The SAS System

The REG Procedure

Correlation
Variable x1 x2 x3 x4 x5 y
x1 1.0000 0.4089 0.4601 -0.5895 -0.0445 0.6559
x2 0.4089 1.0000 0.4040 -0.6263 -0.0411 0.0452
x3 0.4601 0.4040 1.0000 -0.2045 -0.4126 0.4053
x4 -0.5895 -0.6263 -0.2045 1.0000 -0.5249 -0.2932
x5 -0.0445 -0.0411 -0.4126 -0.5249 1.0000 -0.0234
y 0.6559 0.0452 0.4053 -0.2932 -0.0234 1.0000

 


 
The SAS System

The REG Procedure
Model: MODEL1
Dependent Variable: y
Stepwise Selection: Step 1

Variable x1 Entered: R-Square = 0.4302 and C(p) = 7.4208

Analysis of Variance
Origine DF Sum of
Squares
Mean
Square
Valore F Pr > F
Model 1 69888 69888 34.72 <.0001
Error 46 92583 2012.67766    
Corrected Total 47 162471      
 
Variable Parameter
Estimate
Standard
Error
Type II SS Valore F Pr > F
Intercept 118.98324 29.18019 33463 16.63 0.0002
x1 1.73287 0.29407 69888 34.72 <.0001

Bounds on condition number: 1, 1

Stepwise Selection: Step 2

 

Variable x2 Entered: R-Square = 0.4899 and C(p) = 4.0341

Analysis of Variance
Origine DF Sum of
Squares
Mean
Square
Valore F Pr > F
Model 2 79587 39793 21.60 <.0001
Error 45 82884 1841.87554    
Corrected Total 47 162471      
 
Variable Parameter
Estimate
Standard
Error
Type II SS Valore F Pr > F
Intercept 117.97339 27.91805 32890 17.86 0.0001
x1 2.02214 0.30827 79254 43.03 <.0001
x2 -0.58434 0.25465 9698.77303 5.27 0.0265

Bounds on condition number: 1.2008, 4.8032

Stepwise Selection: Step 3

 

Variable x3 Entered: R-Square = 0.5254 and C(p) = 2.8267

Analysis of Variance
Origine DF Sum of
Squares
Mean
Square
Valore F Pr > F
Model 3 85362 28454 16.24 <.0001
Error 44 77109 1752.48747    
Corrected Total 47 162471      
 
Variable Parameter
Estimate
Standard
Error
Type II SS Valore F Pr > F
Intercept 130.81539 28.13606 37883 21.62 <.0001
x1 1.81605 0.32141 55948 31.92 <.0001
x2 -0.70899 0.25771 13264 7.57 0.0086
x3 0.68625 0.37804 5774.95062 3.30 0.0763

Bounds on condition number: 1.372, 12.09

All variables left in the model are significant at the 0.1500 level.

No other variable met the 0.1500 significance level for entry into the model.

 

Summary of Stepwise Selection
Step Variable
Entered
Variable
Removed
Number
Vars In
Partial
R-Square
Model
R-Square
C(p) Valore F Pr > F
1 x1   1 0.4302 0.4302 7.4208 34.72 <.0001
2 x2   2 0.0597 0.4899 4.0341 5.27 0.0265
3 x3   3 0.0355 0.5254 2.8267 3.30 0.0763

 


