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\252x06041021.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
Constant
-782.8
265.1
livsqft
704.6
213.8
lotsqft
-2.900
3.283
loc1
569.4
190.3
loc 2
423.3
139.0
baths
18.121
4.392
lot1
5.775
4.709
lot2
-1.071
5.196
liv1
-349.3
117.8
liv2
-196.54
79.91
livsqsq
-125.48
39.56
S = 6.49288
R-Sq = 97.5%
T
P
VIF
-2.95 0.008
3.30 0.004 8142.7
-0.88 0.388
76.1
2.99 0.007 5725.1
3.05 0.007 3054.2
4.13 0.001
2.3
1.23 0.235
520.6
-0.21 0.839
997.7
-2.96 0.008 4382.0
-2.46 0.024 3414.8
-3.17 0.005 4606.9
R-Sq(adj) = 96.2%
Analysis of Variance
Source
DF
SS
Regression
10 31197.6
Residual Error 19
801.0
Total
29 31998.6
MS
3119.8
42.2
F
74.00
P
0.000
1
252y0641s1
Source
livsqft
lotsqft
loc1
loc 2
baths
lot1
lot2
liv1
liv2
livsqsq
DF
1
1
1
1
1
1
1
1
1
1
12/6/06
Seq SS
29642.7
126.4
2.9
492.5
472.4
4.2
27.5
0.0
4.7
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
Regression
9 30739.9
Residual Error 20
1258.7
Total
29 31998.6
Source
lotsqft
loc1
loc 2
baths
lot1
lot2
liv1
liv2
livsqsq
DF
1
1
1
1
1
1
1
1
1
MS
3415.5
62.9
F
54.27
P
0.000
Seq SS
26347.5
61.3
3609.1
509.1
8.0
47.0
59.8
55.1
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.
2
252y0641s1
12/6/06
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
Regression
7 30711.8
Residual Error 22
1286.8
Total
29 31998.6
Source
lotsqft
loc1
loc 2
baths
liv1
liv2
livsqsq
DF
1
1
1
1
1
1
1
MS
4387.4
58.5
F
75.01
P
0.000
Seq SS
26347.5
61.3
3609.1
509.1
2.4
1.3
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
Regression
5 30536.6
Residual Error 24
1462.0
Total
29 31998.6
Source
lotsqft
baths
liv1
liv2
livsqsq
DF
1
1
1
1
1
MS
6107.3
60.9
F
100.26
P
0.000
Seq SS
26347.5
168.4
123.9
3761.5
135.3
3
252y0641s1
12/6/06
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
Constant
86.77
11.08
baths
11.090
4.267
liv1
-16.988
5.214
liv2
-10.148
3.149
livsqsq
9.915
1.622
S = 8.03608
R-Sq = 95.0%
T
P VIF
7.83 0.000
2.60 0.015 1.4
-3.26 0.003 5.6
-3.22 0.004 3.5
6.11 0.000 5.1
R-Sq(adj) = 94.1%
Analysis of Variance
Source
DF
SS
Regression
4 30384.2
Residual Error 25
1614.5
Total
29 31998.6
MS
7596.0
64.6
Source
baths
liv1
liv2
livsqsq
DF
1
1
1
1
F
117.62
P
0.000
Seq SS
8914.5
8231.0
10825.9
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
Vars
1
1
2
2
3
3
4
R-Sq
91.9
45.3
92.6
92.2
93.6
92.9
95.0
R-Sq(adj)
91.6
43.3
92.1
91.6
92.9
92.0
94.1
Mallows
C-p
14.3
245.3
12.5
14.7
9.8
13.4
5.0
S
9.6448
25.013
9.3441
9.6171
8.8812
9.3746
8.0361
b
a
t
h
s
l
i
v
1
l
i
v
2
l
i
v
s
q
s
q
X
X
X
X
X
X
X X X
X X
X
X X X X
4
252y0641s1
12/6/06
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
Constant
-782.8
265.1
livsqft
704.6
213.8
lotsqft
-2.900
3.283
loc1
569.4
190.3
loc 2
423.3
139.0
baths
18.121
4.392
lot1
5.775
4.709
lot2
-1.071
5.196
liv1
-349.3
117.8
liv2
-196.54
79.91
livsqsq
-125.48
39.56
S = 6.49288
R-Sq = 97.5%
T
P
-2.95 0.008
3.30 0.004
-0.88 0.388
2.99 0.007
3.05 0.007
4.13 0.001
1.23 0.235
-0.21 0.839
-2.96 0.008
-2.46 0.024
-3.17 0.005
R-Sq(adj) = 96.2%
