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Comparison of Alternative Models

Стр 1 из 4Следующая ⇒


Model Correlation R-Squared
Linear 0, 5337 28, 48%
Squared-Y 0, 5336 28, 48%
Square root-Y 0, 5309 28, 18%
Exponential 0, 5262 27, 69%
Squared-Y square root-X 0, 5236 27, 42%
Square root-X 0, 5223 27, 28%
Double square root 0, 5191 26, 94%
Logarithmic-Y square root-X 0, 5140 26, 42%
Reciprocal-Y -0, 5110 26, 12%
Squared-X 0, 4989 24, 89%
Square root-Y squared-X 0, 4975 24, 75%
Double squared 0, 4962 24, 62%
Logarithmic-Y squared-X 0, 4942 24, 42%
Reciprocal-Y squared-X -0, 4816 23, 20%
Squared-Y logarithmic-X 0, 4658 21, 70%
Logarithmic-X 0, 4637 21, 51%
Square root-Y logarithmic-X 0, 4604 21, 20%
Multiplicative 0, 4556 20, 75%
Reciprocal-X -0, 2204 4, 86%
Squared-Y reciprocal-X -0, 2198 4, 83%
S-curve model -0, 2183 4, 76%
Double reciprocal 0, 2133 4, 55%
Reciprocal-Y square root-X < no fit>  
Reciprocal-Y logarithmic-X < no fit>  
Square root-Y reciprocal-X < no fit>  
Logistic < no fit>  
Log probit < no fit>  

 

2) Модель линейного тренда с константой

 

Simple Regression - ConsGOODS vs. num (num< 125)

Dependent variable: ConsGOODS

Independent variable: num

Selection variable: num< 125

Linear model: Y = a + b*X

 

Coefficients

  Least Squares Standard T   Resistant
Parameter Estimate Error Statistic P-Value Estimate
Intercept 824, 41 26, 1039 31, 5819 0, 0000 815, 293
Slope 2, 52608 0, 362432 6, 96981 0, 0000 3, 04355

 

Analysis of Variance

Source Sum of Squares Df Mean Square F-Ratio P-Value
Model 1, 01379E6 1, 01379E6 48, 58 0, 0000
Residual 2, 54606E6 20869, 3    
Total (Corr.) 3, 55985E6      

 

Correlation Coefficient = 0, 533653

R-squared = 28, 4786 percent

R-squared (adjusted for d.f.) = 27, 8923 percent

Standard Error of Est. = 144, 462

Mean absolute error = 111, 967

Durbin-Watson statistic = 0, 110215 (P=0, 0000)

Lag 1 residual autocorrelation = 0, 944686

Half-slope = 0, 384949

 

ConsGOODS = 824, 41 + 2, 52608*num

 

 

3) Линейно-логарифмическая функция 2-го порядка:

 

 

Multiple Regression - (ConsGOODS) (num< 125)

Dependent variable: (ConsGOODS)

Independent variables:

log(num)

2*log(num)^2

Selection variable: num< 125

 

    Standard T  
Parameter Estimate Error Statistic P-Value
CONSTANT 951, 229 100, 77 9, 43958 0, 0000
log(num) -136, 183 64, 9837 -2, 09565 0, 0382
2*log(num)^2 17, 7058 5, 10025 3, 47155 0, 0007

 

Analysis of Variance

Source Sum of Squares Df Mean Square F-Ratio P-Value
Model 1, 01868E6 509339, 24, 25 0, 0000
Residual 2, 54117E6 21001, 4    
Total (Corr.) 3, 55985E6      

 

R-squared = 28, 6157 percent

R-squared (adjusted for d.f.) = 27, 4358 percent

Standard Error of Est. = 144, 919

Mean absolute error = 113, 994

Durbin-Watson statistic = 0, 117019 (P=0, 0000)

Lag 1 residual autocorrelation = 0, 93726

 

Stepwise regression

Method: backward selection

F-to-enter: 4, 0

F-to-remove: 4, 0

 

Step 0:

2 variables in the model. 121 d.f. for error.

R-squared = 28, 62% Adjusted R-squared = 27, 44% MSE = 21001, 4

 

Final model selected.

 

The StatAdvisor

The output shows the results of fitting a multiple linear regression model to describe the relationship between (ConsGOODS) and 2 independent variables. The equation of the fitted model is

 

(ConsGOODS) = 951, 229 - 136, 183*log(num) + 17, 7058*2*log(num)^2

 

 

Regression Results for (ConsGOODS)

  Fitted Stnd. Error Lower 95, 0% Upper 95, 0% Lower 95, 0% Upper 95, 0%
Row Value CL for Forecast CL for Forecast CL for Forecast CL for Mean CL for Mean
1119, 23 146, 98 828, 247 1410, 22 1070, 67 1167, 79
1120, 87 147, 02 829, 809 1411, 94 1071, 84 1169, 91
1122, 51 147, 061 831, 361 1413, 66 1072, 99 1172, 03
1124, 13 147, 103 832, 904 1415, 36 1074, 14 1174, 13
1125, 75 147, 144 834, 438 1417, 06 1075, 28 1176, 22
1127, 36 147, 186 835, 963 1418, 75 1076, 41 1178, 31

 

4) Парабола третьего порядка:

 

Multiple Regression - ConsGOODS (num< 125)

Dependent variable: ConsGOODS

Independent variables:

(num)

num^2

num^3

Selection variable: num< 125

 

    Standard T  
Parameter Estimate Error Statistic P-Value
CONSTANT 829, 366 25, 6645 32, 3157 0, 0000
num^2 0, 0739677 0, 0166027 4, 45515 0, 0000
num^3 -0, 000476454 0, 000140127 -3, 40016 0, 0009

 

Analysis of Variance

Source Sum of Squares Df Mean Square F-Ratio P-Value
Model 1, 11925E6 559623, 27, 74 0, 0000
Residual 2, 4406E6 20170, 3    
Total (Corr.) 3, 55985E6      

 

R-squared = 31, 4408 percent

R-squared (adjusted for d.f.) = 30, 3076 percent

Standard Error of Est. = 142, 022

Mean absolute error = 111, 399

Durbin-Watson statistic = 0, 115369 (P=0, 0000)

Lag 1 residual autocorrelation = 0, 939841

 

Stepwise regression

Method: backward selection

F-to-enter: 4, 0

F-to-remove: 4, 0

 

Step 0:

3 variables in the model. 120 d.f. for error.

R-squared = 32, 10% Adjusted R-squared = 30, 40% MSE = 20143, 1

 

Step 1:

Removing variable (num) with F-to-remove =1, 16343

2 variables in the model. 121 d.f. for error.

R-squared = 31, 44% Adjusted R-squared = 30, 31% MSE = 20170, 3

 

Final model selected.

 

 

ConsGOODS = 829, 366 + 0, 0739677*num^2 - 0, 000476454*num^3

 

Regression Results for ConsGOODS

  Fitted Stnd. Error Lower 95, 0% Upper 95, 0% Lower 95, 0% Upper 95, 0%
Row Value CL for Forecast CL for Forecast CL for Forecast CL for Mean CL for Mean
1054, 54 149, 613 758, 337 1350, 73 961, 387 1147, 68
1050, 59 150, 354 752, 923 1348, 25 952, 876 1148, 3
1046, 43 151, 156 747, 175 1345, 68 943, 978 1148, 88
1042, 05 152, 024 741, 083 1343, 03 934, 69 1149, 42
1037, 46 152, 959 734, 638 1340, 29 925, 011 1149, 91
1032, 65 153, 966 727, 833 1337, 47 914, 937 1150, 36

 

 

5) Логистическая функция: , где

 

Multiple Regression - ConsGOODS (num< 125)

Dependent variable: ConsGOODS

Independent variables:

1/(1+0.55*exp(-0.013*num))

Selection variable: num< 125

 

    Standard T  
Parameter Estimate Error Statistic P-Value
1/(1+0.55*exp(-0.013*num)) 1237, 5 16, 1446 76, 6508 0, 0000

 

Analysis of Variance

Source Sum of Squares Df Mean Square F-Ratio P-Value
Model 1, 2068E8 1, 2068E8 5875, 34 0, 0000
Residual 2, 52644E6 20540, 2    
Total 1, 23207E8      

 

R-squared = 97, 9494 percent

R-squared (adjusted for d.f.) = 97, 9494 percent

Standard Error of Est. = 143, 318

Mean absolute error = 114, 351

Durbin-Watson statistic = 0, 111105

Lag 1 residual autocorrelation = 0, 943892

 

Stepwise regression

Method: backward selection

F-to-enter: 4, 0

F-to-remove: 4, 0

 

Final model selected.

 

 

ConsGOODS = 1237, 5*1/(1+0.55*exp(-0.013*num))

 


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