 
The SAS System

The REG Procedure
Model: MODEL1
Dependent Variable: y

Output Statistics
Obs Dep Var
y
Predicted
Value
Std Error
Mean Predict
95% CL Mean Residual
1 256.0000 276.8560 8.6537 259.4156 294.2963 -20.8560
2 275.0000 299.6079 9.1266 281.2144 318.0015 -24.6079
3 327.0000 291.3511 12.2918 266.5787 316.1235 35.6489
4 297.0000 272.6351 12.8872 246.6626 298.6075 24.3649
5 256.0000 242.7303 15.0204 212.4587 273.0020 13.2697
6 312.0000 314.0606 10.5647 292.7689 335.3524 -2.0606
7 374.0000 281.5394 12.6278 256.0898 306.9891 92.4606
8 257.0000 306.4882 10.2529 285.8248 327.1516 -49.4882
9 257.0000 268.1730 11.8070 244.3775 291.9686 -11.1730
10 336.0000 320.2620 9.6589 300.7958 339.7282 15.7380
11 269.0000 266.3342 10.7499 244.6691 287.9992 2.6658
12 213.0000 249.9560 9.3641 231.0838 268.8282 -36.9560
13 308.0000 291.0832 8.8216 273.3045 308.8620 16.9168
14 273.0000 299.5356 8.5872 282.2293 316.8420 -26.5356
15 256.0000 310.4901 7.5161 295.3424 325.6377 -54.4901
16 287.0000 306.4919 11.7914 282.7278 330.2559 -19.4919
17 290.0000 297.6287 6.8520 283.8193 311.4380 -7.6287
18 217.0000 258.3756 10.4235 237.3685 279.3827 -41.3756
19 198.0000 246.3177 9.0436 228.0915 264.5438 -48.3177
20 217.0000 240.2879 8.9879 222.1740 258.4019 -23.2879
21 195.0000 264.8071 8.4966 247.6833 281.9310 -69.8071
22 183.0000 235.2452 10.8220 213.4349 257.0556 -52.2452
23 222.0000 240.6558 9.4040 221.7032 259.6083 -18.6558
24 283.0000 284.2027 24.7132 234.3964 334.0089 -1.2027
25 217.0000 229.3234 10.2420 208.6820 249.9647 -12.3234
26 231.0000 229.3027 13.1657 202.7688 255.8365 1.6973
27 329.0000 278.1225 6.4853 265.0522 291.1929 50.8775
28 294.0000 292.8826 8.4642 275.8241 309.9412 1.1174
29 232.0000 276.4611 7.9748 260.3890 292.5332 -44.4611
30 369.0000 294.9096 10.8760 272.9905 316.8287 74.0904
31 302.0000 285.1439 9.9520 265.0869 305.2008 16.8561
32 269.0000 288.7948 7.7654 273.1446 304.4450 -19.7948
33 291.0000 299.3014 7.1084 284.9755 313.6274 -8.3014
34 323.0000 298.4798 12.3295 273.6313 323.3283 24.5202
35 198.0000 237.6002 11.2216 214.9846 260.2159 -39.6002
36 282.0000 258.2657 7.6073 242.9341 273.5973 23.7343
37 246.0000 281.8301 7.3097 267.0983 296.5620 -35.8301
38 309.0000 294.8292 12.7168 269.2001 320.4582 14.1708
39 309.0000 294.9897 22.1483 250.3527 339.6267 14.0103
40 334.0000 301.2347 8.5034 284.0973 318.3722 32.7653
41 284.0000 310.4698 12.7589 284.7561 336.1836 -26.4698
42 454.0000 368.6764 18.1752 332.0468 405.3061 85.3236
43 344.0000 325.5842 13.7797 297.8131 353.3553 18.4158
44 307.0000 270.6389 8.9182 252.6654 288.6124 36.3611
45 333.0000 282.0663 7.2742 267.4061 296.7264 50.9337
46 343.0000 283.8297 6.3183 271.0961 296.5633 59.1703
47 421.0000 503.8893 32.0152 439.3669 568.4117 -82.8893
48 380.0000 307.2585 12.8545 281.3520 333.1649 72.7415
 
Sum of Residuals 0
Sum of Squared Residuals 77109
Predicted Residual SS (PRESS) 122358

 


 
The SAS System

The REG Procedure
Model: MODEL1
Dependent Variable: y

Analysis of Variance
Origine DF Sum of
Squares
Mean
Square
Valore F Pr > F
Model 3 85362 28454 16.24 <.0001
Error 44 77109 1752.48747    
Corrected Total 47 162471      
 
Root MSE 41.86272 R-Square 0.5254
Dependent Mean 286.64583 Adj R-Sq 0.4930
Coeff Var 14.60434    
 
Parameter Estimates
Variable DF Parameter
Estimate
Standard
Error
Valore t Pr > |t|
Intercept 1 130.81539 28.13606 4.65 <.0001
x1 1 1.81605 0.32141 5.65 <.0001
x2 1 -0.70899 0.25771 -2.75 0.0086
x3 1 0.68625 0.37804 1.82 0.0763

 


 

The REG Procedure

 


 

The REG Procedure

 


 

The REG Procedure