1138 1295044 25.6 39.0 0 1 0 0.0 25.6
53 1164 1354896 29.4 41.8 0 0 1 0.0 0.0
54 1171 1371241 32.2 48.4 0 1 0 0.0 32.2
55 1237 1530169 17.0 39.8 0 1 0 0.0 17.0
56 1249 1560001 22.0 47.2 0 1 0 0.0 22.0
57 1298 1684804 23.6 45.2 0 0 1 0.0 0.0
58 1435 2059225 21.4 38.8 0 1 0 0.0 21.4
59 1602 2566404 31.0 47.4 0 0 1 0.0 0.0
60 1804 3254416 30.6 45.4 0 1 0 0.0 30.6
MTB > describe c1 c2 c3 c4
Descriptive Statistics: Sq.ft, Sqftsq, Assessed, Market
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
Sq.ft 60 0 941.7 31.4 242.8 521.0 770.3 924.5 1060.0
Sqftsq 60 0 944851 67432 522330 271441 593317 854703 1123600
Assessed 60 0 23.560 0.752 5.824 4.600 21.450 23.900 27.750
Market 60 0 37.800 0.769 5.955 19.400 34.650 38.400 42.100
Variable Maximum
Sq.ft 1804.0
Sqftsq 3254416
Assessed 32.200
Market 48.400
1