PropVal1 Example 1 Obs y x1 x2 x3 x4 x5 x6 x7 x8 x9 1 25.9 4.9176 1.0 3.4720 0.998 1.0 7 4 42 0 2 29.5 5.0208 1.0 3.5310 1.500 2.0 7 4 62 0 3 27.9 4.5429 1.0 2.2750 1.175 1.0 6 3 40 0 4 25.9 4.5573 1.0 4.0500 1.232 1.0 6 3 54 0 5 29.9 5.0597 1.0 4.4550 0.988 1.0 6 3 56 0 6 30.9 5.8980 1.0 5.8500 1.240 1.0 7 3 51 1 7 28.9 5.6039 1.0 9.5200 1.501 0.0 6 3 32 0 8 35.9 5.8282 1.0 6.4350 1.225 2.0 6 3 32 0 9 31.5 5.3003 1.0 4.9883 1.552 1.0 6 3 30 0 10 31.0 6.2712 1.0 5.5200 0.975 1.0 5 2 30 0 11 30.0 5.0500 1.0 5.0000 1.020 0.0 5 2 46 1 12 36.9 8.2464 1.5 5.1500 1.664 2.0 8 4 50 0 13 41.9 6.6969 1.5 6.9020 1.488 1.5 7 3 22 1 14 40.5 7.7841 1.5 7.1020 1.376 1.0 6 3 17 0 15 43.9 9.0384 1.0 7.8000 1.500 1.5 7 3 23 0 16 37.5 5.9894 1.0 5.5200 1.256 2.0 6 3 40 1 17 37.9 7.5422 1.5 5.0000 1.690 1.0 6 3 22 0 18 44.5 8.7951 1.5 9.8900 1.890 2.0 8 4 50 1 19 37.9 6.0831 1.5 6.7265 1.652 1.0 6 3 44 0 20 38.9 8.3607 1.5 9.1500 1.777 2.0 8 4 48 1 21 36.9 8.1400 1.0 8.0000 1.504 2.0 7 3 3 0 22 45.8 9.1416 1.5 7.3262 1.831 1.5 8 4 31 0 PropVal1 Example 2 The REG Procedure Model: MODEL1 Dependent Variable: y Sale price of house ($1000) Number of Observations Read 22 Number of Observations Used 22 Forward Selection: Step 1 Variable x2 Entered: R-Square = 0.4889 and C(p) = 20.0026 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 386.12222 386.12222 19.13 0.0003 Error 20 403.70732 20.18537 Corrected Total 21 789.82955 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 14.41071 4.80302 181.71010 9.00 0.0071 x2 17.41786 3.98245 386.12222 19.13 0.0003 Bounds on condition number: 1, 1 ----------------------------------------------------------------------------------------------- Forward Selection: Step 2 Variable x3 Entered: R-Square = 0.6510 and C(p) = 9.9513 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 514.14533 257.07266 17.72 <.0001 Error 19 275.68422 14.50970 Corrected Total 21 789.82955 PropVal1 Example 3 The REG Procedure Model: MODEL1 Dependent Variable: y Sale price of house ($1000) Forward Selection: Step 2 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 11.64356 4.17736 112.72645 7.77 0.0117 x2 12.86452 3.70814 174.63616 12.04 0.0026 x3 1.34117 0.45151 128.02310 8.82 0.0079 Bounds on condition number: 1.2061, 4.8245 ----------------------------------------------------------------------------------------------- Forward Selection: Step 3 Variable x5 Entered: R-Square = 0.7411 and C(p) = 5.2462 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 585.37428 195.12476 17.18 <.0001 Error 18 204.45527 11.35863 Corrected Total 21 789.82955 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 10.13742 3.74465 83.24500 7.33 0.0144 x2 11.13408 3.35285 125.25796 11.03 0.0038 x3 1.25746 0.40088 111.75977 9.84 0.0057 x5 3.13383 1.25144 71.22895 6.27 0.0221 Bounds on condition number: 1.2596, 10.661 ----------------------------------------------------------------------------------------------- Forward Selection: Step 4 Variable x8 Entered: R-Square = 0.7976 and C(p) = 3.0485 PropVal1 Example 4 The REG Procedure Model: MODEL1 Dependent Variable: y Sale price of house ($1000) Forward Selection: Step 4 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 629.96710 157.49177 16.75 <.0001 Error 17 159.86245 9.40367 Corrected Total 21 789.82955 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 15.41826 4.18208 127.81536 13.59 0.0018 x2 11.31780 3.05187 129.32670 13.75 0.0017 x3 0.97451 0.38721 59.56350 6.33 0.0222 x5 3.30073 1.14124 78.66148 8.36 0.0101 x8 -0.10653 0.04892 44.59282 4.74 0.0438 Bounds on condition number: 1.3687, 19.419 ----------------------------------------------------------------------------------------------- Forward Selection: Step 5 Variable x7 Entered: R-Square = 0.8094 and C(p) = 4.1682 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 5 639.31847 127.86369 13.59 <.0001 Error 16 150.51108 9.40694 Corrected Total 21 789.82955 PropVal1 Example 5 The REG Procedure Model: MODEL1 Dependent Variable: y Sale price of house ($1000) Forward Selection: Step 5 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 17.15853 4.53238 134.82070 14.33 0.0016 x2 12.53281 3.28667 136.78329 14.54 0.0015 x3 1.00320 0.38834 62.77547 6.67 0.0200 x5 4.06242 1.37350 82.29238 8.75 0.0093 x7 -1.64940 1.65429 9.35137 0.99 0.3336 x8 -0.08225 0.05466 21.29784 2.26 0.1519 Bounds on condition number: 2.1158, 39.738 ----------------------------------------------------------------------------------------------- Forward Selection: Step 6 Variable x6 Entered: R-Square = 0.8206 and C(p) = 5.3380 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 6 648.13843 108.02307 11.44 <.0001 Error 15 141.69111 9.44607 Corrected Total 21 789.82955 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 13.73924 5.75756 53.78984 5.69 0.0306 x2 12.21025 3.31037 128.51276 13.60 0.0022 x3 0.81545 0.43496 33.20156 3.51 0.0804 x5 3.60262 1.45629 57.80872 6.12 0.0258 x6 1.84457 1.90891 8.81997 0.93 0.3492 x7 -3.73627 2.72255 17.79006 1.88 0.1901 x8 -0.07949 0.05485 19.84071 2.10 0.1678 Bounds on condition number: 6.7333, 112.93 ----------------------------------------------------------------------------------------------- No other variable met the 0.5000 significance level for entry into the model. PropVal1 Example 6 The REG Procedure Model: MODEL1 Dependent Variable: y Sale price of house ($1000) Summary of Forward Selection Variable Number Partial Model Step Entered Label Vars In R-Square R-Square C(p) F Value Pr > F 1 x2 Number of baths 1 0.4889 0.4889 20.0026 19.13 0.0003 2 x3 Lot size (1000 sq ft) 2 0.1621 0.6510 9.9513 8.82 0.0079 3 x5 Number of garage stalls 3 0.0902 0.7411 5.2462 6.27 0.0221 4 x8 Age of home (years) 4 0.0565 0.7976 3.0485 4.74 0.0438 5 x7 Number of bedrooms 5 0.0118 0.8094 4.1682 0.99 0.3336 6 x6 Number of rooms 6 0.0112 0.8206 5.3380 0.93 0.3492 PropVal1 Example 7 The REG Procedure Model: MODEL1 Dependent Variable: y Sale price of house ($1000) Number of Observations Read 22 Number of Observations Used 22 Backward Elimination: Step 0 All Variables Entered: R-Square = 0.8252 and C(p) = 9.0000 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 8 651.72866 81.46608 7.67 0.0007 Error 13 138.10088 10.62314 Corrected Total 21 789.82955 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 14.06643 6.57239 48.66017 4.58 0.0519 x2 10.79159 4.28418 67.40442 6.35 0.0257 x3 0.66258 0.53860 16.07671 1.51 0.2404 x4 2.87675 4.98306 3.54051 0.33 0.5736 x5 3.50009 1.56688 53.00755 4.99 0.0437 x6 1.65292 2.19591 6.01911 0.57 0.4650 x7 -3.87234 3.38160 13.93014 1.31 0.2728 x8 -0.08122 0.06878 14.81306 1.39 0.2588 x9 0.38527 2.10346 0.35637 0.03 0.8575 Bounds on condition number: 7.9229, 238.53 ----------------------------------------------------------------------------------------------- Backward Elimination: Step 1 Variable x9 Removed: R-Square = 0.8247 and C(p) = 7.0335 PropVal1 Example 8 The REG Procedure Model: MODEL1 Dependent Variable: y Sale price of house ($1000) Backward Elimination: Step 1 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 7 651.37229 93.05318 9.41 0.0002 Error 14 138.45726 9.88980 Corrected Total 21 789.82955 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 13.62261 5.89476 52.81723 5.34 0.0366 x2 10.98001 4.01272 74.04856 7.49 0.0161 x3 0.69348 0.49353 19.52704 1.97 0.1818 x4 2.69313 4.70968 3.23385 0.33 0.5765 x5 3.54458 1.49355 55.70264 5.63 0.0325 x6 1.80830 1.95426 8.46766 0.86 0.3705 x7 -4.16214 2.88359 20.60408 2.08 0.1709 x8 -0.07469 0.05675 17.13152 1.73 0.2093 Bounds on condition number: 6.7404, 168.05 ----------------------------------------------------------------------------------------------- Backward Elimination: Step 2 Variable x4 Removed: R-Square = 0.8206 and C(p) = 5.3380 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 6 648.13843 108.02307 11.44 <.0001 Error 15 141.69111 9.44607 Corrected Total 21 789.82955 PropVal1 Example 9 The REG Procedure Model: MODEL1 Dependent Variable: y Sale price of house ($1000) Backward Elimination: Step 2 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 13.73924 5.75756 53.78984 5.69 0.0306 x2 12.21025 3.31037 128.51276 13.60 0.0022 x3 0.81545 0.43496 33.20156 3.51 0.0804 x5 3.60262 1.45629 57.80872 6.12 0.0258 x6 1.84457 1.90891 8.81997 0.93 0.3492 x7 -3.73627 2.72255 17.79006 1.88 0.1901 x8 -0.07949 0.05485 19.84071 2.10 0.1678 Bounds on condition number: 6.7333, 112.93 ----------------------------------------------------------------------------------------------- Backward Elimination: Step 3 Variable x6 Removed: R-Square = 0.8094 and C(p) = 4.1682 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 5 639.31847 127.86369 13.59 <.0001 Error 16 150.51108 9.40694 Corrected Total 21 789.82955 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 17.15853 4.53238 134.82070 14.33 0.0016 x2 12.53281 3.28667 136.78329 14.54 0.0015 x3 1.00320 0.38834 62.77547 6.67 0.0200 x5 4.06242 1.37350 82.29238 8.75 0.0093 x7 -1.64940 1.65429 9.35137 0.99 0.3336 x8 -0.08225 0.05466 21.29784 2.26 0.1519 Bounds on condition number: 2.1158, 39.738 ----------------------------------------------------------------------------------------------- Backward Elimination: Step 4 PropVal1 Example 10 The REG Procedure Model: MODEL1 Dependent Variable: y Sale price of house ($1000) Backward Elimination: Step 4 Variable x7 Removed: R-Square = 0.7976 and C(p) = 3.0485 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 629.96710 157.49177 16.75 <.0001 Error 17 159.86245 9.40367 Corrected Total 21 789.82955 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 15.41826 4.18208 127.81536 13.59 0.0018 x2 11.31780 3.05187 129.32670 13.75 0.0017 x3 0.97451 0.38721 59.56350 6.33 0.0222 x5 3.30073 1.14124 78.66148 8.36 0.0101 x8 -0.10653 0.04892 44.59282 4.74 0.0438 Bounds on condition number: 1.3687, 19.419 ----------------------------------------------------------------------------------------------- All variables left in the model are significant at the 0.1000 level. Summary of Backward Elimination Variable Number Partial Model Step Removed Label Vars In R-Square R-Square C(p) F Value Pr > F 1 x9 Number of fireplaces 7 0.0005 0.8247 7.0335 0.03 0.8575 2 x4 Living space (sq ft x 1000) 6 0.0041 0.8206 5.3380 0.33 