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 |