Regression Forecasting
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Input No. of Variables No. of Observations Dependent 94.20 46.26 33.67 69.79 58.00 22.91 79.94 24.33 5.72 53.25 44.33 46.00 24.49 38.83 19.80 21.17 22.00 23.00 39.83 64.21
Indep1 103.63 52.06 43.12 70.95 67.98 28.23 89.26 31.88 9.15 56.30 51.74 51.41 33.98 43.20 25.22 28.18 28.72 27.74 40.47 67.30
Indep2 60.14 10.93 18.97 47.55 30.07 17.13 59.46 -0.88 -27.06 44.46 21.47 19.79 -2.75 2.04 -16.86 12.33 -17.54 -11.43 36.39 49.12
Indep3 45.08 7.14 40.19 40.57 42.06 85.04 97.38 54.63 20.33 77.93 12.79 14.35 95.47 58.81 4.07 7.43 19.94 20.19 70.21 49.64
Page 1
Input
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Input
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Input 4 20
Page 4
Input
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Input
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Input 0
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Input
Page 8
Input
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Input
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Input
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Input
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Input
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Input
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Input
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Input
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Input
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Input
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Input
20
10
0.91
Actual Predicted Residual e^2 (e-et-1)^2 94.2 94.86 0.65 46.26 45.41 -0.85 0.72 2.26 33.67 38.05 4.37 19.14 27.3 69.79 65.42 -4.37 19.13 76.54 58 60.66 2.66 7.1 49.55 22.91 24.09 1.18 1.4 2.2 79.94 81.34 1.41 1.98 0.05 24.33 25.63 1.3 1.69 0.01 5.72 3.66 -2.06 4.24 11.29 53.25 51.69 -1.57 2.46 0.24 44.33 46.33 2 3.99 12.71 46 45.8 -0.2 0.04 4.83 24.49 26.31 1.82 3.32 4.09 38.83 35.6 -3.23 10.45 25.56 19.8 19.04 -0.76 0.58 6.12 21.17 25.14 3.97 15.79 22.39 22 21.61 -0.39 0.16 19.07 23 21.52 -1.48 2.18 1.18 39.83 37.29 -2.54 6.44 1.12 64.21 62.29 -1.92 3.7 0.38
Page 19
2.55 d 1 dl 1.68 du
0 Positive Autocorrelation dete 1 Positive Autocorrelation may 1.68 No Autocorrelation detected 2.32 Negative Autocorrelation ma 3 Negative Autocorrelation de 4 Negative Autocorrelation de
4 Negative Autocorrelation ma
Input
104.51
266.9
Page 20
Input
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Input
Positive Autocorrelation detected Positive Autocorrelation maybe present No Autocorrelation detected Negative Autocorrelation maybe present Negative Autocorrelation detected Negative Autocorrelation detected
Negative Autocorrelation maybe present
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Input
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Input
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Output
Equation Parameters
Intercept Indep1 Indep2 Indep3
Independent Analysis
Coefficients
Standard Error
-0.357 0.856 0.125 -0.022
2.290 0.055 0.053 0.022
=
R Squared
98.57% 81.60% 7.59%
Gradient
Dl=1.20 Du=1.41
Intercept
0.97 0.79 0.21
Auto Correlation
-4.60 27.66 32.57
Tests for Multicolinearity between Independent Variables
DW-Stat
Adjusted RSquared against other Indep
2.43 1.90 1.71
76.97% 79.68% 14.43%
0.86*Indep1 + 0.12*Indep2 + -0.02*Indep3 + -0.36 (+/- 2.56)
