1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 1 15:45 Thursday, June 28, 2001 Obs X Y1 Y2 Y3 Y4 X2 X3 1 14 620 625 590 590 196 2744 2 21 910 820 910 910 441 9261 3 28 1315 1215 1305 1205 784 21952 4 35 1635 1515 1730 1605 1225 42875 5 42 2120 2110 2140 1915 1764 74088 6 49 2300 2320 2725 2035 2401 117649 7 56 2600 2805 2890 2140 3136 175616 8 63 2925 2940 3685 2520 3969 250047 9 70 3110 3255 3920 2710 4900 343000 10 77 3315 3620 4325 2870 5929 456533 11 84 3535 4015 4410 3020 7056 592704 12 91 3710 4235 4485 3025 8281 753571 13 98 3935 4315 4515 3030 9604 941192 14 105 4145 4435 4480 3025 11025 1157625 15 112 4465 4495 4520 3040 12544 1404928 16 119 4510 4475 4545 3177 14161 1685159 17 126 4530 4535 4525 3180 15876 2000376 18 133 4545 4520 4560 3180 17689 2352637 19 140 4570 4600 4565 3257 19600 2744000 20 147 4605 4600 4626 3166 21609 3176523 21 154 4600 4600 4566 3214 23716 3652264 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 2 15:45 Thursday, June 28, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y3 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 30305600 30305600 70.60 <.0001 Error 19 8156429 429286 Corrected Total 20 38462029 Root MSE 655.19900 R-Square 0.7879 Dependent Mean 3524.61905 Adj R-Sq 0.7768 Coeff Var 18.58921 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Intercept 1 1143.95931 317.37074 3.60 0.0019 260881728 X 1 28.34119 3.37310 8.40 <.0001 30305600 Parameter Estimates Variable DF Type II SS Intercept 1 5577426 X 1 30305600 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 3 15:45 Thursday, June 28, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y3 Output Statistics Dep Var Predicted Std Error Std Error Student Obs Y3 Value Mean Predict Residual Residual Residual 1 590.0000 1541 276.0318 -950.7359 594.2 -1.600 2 910.0000 1739 256.1265 -829.1242 603.1 -1.375 3 1305 1938 236.9031 -632.5126 610.9 -1.035 4 1730 2136 218.5414 -405.9009 617.7 -0.657 5 2140 2334 201.2776 -194.2892 623.5 -0.312 6 2725 2533 185.4185 192.3225 628.4 0.306 7 2890 2731 171.3546 158.9342 632.4 0.251 8 3685 2929 159.5613 755.5459 635.5 1.189 9 3920 3128 150.5730 792.1576 637.7 1.242 10 4325 3326 144.9127 998.7693 639.0 1.563 11 4410 3525 142.9761 885.3810 639.4 1.385 12 4485 3723 144.9127 761.9926 639.0 1.193 13 4515 3921 150.5730 593.6043 637.7 0.931 14 4480 4120 159.5613 360.2160 635.5 0.567 15 4520 4318 171.3546 201.8277 632.4 0.319 16 4545 4517 185.4185 28.4394 628.4 0.0453 17 4525 4715 201.2776 -189.9489 623.5 -0.305 18 4560 4913 218.5414 -353.3372 617.7 -0.572 19 4565 5112 236.9031 -546.7255 610.9 -0.895 20 4626 5310 256.1265 -684.1139 603.1 -1.134 21 4566 5509 276.0318 -942.5022 594.2 -1.586 Output Statistics Cook's Obs -2-1 0 1 2 D 1 | ***| | 0.276 2 | **| | 0.170 3 | **| | 0.081 4 | *| | 0.027 5 | | | 0.005 6 | | | 0.004 7 | | | 0.002 8 | |** | 0.045 9 | |** | 0.043 10 | |*** | 0.063 11 | |** | 0.048 12 | |** | 0.037 13 | |* | 0.024 14 | |* | 0.010 15 | | | 0.004 16 | | | 0.000 17 | | | 0.005 18 | *| | 0.020 19 | *| | 0.060 20 | **| | 0.116 21 | ***| | 0.271 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 4 15:45 Thursday, June 28, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y3 Sum of Residuals 0 Sum of Squared Residuals 8156429 Predicted Residual SS (PRESS) 10254319 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 5 15:45 Thursday, June 28, 2001 Plot of Y3*X. Legend: A = 1 obs, B = 2 obs, etc. Y3 | | 5000 + | | | | A A A A 4500 + A A A A A A | A | A | | 4000 + | A | | A | 3500 + | | | | 3000 + | A | | A | 2500 + | | | | A 2000 + | | | A | 1500 + | | A | | 1000 + | A | | | A 500 + | ---+---------+---------+---------+---------+---------+-- 0 35 70 105 140 175 X 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 6 15:45 Thursday, June 28, 2001 Plot of YRES*YPRED. Legend: A = 1 obs, B = 2 obs, etc. 1000 + A | | | A | | A 750 + A A | | | | A | 500 + | | | A | | 250 + | A A R | A e | s | i | A d 0 + u | a | l | | | A A -250 + | | A | | A | -500 + | A | | A | A | -750 + | | A | | | A A -1000 + --+-----------+-----------+-----------+-----------+-----------+- 1540.74 2334.29 3127.84 3921.40 4714.95 5508.50 Predicted Value of Y3 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 7 15:45 Thursday, June 28, 2001 Plot of YRES*X. Legend: A = 1 obs, B = 2 obs, etc. 1000 + A | | | A | | A 750 + A A | | | | A | 500 + | | | A | | 250 + | A A R | A e | s | i | A d 0 + u | a | l | | | A A -250 + | | A | | A | -500 + | A | | A | A | -750 + | | A | | | A A -1000 + ---+---------+---------+---------+---------+---------+-- 0 35 70 105 140 175 X 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 8 15:45 Thursday, June 28, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Moments N 21 Sum Weights 21 Mean 0 Sum Observations 0 Std Deviation 638.60899 Variance 407821.442 Skewness 0.04415067 Kurtosis -1.3142913 Uncorrected SS 8156428.85 Corrected SS 8156428.85 Coeff Variation . Std Error Mean 139.355907 Basic Statistical Measures Location Variability Mean 0.00000 Std Deviation 638.60899 Median 28.43939 Variance 407821 Mode . Range 1950 Interquartile Range 1140 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M 0.5 Pr >= |M| 1.0000 Signed Rank S 0.5 Pr >= |S| 0.9866 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.938739 Pr < W 0.2057 Kolmogorov-Smirnov D 0.119713 Pr > D >0.1500 Cramer-von Mises W-Sq 0.051191 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.38305 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 998.7693 99% 998.7693 95% 885.3810 90% 792.1576 75% Q3 593.6043 50% Median 28.4394 25% Q1 -546.7255 10% -829.1242 5% -942.5022 1% -950.7359 0% Min -950.7359 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 9 15:45 Thursday, June 28, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Extreme Observations ------Lowest----- -----Highest----- Value Obs Value Obs -950.736 1 755.546 8 -942.502 21 761.993 12 -829.124 2 792.158 9 -684.114 20 885.381 11 -632.513 3 998.769 10 Frequency Counts Percents Percents Value Count Cell Cum Value Count Cell Cum -950.7359307 1 4.8 4.8 158.9341991 1 4.8 57.1 -942.5021645 1 4.8 9.5 192.3225108 1 4.8 61.9 -829.1242424 1 4.8 14.3 201.8277056 1 4.8 66.7 -684.1138528 1 4.8 19.0 360.2160173 1 4.8 71.4 -632.5125541 1 4.8 23.8 593.6043290 1 4.8 76.2 -546.7255411 1 4.8 28.6 755.5458874 1 4.8 81.0 -405.9008658 1 4.8 33.3 761.9926407 1 4.8 85.7 -353.3372294 1 4.8 38.1 792.1575758 1 4.8 90.5 -194.2891775 1 4.8 42.9 885.3809524 1 4.8 95.2 -189.9489177 1 4.8 47.6 998.7692641 1 4.8 100.0 28.4393939 1 4.8 52.4 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 10 15:45 Thursday, June 28, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Stem Leaf # