23:12 Saturday, July 17, 2010
Temperature differences and its relationship to Gas Consumption
Obs type
TDiff
KWh IDMN id_TDIFFN IDMS id_TDIFFS
1 New
20.1
65.3
1
20.1
0
0.0
2 New
21.1
66.5
1
21.1
0
0.0
3 New
21.9
67.8
1
21.9
0
0.0
4 New
22.6
73.2
1
22.6
0
0.0
5 New
23.4
75.3
1
23.4
0
0.0
6 New
24.2
81.1
1
24.2
0
0.0
7 New
24.9
82.2
1
24.9
0
0.0
8 New
25.1
85.7
1
25.1
0
0.0
9 New
26.0
90.9
1
26.0
0
0.0
10 New
27.2
87.4
1
27.2
0
0.0
11 New
28.8
94.9
1
28.8
0
0.0
12 New
29.2
93.9
1
29.2
0
0.0
13 New
30.6
87.1
1
30.6
0
0.0
14 New
30.8
84.2
1
30.8
0
0.0
15 New
32.6 106.6
1
32.6
0
0.0
16 New
32.4 111.3
1
32.4
0
0.0
17 New
34.8 100.9
1
34.8
0
0.0
18 New
35.9 101.9
1
35.9
0
0.0
19 New
36.0 110.1
1
36.0
0
0.0
20 New
36.5 119.1
1
36.5
0
0.0
21 Standard 20.3
70.3
0
0.0
1
20.3
22 Standard 20.7
70.7
0
0.0
1
20.7
23 Standard 20.9
72.9
0
0.0
1
20.9
24 Standard 22.8
77.6
0
0.0
1
22.8
25 Standard 23.1
79.3
0
0.0
1
23.1
26 Standard 24.8
86.5
0
0.0
1
24.8
27 Standard 25.9
90.6
0
0.0
1
25.9
28 Standard 26.1
91.9
0
0.0
1
26.1
29 Standard 27.0
94.5
0
0.0
1
27.0
30 Standard 27.2
92.7
0
0.0
1
27.2
31 Standard 29.8 104.8
0
0.0
1
29.8
32 Standard 30.2 103.2
0
0.0
1
30.2
33 Standard 30.6
91.2
0
0.0
1
30.6
34 Standard 31.8
89.6
0
0.0
1
31.8
35 Standard 33.2 116.2
0
0.0
1
33.2
36 Standard 33.4 116.9
0
0.0
1
33.4
37 Standard 34.2 105.1
0
0.0
1
34.2
38 Standard 35.1 106.1
0
0.0
1
35.1
1
23:12 Saturday, July 17, 2010
Temperature differences and its relationship to Gas Consumption
Obs type
TDiff
KWh IDMN id_TDIFFN IDMS id_TDIFFS
39 Standard 36.2 117.8
0
0.0
1
36.2
40 Standard 36.5 120.3
0
0.0
1
36.5
2
23:12 Saturday, July 17, 2010
Temperature differences and its relationship to Gas Consumption
1. Correlation coefficients
The CORR Procedure
type=New
2 Variables: TDiff
KWh
Simple Statistics
Variable
N
Mean
Std Dev
Sum Minimum
Maximum
5.31091 564.10000 20.10000
36.50000
TDiff
20 28.20500
KWh
20 89.27000 15.61160
1785 65.30000 119.10000
Pearson Correlation Coefficients, N = 20
Prob > |r| under H0: Rho=0
TDiff
KWh
TDiff
1.00000
0.92423
<.0001
KWh
0.92423
<.0001
1.00000
3
23:12 Saturday, July 17, 2010
Temperature differences and its relationship to Gas Consumption
1. Correlation coefficients
The CORR Procedure
type=Standard
2 Variables: TDiff
KWh
Simple Statistics
Variable
N
Mean
Std Dev
Sum Minimum
Maximum
5.34572 569.80000 20.30000
36.50000
TDiff
20 28.49000
KWh
20 94.91000 16.00315
1898 70.30000 120.30000
Pearson Correlation Coefficients, N = 20
Prob > |r| under H0: Rho=0
TDiff
KWh
TDiff
1.00000
0.93187
<.0001
KWh
0.93187
<.0001
1.00000
4
23:12 Saturday, July 17, 2010
5
Temperature differences and its relationship to Gas Consumption
140
140
120
120
100
100
80
80
60
60
20
21
22
23
24
25
26
27
28
29
30
31
TDiff
type
New
Standard
32
33
34
35
36
37
KWh
KWh
2. Plot KWh vs TDiff by type and overall
23:12 Saturday, July 17, 2010
Temperature differences and its relationship to Gas Consumption
3. KWh = TDiff by type
The REG Procedure
Model: MODEL1
Dependent Variable: KWh
type=New
Number of Observations Read
20
Number of Observations Used
20
Analysis of Variance
Source
DF
Model
Sum of
Squares
Mean
Square F Value
1 3955.57134 3955.57134
Error
18
Corrected Total
19 4630.72200
Root MSE
675.15066
105.46 <.0001
37.50837
6.12441 R-Square 0.8542
Dependent Mean 89.27000 Adj R-Sq
Coeff Var
Pr > F
0.8461
6.86054
Parameter Estimates
Variable DF
Parameter Standard
Estimate
Error t Value Pr > |t|
Intercept
1
12.64244
7.58644
1.67 0.1129
TDiff
1
2.71681
0.26456
10.27 <.0001
6
23:12 Saturday, July 17, 2010
Temperature differences and its relationship to Gas Consumption
3. KWh = TDiff by type
The REG Procedure
Model: MODEL1
Dependent Variable: KWh
type=Standard
Number of Observations Read
20
Number of Observations Used
20
Analysis of Variance
Source
DF
Model
Sum of
Squares
Mean
Square F Value
1 4225.43045 4225.43045
Error
18
Corrected Total
19 4865.91800
Root MSE
640.48755
118.75 <.0001
35.58264
5.96512 R-Square 0.8684
Dependent Mean 94.91000 Adj R-Sq
Coeff Var
Pr > F
0.8611
6.28503
Parameter Estimates
Variable DF
Parameter Standard
Estimate
Error t Value Pr > |t|
Intercept
1
15.43239
7.41434
2.08 0.0519
TDiff
1
2.78967
0.25600
10.90 <.0001
7
23:12 Saturday, July 17, 2010
Temperature differences and its relationship to Gas Consumption
4.separate intercepts and separate slopes
The REG Procedure
Model: MODEL1
Dependent Variable: KWh
Number of Observations Read
40
Number of Observations Used
40
Note: No intercept in model. R-Square is redefined.
Analysis of Variance
Source
DF
Sum of
Squares
4
347722
Model
Mean
Square F Value
86930 2378.69 <.0001
Error
36 1315.63821 36.54551
Uncorrected Total
40
Root MSE
Pr > F
349037
6.04529 R-Square 0.9962
Dependent Mean 92.09000 Adj R-Sq
Coeff Var
0.9958
6.56454
Parameter Estimates
Variable
DF
Parameter Standard
Estimate
Error t Value Pr > |t|
IDMN
1
12.64244
7.48843
1.69 0.1000
IDMS
1
15.43239
7.51399
2.05 0.0473
id_TDIFFN
1
2.71681
0.26114
10.40 <.0001
id_TDIFFS
1
2.78967
0.25944
10.75 <.0001
8
23:12 Saturday, July 17, 2010
Temperature differences and its relationship to Gas Consumption
5. KWh = TDiff Common intercept and common slope
The REG Procedure
Model: MODEL1
Dependent Variable: KWh
Number of Observations Read
40
Number of Observations Used
40
Analysis of Variance
Source
DF
Model
Sum of
Squares
Mean
Square F Value
1 8262.10795 8262.10795
Error
38 1552.62805
Corrected Total
39 9814.73600
Root MSE
202.21 <.0001
40.85863
6.39208 R-Square 0.8418
Dependent Mean 92.09000 Adj R-Sq
Coeff Var
Pr > F
0.8376
6.94112
Parameter Estimates
Variable DF
Parameter Standard
Estimate
Error t Value Pr > |t|
Intercept
1
13.67255
5.60639
2.44 0.0195
TDiff
1
2.76629
0.19453
14.22 <.0001
9
23:12 Saturday, July 17, 2010
Temperature differences and its relationship to Gas Consumption
6.Separate intercepts and common slope
The REG Procedure
Model: MODEL1
Dependent Variable: KWh
Number of Observations Read
40
Number of Observations Used
40
Note: No intercept in model. R-Square is redefined.