Analysis of Variance
Source
DF
SS
Regression
10 31197.6
Residual Error 19
801.0
Total
29 31998.6
MS
3119.8
42.2
Source
livsqft
lotsqft
loc1
loc 2
baths
lot1
lot2
liv1
liv2
livsqsq
DF
1
1
1
1
1
1
1
1
1
1
F
74.00
P
0.000
Seq SS
29642.7
126.4
2.9
492.5
472.4
4.2
27.5
0.0
4.7
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
Constant
-636.8
241.4
livsqft
573.8
187.6
lotsqft
-0.241
1.789
loc1
462.9
173.0
loc 2
350.9
128.0
baths
14.910
3.674
liv1
-247.23
87.63
liv2
-173.97
59.10
livsqsq
-103.43
35.91
S = 6.51098
R-Sq = 97.2%
T
P
-2.64 0.015
3.06 0.006
-0.13 0.894
2.68 0.014
2.74 0.012
4.06 0.001
-2.82 0.010
-2.94 0.008
-2.88 0.009
R-Sq(adj) = 96.2%
5
252y0641s1
12/6/06
Analysis of Variance
Source
DF
SS
Regression
8 31108.4
Residual Error 21
890.3
Total
29 31998.6
Source
livsqft
lotsqft
loc1
loc 2
baths
liv1
liv2
livsqsq
DF
1
1
1
1
1
1
1
1
MS
3888.5
42.4
F
91.73
P
0.000
Seq SS
29642.7
126.4
2.9
492.5
472.4
2.5
17.3
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
Constant
-633.6
234.9
livsqft
569.6
180.8
loc1
461.3
168.7
loc 2
349.5
124.7
baths
14.822
3.534
liv1
-246.77
85.58
liv2
-173.49
57.66
livsqsq
-102.93
34.92
S = 6.36403
R-Sq = 97.2%
T
P
-2.70 0.013
3.15 0.005
2.74 0.012
2.80 0.010
4.19 0.000
-2.88 0.009
-3.01 0.006
-2.95 0.007
R-Sq(adj) = 96.3%
Analysis of Variance
Source
DF
SS
Regression
7 31107.6
Residual Error 22
891.0
Total
29 31998.6
MS
4443.9
40.5
Source
livsqft
loc1
loc 2
baths
liv1
liv2
livsqsq
DF
1
1
1
1
1
1
1
F
109.72
P
0.000
Seq SS
29642.7
10.8
597.7
484.7
3.3
16.4
352.0
6
252y0641s1
12/6/06
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
Constant
-633.6
234.9
livsqft
569.6
180.8
loc1
461.3
168.7
loc 2
349.5
124.7
baths
14.822
3.534
liv1
-246.77
85.58
liv2
-173.49
57.66
livsqsq
-102.93
34.92
S = 6.36403
R-Sq = 97.2%
T
P
VIF
-2.70 0.013
3.15 0.005 6060.8
2.74 0.012 4682.2
2.80 0.010 2559.1
4.19 0.000
1.5
-2.88 0.009 2406.6
-3.01 0.006 1851.0
-2.95 0.007 3736.4
R-Sq(adj) = 96.3%
Analysis of Variance
Source
DF
SS
Regression
7 31107.6
Residual Error 22
891.0
Total
29 31998.6
MS
4443.9
40.5
Source
livsqft
loc1
loc 2
baths
liv1
liv2
livsqsq
DF
1
1
1
1
1
1
1
F
109.72
P
0.000
Seq SS
29642.7
10.8
597.7
484.7
3.3
16.4
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
Constant
1
13.59
2
16.80
3
59.44
4
53.49
livsqft
T-Value
P-Value
62.8
18.77
0.000
62.2
19.15
0.000
45.9
6.17
0.000
38.0
5.53
0.000
-0.40
-1.76
0.090
-1.22
-3.03
0.005
-1.51
-4.21
0.000
-21.6
-2.39
0.024
-25.8
-3.27
0.003
lot2
T-Value
P-Value
loc1
T-Value
P-Value
baths
T-Value
P-Value
11.8
3.18
0.004
7
252y0641s1
12/6/06
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
lot2
loc1
livsqft
-0.109
0.565
lot2
-0.735
0.000
-0.497
0.005
loc1
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\252x06041021.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
price
livsqft
lotsqft
loc1
loc 2
baths
lot1
lot2
liv1
liv2
livsqsq
N
30
30
30
30
30
30
30
30
30
30
30
N*
0
0
0
0
0
0
0
0
0
0
0
Variable
price
livsqft
lotsqft
loc1
loc 2
baths
lot1
lot2
liv1
liv2
livsqsq
Maximum
199.40
3.0000
22.000
1.0000
1.0000
3.0000
15.00
17.00
1.600
2.000
9.000
Mean
134.23
1.9200
15.267
0.3333
0.3333
2.0333
4.00
5.07
0.467
0.610
3.937
SE Mean
6.06
0.0929
0.585
0.0875
0.0875
0.0756
1.07
1.34
0.124
0.161
0.378
StDev
33.22
0.5088
3.205
0.4795
0.4795
0.4138
5.84
7.33
0.677
0.882
2.069
Minimum
87.90
1.2000
10.000
0.0000
0.0000
1.0000
0.00
0.00
0.000
0.000
1.440
Q1
109.45
1.5000
12.000
0.0000
0.0000
2.0000
0.00
0.00
0.000
0.000
2.250
Median
124.20
1.8500
15.000
0.0000
0.0000
2.0000
0.00
0.00
0.000
0.000
3.425
Q3
164.25
2.4000
18.000
1.0000
1.0000
2.0000
10.50
15.00
1.225
1.725
5.760
8
252y0641s1
12/6/06
MTB > print c1 - c11
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
price
102.20
103.95
87.90
110.00
97.00
95.70
113.60
109.60
110.80
90.60
109.00
133.00
134.00
120.30
137.00
122.40
121.70
126.00
128.00
117.50
158.70
186.80
172.40
151.20
179.10
182.30
195.85
168.00
199.40
163.00
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
livsqsq
2.25
1.44
1.44
2.56
1.96
1.44
2.56
2.25
2.25
1.69
2.56
3.61
3.24
4.00
4.00
2.89
3.24
3.61
4.00
2.56
5.76
6.76
5.29
4.84
7.84
7.29
9.00
5.76
6.25
5.76
livsqft
1.5
1.2
1.2
1.6
1.4
1.2
1.6
1.5
1.5
1.3
1.6
1.9
1.8
2.0
2.0
1.7
1.8
1.9
2.0
1.6
2.4
2.6
2.3
2.2
2.8
2.7
3.0
2.4
2.5
2.4
lotsqft
12
10
10
15
12
10
15
12
12
12
13
15
15
17
17
15
15
16
16
13
18
18
16
16
20
20
22
18
20
18
loc1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
loc 2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
baths
2
2
2
2
1
2
2
2
2
1
2
2
2
2
3
2
2
2
2
2
2
2
2
2
2
2
3
2
3
2
lot1
12
10
10
15
12
10
15
12
12
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
lot2
0
0
0
0
0
0
0
0
0
0
13
15
15
17
17
15
15
16
16
13
0
0
0
0
0
0
0
0
0
0
liv1
1.5
1.2
1.2
1.6
1.4
1.2
1.6
1.5
1.5
1.3
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
liv2
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
1.6
1.9
1.8
2.0
2.0
1.7
1.8
1.9
2.0
1.6
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
9
252y0641s1
12/6/06
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\252x06041022.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
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
Regression
7 1706.22
Residual Error 52
386.18
Total
59 2092.40
Source
Sq.ft
Sqftsq
Assessed
Low
Med
AL
AM
DF
1
1
1
1
1
1
1
MS
243.75
7.43
F
32.82
VIF
31.3
29.6
64.9
257.6
314.7
133.8
265.9
P
0.000
Seq SS
1173.10
231.97
177.38
107.14
3.57
12.13
0.93
10
252y0641s1
12/6/06
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
Constant
3.691
4.390
0.84 0.404
Sq.ft
0.044273
0.007962
5.56 0.000
Sqftsq
-0.00001498 0.00000360 -4.16 0.000
Assessed
0.33686
0.07850
4.29 0.000
AL
-0.22961
0.07316 -3.14 0.003
AM
-0.02893
0.05321 -0.54 0.589
S = 2.67918
R-Sq = 81.5%
R-Sq(adj) = 79.8%
Analysis of Variance
Source
DF
SS
Regression
5 1704.79
Residual Error 54
387.61
Total
59 2092.40
Source
Sq.ft
Sqftsq
Assessed
AL
AM
DF
1
1
1
1
1
MS
340.96
7.18
F
47.50
VIF
30.7
29.1
1.7
2.9
3.1
P
0.000
Seq SS
1173.10
231.97
177.38
120.21
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.
11
252y0641s1
12/6/06
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
Vars
1
1
2
2
3
3
4
4
5
R-Sq
56.1
44.9
67.9
67.2
75.6
75.5
81.4
78.1
81.5
R-Sq(adj)
55.3
44.0
66.7
66.0
74.3
74.2
80.0
76.5
79.8
Mallows
C-p
72.1
104.6
39.7
41.8
19.0
19.4
4.3
13.9
6.0
S
3.9812
4.4582
3.4347
3.4725
3.0176
3.0242
2.6620
2.8867
2.6792
S
q
.
f
t
X
S
q
f
t
s
q
A
s
s
e
s
s
e A A
d L M
X
X
X
X
X
X
X
X
X
X
X X
X X
X X X
X X
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
Regression
7 1706.22
Residual Error 52
386.18
Total
59 2092.40
Source
Sq.ft
Sqftsq
Assessed
Low
Med
AL
AM
DF
1
1
1
1
1
1
1
MS
243.75
7.43
F
32.82
P
0.000
Seq SS
1173.10
231.97
177.38
107.14
3.57
12.13
0.93
Unusual Observations
Obs Sq.ft Market
Fit
2
538 19.400 26.297
3
544 25.200 30.544
10
712 42.400 34.179
30
923 30.000 32.106
57
1298 45.200 44.904
SE Fit
1.433
1.188
0.696
1.752
2.670
Residual
-6.897
-5.344
8.221
-2.106
0.296
St Resid
-2.98R
-2.18R
3.12R
-1.01 X
0.54 X
12
252y0641s1
12/6/06
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
Regression
7 1706.22
Residual Error 52
386.18
Total
59 2092.40
Source
Sq.ft
Sqftsq
Low
Med
AL
AM
AH
DF
1
1
1
1
1
1
1
MS
243.75
7.43
F
32.82
P
0.000
Seq SS
1173.10
231.97
202.81
8.68
9.22
79.92
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%
13
252y0641s1
12/6/06
Analysis of Variance
Source
DF
SS
Regression
6 1705.71
Residual Error 53
386.69
Total
59 2092.40
Source
Sq.ft
Sqftsq
Low
Med
AL
AM
DF
1
1
1
1
1
1
MS
284.28
7.30
F
38.96
P
0.000
Seq SS
1173.10
231.97
202.81
8.68
9.22
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
Sq.ft
Sqftsq
Low
Med
AM
DF
1
1
1
1
1
Seq SS
1173.10
231.97
202.81
8.68
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.