0.5765 3 x6 Number of rooms 5 0.0112 0.8094 4.1682 0.93 0.3492 4 x7 Number of bedrooms 4 0.0118 0.7976 3.0485 0.99 0.3336 PropVal1 Example 11 The REG Procedure Model: MODEL1 Dependent Variable: y Sale price of house ($1000) Number of Observations Read 22 Number of Observations Used 22 Stepwise Selection: Step 1 Variable x2 Entered: R-Square = 0.4889 and C(p) = 20.0026 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 386.12222 386.12222 19.13 0.0003 Error 20 403.70732 20.18537 Corrected Total 21 789.82955 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 14.41071 4.80302 181.71010 9.00 0.0071 x2 17.41786 3.98245 386.12222 19.13 0.0003 Bounds on condition number: 1, 1 ----------------------------------------------------------------------------------------------- Stepwise Selection: Step 2 Variable x3 Entered: R-Square = 0.6510 and C(p) = 9.9513 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 514.14533 257.07266 17.72 <.0001 Error 19 275.68422 14.50970 Corrected Total 21 789.82955 PropVal1 Example 12 The REG Procedure Model: MODEL1 Dependent Variable: y Sale price of house ($1000) Stepwise Selection: Step 2 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 11.64356 4.17736 112.72645 7.77 0.0117 x2 12.86452 3.70814 174.63616 12.04 0.0026 x3 1.34117 0.45151 128.02310 8.82 0.0079 Bounds on condition number: 1.2061, 4.8245 ----------------------------------------------------------------------------------------------- Stepwise Selection: Step 3 Variable x5 Entered: R-Square = 0.7411 and C(p) = 5.2462 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 585.37428 195.12476 17.18 <.0001 Error 18 204.45527 11.35863 Corrected Total 21 789.82955 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 10.13742 3.74465 83.24500 7.33 0.0144 x2 11.13408 3.35285 125.25796 11.03 0.0038 x3 1.25746 0.40088 111.75977 9.84 0.0057 x5 3.13383 1.25144 71.22895 6.27 0.0221 Bounds on condition number: 1.2596, 10.661 ----------------------------------------------------------------------------------------------- Stepwise Selection: Step 4 Variable x8 Entered: R-Square = 0.7976 and C(p) = 3.0485 PropVal1 Example 13 The REG Procedure Model: MODEL1 Dependent Variable: y Sale price of house ($1000) Stepwise Selection: Step 4 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 4 629.96710 157.49177 16.75 <.0001 Error 17 159.86245 9.40367 Corrected Total 21 789.82955 Parameter Standard Variable Estimate Error Type II SS F Value Pr > F Intercept 15.41826 4.18208 127.81536 13.59 0.0018 x2 11.31780 3.05187 129.32670 13.75 0.0017 x3 0.97451 0.38721 59.56350 6.33 0.0222 x5 3.30073 1.14124 78.66148 8.36 0.0101 x8 -0.10653 0.04892 44.59282 4.74 0.0438 Bounds on condition number: 1.3687, 19.419 ----------------------------------------------------------------------------------------------- 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 Variable Variable Number Partial Model Step Entered Removed Label Vars In R-Square R-Square C(p) F Value 1 x2 Number of baths 1 0.4889 0.4889 20.0026 19.13 2 x3 Lot size (1000 sq ft) 2 0.1621 0.6510 9.9513 8.82 3 x5 Number of garage stalls 3 0.0902 0.7411 5.2462 6.27 4 x8 Age of home (years) 4 0.0565 0.7976 3.0485 4.74 Summary of Stepwise Selection Step Pr > F 1 0.0003 2 0.0079 3 0.0221 PropVal1 Example 14 The REG Procedure Model: MODEL1 Dependent Variable: y Sale price of house ($1000) Summary of Stepwise Selection Step Pr > F 4 0.0438