Independent R-Square Matrix 100%
78%
8%
Indep1
78%
100%
19%
Indep2
8%
19%
100%
Indep3
Actual versus Predicted Trend R-Squared Matrix
100
f(x) = 0.99x + 0.44 R² = 0.99
90 80
Predicted
Step 2 - Forecasting
Independent Variable Indep1 Indep2 Indep3
70 60
Linear
Multiple Regression Equation
Exponential
498.8907
2nd Ord Polynomial
2.5609
F - Statistic
3rd Ord Polynomial
Standard Error
98.94% of the change in can be explained by the change in the 3 Independent Variables Adjusted for Sample Size bias 2.55384 Durbin-Watson Statistic Critical D-W Values: Lower (Dl)=1.00; Upper (Du)=1.68 to +/- on result of Regression Equation Therefore Negative Autocorrelation maybe present at 95% Confidence Therefore analysis IS Significant 3.12735 Critical F-Statistic at 95% Confidence (Significance holds to 100.0% Level of Confidence)
Indep3
0.9874
Indep2
0.9894
Adjusted R Square
Indep1
R Square
33% 31% 18%
33% 22% 3%
11% ### 2%
20% 10% 1%
50 40 30 20 10 10
20
30
40
50
Actual
60
70
80
90
100 Number of Periods to Forecast
10
Choose Method Linear Linear Linear
-0.36 Time Period
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 31 32 33 34 35 36
Forecast Output 0.86
Indep1
103.63 52.06 43.12 70.95 67.98 28.23 89.26 31.88 9.15 56.30 51.74 51.41 33.98 43.20 25.22 28.18 28.72 27.74 40.47 67.30 29.20 27.45 25.71 23.96 22.22 20.47 18.72 16.98 15.23 13.49 11.74
0.12
Indep2
60.14 10.93 18.97 47.55 30.07 17.13 59.46 -0.88 -27.06 44.46 21.47 19.79 -2.75 2.04 -16.86 12.33 -17.54 -11.43 36.39 49.12 2.88 1.47 0.06 -1.35 -2.75 -4.16 -5.57 -6.98 -8.39 -9.80 -11.21
-0.02 Indep3
45.08 7.14 40.19 40.57 42.06 85.04 97.38 54.63 20.33 77.93 12.79 14.35 95.47 58.81 4.07 7.43 19.94 20.19 70.21 49.64
Dependent
94.20 46.26 33.67 69.79 58.00 22.91 79.94 24.33 5.72 53.25 44.33 46.00 24.49 38.83 19.80 21.17 22.00 23.00 39.83 64.21 24.99 23.32 21.65 19.98 18.31 16.64 14.97 13.30 11.63 9.97 8.30
Time Period
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74
Indep1
Indep2
Indep3
Dependent
Time Period
75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112
Indep1
Indep2
Indep3
Dependent
Time Period
113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150
Indep1
Indep2
Indep3
Dependent
Indep1 103.63 52.06 43.12 70.95 67.98 28.23 89.26 31.88 9.15 56.30 51.74 51.41 33.98 43.20 25.22 28.18 28.72 27.74 40.47 67.30
Indep2 60.14 10.93 18.97 47.55 30.07 17.13 59.46 -0.88 -27.06 44.46 21.47 19.79 -2.75 2.04 -16.86 12.33 -17.54 -11.43 36.39 49.12
Indep3 45.08 7.14 40.19 40.57 42.06 85.04 97.38 54.63 20.33 77.93 12.79 14.35 95.47 58.81 4.07 7.43 19.94 20.19 70.21 49.64
Page 1
Input
Page 2
Input
Page 3
Input 4 20
Page 4
Input
Page 5
Input
Page 6
Input 0
Page 7
Input
Page 8
Input
Page 9
Input
Page 10
Input
Page 11
Input
Page 12
Input
Page 13
Input
Page 14
Input
Page 15
Input
Page 16
Input
Page 17
Input
Page 18
Input
20
10
0.91
Actual Predicted Residual e^2 (e-et-1)^2 94.2 94.86 0.65 46.26 45.41 -0.85 0.72 2.26 33.67 38.05 4.37 19.14 27.3 69.79 65.42 -4.37 19.13 76.54 58 60.66 2.66 7.1 49.55 22.91 24.09 1.18 1.4 2.2 79.94 81.34 1.41 1.98 0.05 24.33 25.63 1.3 1.69 0.01 5.72 3.66 -2.06 4.24 11.29 53.25 51.69 -1.57 2.46 0.24 44.33 46.33 2 3.99 12.71 46 45.8 -0.2 0.04 4.83 24.49 26.31 1.82 3.32 4.09 38.83 35.6 -3.23 10.45 25.56 19.8 19.04 -0.76 0.58 6.12 21.17 25.14 3.97 15.79 22.39 22 21.61 -0.39 0.16 19.07 23 21.52 -1.48 2.18 1.18 39.83 37.29 -2.54 6.44 1.12 64.21 62.29 -1.92 3.7 0.38