14
252y0641s1
12/6/06
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
Constant
1
20.508
2
26.164
3
10.370
4
4.939
Sq.ft
T-Value
P-Value
0.0184
8.60
0.000
0.0137
7.13
0.000
0.0445
5.10
0.000
0.0450
5.61
0.000
-6.4
-5.55
0.000
-5.3
-4.84
0.000
-4.1
-3.82
0.000
-0.00001
-3.60
0.001
-0.00001
-4.11
0.000
Low
T-Value
P-Value
Sqftsq
T-Value
P-Value
Assessed
T-Value
P-Value
0.229
3.34
0.002
S
R-Sq
R-Sq(adj)
Mallows C-p
3.98
56.06
55.31
67.8
3.24
71.48
70.48
26.3
2.94
76.84
75.60
13.2
2.71
80.75
79.35
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
0.981
0.000
Assessed
0.347
0.333
0.007
0.009
Cell Contents: Pearson correlation
P-Value
Sqftsq
MTB > print c1 c2 c3 c4 c5 c6 c7 c9 c10
Data Display
Row
1
2
3
4
5
6
7
8
9
10
11
12
Sq.ft
521
538
544
577
661
662
677
691
694
712
721
722
Sqftsq
271441
289444
295936
332929
436921
438244
458329
477481
481636
506944
519841
521284
Assessed
7.8
28.2
23.2
22.2
23.8
19.6
22.8
22.6
28.0
21.2
21.6
7.4
Market
26.0
19.4
25.2
26.2
31.0
34.6
36.4
33.0
37.4
42.4
32.8
25.6
Low
1
1
0
1
1
0
0
1
0
0
0
1
Med
0
0
1
0
0
1
1
0
1
1
1
0
High
0
0
0
0
0
0
0
0
0
0
0
0
AL
7.8
28.2
0.0
22.2
23.8
0.0
0.0
22.6
0.0
0.0
0.0
7.4
AM
0.0
0.0
23.2
0.0
0.0
19.6
22.8
0.0
28.0
21.2
21.6
0.0
15
252y0641s1
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
743
760
767
780
787
802
814
815
825
834
838
858
883
890
899
918
920
923
926
931
965
966
967
1011
1011
1024
1033
1040
1047
1051
1052
1056
1060
1060
1070
1075
1079
1100
1106
1138
1164
1171
1237
1249
1298
1435
1602
1804
12/6/06
552049
577600
588289
608400
619369
643204
662596
664225
680625
695556
702244
736164
779689
792100
808201
842724
846400
851929
857476
866761
931225
933156
935089
1022121
1022121
1048576
1067089
1081600
1096209
1104601
1106704
1115136
1123600
1123600
1144900
1155625
1164241
1210000
1223236
1295044
1354896
1371241
1530169
1560001
1684804
2059225
2566404
3254416
26.2
26.6
22.2
22.6
22.4
25.4
14.8
14.4
28.2
18.0
25.6
22.4
25.8
20.2
23.2
32.2
20.8
4.6
18.2
24.6
14.6
30.2
26.0
28.0
26.0
27.0
25.2
22.4
30.0
26.4
20.2
25.8
29.2
24.0
22.8
30.4
24.2
30.0
31.6
25.6
29.4
32.2
17.0
22.0
23.6
21.4
31.0
30.6
34.8
35.8
33.6
31.0
39.2
36.0
34.8
34.4
38.0
34.6
35.6
35.8
39.6
35.0
37.6
41.2
31.2
30.0
37.4
38.0
37.2
44.0
44.2
43.6
38.4
42.2
40.4
40.4
43.6
41.4
39.6
41.8
44.8
38.4
43.6
42.8
40.6
41.6
42.8
39.0
41.8
48.4
39.8
47.2
45.2
38.8
47.4
45.4
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0.0
0.0
22.2
22.6
0.0
0.0
0.0
0.0
0.0
18.0
0.0
22.4
0.0
0.0
0.0
0.0
20.8
4.6
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
26.2
26.6
0.0
0.0
22.4
25.4
14.8
14.4
28.2
0.0
25.6
0.0
25.8
20.2
23.2
32.2
0.0
0.0
18.2
24.6
14.6
30.2
26.0
28.0
26.0
27.0
25.2
22.4
30.0
26.4
20.2
25.8
0.0
24.0
22.8
30.4
24.2
30.0
31.6
25.6
0.0
32.2
17.0
22.0
0.0
21.4
0.0
30.6
MTB > describe c1 c2 c3 c4
Descriptive Statistics: Sq.ft, Sqftsq, Assessed, Market
Variable
Sq.ft
Sqftsq
Assessed
Market
N
60
60
60
60
N*
0
0
0
0
Variable
Sq.ft
Sqftsq
Assessed
Market
Maximum
1804.0
3254416
32.200
48.400
Mean
941.7
944851
23.560
37.800
SE Mean
31.4
67432
0.752
0.769
StDev
242.8
522330
5.824
5.955
Minimum
521.0
271441
4.600
19.400
Q1
770.3
593317
21.450
34.650
Median
924.5
854703
23.900
38.400
Q3
1060.0
1123600
27.750
42.100
16