Analysis of Variance
Source
Model
DF
Sum of
Squares
3
347720
Mean
Square F Value
115907 3256.13 <.0001
Error
37 1317.06994 35.59648
Uncorrected Total
40
Root MSE
349037
5.96628 R-Square 0.9962
Dependent Mean 92.09000 Adj R-Sq
Coeff Var
Pr > F
0.9959
6.47875
Parameter Estimates
Variable DF
Parameter Standard
Estimate
Error t Value Pr > |t|
IDMN
1
11.60823
5.29410
2.19 0.0347
IDMS
1
16.46349
5.34422
3.08 0.0039
TDiff
1
2.75348
0.18164
15.16 <.0001
10
23:12 Saturday, July 17, 2010
Temperature differences and its relationship to Gas Consumption
6.Separate intercepts and common slope
The CAPABILITY Procedure
Variable: resid (Residual)
Moments
N
40 Sum Weights
Mean
40
0 Sum Observations
Std Deviation
Skewness
5.8112842 Variance
0
33.7710241
-0.5444182 Kurtosis
-0.0307948
Uncorrected SS 1317.06994 Corrected SS
1317.06994
Coeff Variation
0.91884471
. Std Error Mean
Basic Statistical Measures
Location
Mean
Variability
0.000000 Std Deviation
5.81128
Median 1.119613 Variance
33.77102
Mode
24.90317
. Range
Interquartile Range
6.62061
Tests for Location: Mu0=0
Test
Statistic
p Value
Student's t
t
0 Pr > |t|
Sign
M
1 Pr >= |M| 0.8746
Signed Rank S
32 Pr >= |S|
Quantiles (Definition 5)
Quantile
Estimate
100% Max
10.47917117
99%
10.47917117
95%
8.39578387
90%
7.34566775
75% Q3
3.63711772
50% Median
1.11961289
25% Q1
-2.98349279
10%
-8.66128283
5%
-10.86755061
1%
-14.42400320
0% Min
-14.42400320
1.0000
0.6727
11
23:12 Saturday, July 17, 2010
Temperature differences and its relationship to Gas Consumption
6.Separate intercepts and common slope
The CAPABILITY Procedure
Variable: resid (Residual)
Extreme Observations
Lowest
Highest
Value Obs
Value Obs
-14.42400320
34
6.98992249
20
-12.21526837
14
7.70141301
9
-9.51983286
33
8.32113139
35
-8.76457331
13
8.47043634
36
-8.55799234
18 10.47917117
16
12
23:12 Saturday, July 17, 2010
13
Temperature differences and its relationship to Gas Consumption
6.Separate intercepts and common slope
35
30
25
Percent
20
15
10
5
0
-14
-10
-6
-2
2
Residual
Curve:
Normal(Mu=0 Sigma=5.8113)
6
10
23:12 Saturday, July 17, 2010
Temperature differences and its relationship to Gas Consumption
6.Separate intercepts and common slope
The CAPABILITY Procedure
Fitted Normal Distribution for resid
Parameters for Normal
Distribution
Parameter Symbol
Mean
Mu
Std Dev
Sigma
Estimate
0
5.811284
Goodness-of-Fit Tests for Normal Distribution
Test
Statistic
DF
p Value
Kolmogorov-Smirnov D
0.09131429
Pr > D
>0.150
Cramer-von Mises
W-Sq
0.06743564
Pr > W-Sq
>0.250
Anderson-Darling
A-Sq
0.39731597
Pr > A-Sq
>0.250
Chi-Square
Chi-Sq 4.88980145
4 Pr > Chi-Sq
Quantiles for Normal
Distribution
Quantile
Percent Observed
Estimated
1.0 -14.42400 -13.519069
5.0 -10.86755
-9.558712
10.0
-8.66128
-7.447460
25.0
-2.98349
-3.919652
50.0
1.11961
-0.000000
75.0
3.63712
3.919652
90.0
7.34567
7.447460
95.0
8.39578
9.558712
99.0
10.47917
13.519069
0.299
14