Page 19
2.55 d 1 dl 1.68 du
0 Positive Autocorrelation dete 1 Positive Autocorrelation may 1.68 No Autocorrelation detected 2.32 Negative Autocorrelation ma 3 Negative Autocorrelation de 4 Negative Autocorrelation de
4 Negative Autocorrelation ma
Input
104.51
266.9
Page 20
Input
Page 21
Input
Positive Autocorrelation detected Positive Autocorrelation maybe present No Autocorrelation detected Negative Autocorrelation maybe present Negative Autocorrelation detected Negative Autocorrelation detected
Negative Autocorrelation maybe present
Page 22
Input
Page 23
Input
Page 24
Output
Equation Parameters
Intercept Indep1 Indep2 Indep3
Independent Analysis
Coefficients
Standard Error
-0.357 0.856 0.125 -0.022
2.290 0.055 0.053 0.022
=
R Squared
98.57% 81.60% 7.59%
Gradient
Dl=1.20 Du=1.41
Intercept
0.97 0.79 0.21
Auto Correlation
-4.60 27.66 32.57
Tests for Multicolinearity between Independent Variables
DW-Stat
Adjusted RSquared against other Indep
2.43 1.90 1.71
76.97% 79.68% 14.43%
0.86*Indep1 + 0.12*Indep2 + -0.02*Indep3 + -0.36 (+/- 2.56)
Independent R-Square Matrix 100%
78%
8%
Indep1
78%
100%
19%
Indep2
8%
19%
100%
Indep3
Actual versus Predicted Trend R-Squared Matrix
100
f(x) = 0.99x + 0.44 R² = 0.99
90 80
Predicted
Step 2 - Forecasting
Independent Variable Indep1 Indep2 Indep3
70 60
Linear
Multiple Regression Equation
Exponential
498.8907
2nd Ord Polynomial
2.5609
F - Statistic
3rd Ord Polynomial
Standard Error
98.94% of the change in can be explained by the change in the 3 Independent Variables Adjusted for Sample Size bias 2.55384 Durbin-Watson Statistic Critical D-W Values: Lower (Dl)=1.00; Upper (Du)=1.68 to +/- on result of Regression Equation Therefore Negative Autocorrelation maybe present at 95% Confidence Therefore analysis IS Significant 3.12735 Critical F-Statistic at 95% Confidence (Significance holds to 100.0% Level of Confidence)
Indep3
0.9874
Indep2
0.9894
Adjusted R Square
Indep1
R Square
33% 31% 18%
33% 22% 3%
11% ### 2%
20% 10% 1%
50 40 30 20 10 10
20
30
40
50
Actual
60
70
80
90
100 Number of Periods to Forecast
10
Choose Method Linear Linear Linear
-0.36 Time Period
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 31 32 33 34 35 36
Forecast Output 0.86
Indep1
103.63 52.06 43.12 70.95 67.98 28.23 89.26 31.88 9.15 56.30 51.74 51.41 33.98 43.20 25.22 28.18 28.72 27.74 40.47 67.30 29.20 27.45 25.71 23.96 22.22 20.47 18.72 16.98 15.23 13.49 11.74
0.12
Indep2
60.14 10.93 18.97 47.55 30.07 17.13 59.46 -0.88 -27.06 44.46 21.47 19.79 -2.75 2.04 -16.86 12.33 -17.54 -11.43 36.39 49.12 2.88 1.47 0.06 -1.35 -2.75 -4.16 -5.57 -6.98 -8.39 -9.80 -11.21
-0.02 Indep3
45.08 7.14 40.19 40.57 42.06 85.04 97.38 54.63 20.33 77.93 12.79 14.35 95.47 58.81 4.07 7.43 19.94 20.19 70.21 49.64
Dependent
94.20 46.26 33.67 69.79 58.00 22.91 79.94 24.33 5.72 53.25 44.33 46.00 24.49 38.83 19.80 21.17 22.00 23.00 39.83 64.21 24.99 23.32 21.65 19.98 18.31 16.64 14.97 13.30 11.63 9.97 8.30
Time Period
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74
Indep1
Indep2
Indep3
Dependent
Time Period
75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112
Indep1
Indep2
Indep3
Dependent
Time Period
113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150
Indep1
Indep2
Indep3
Dependent
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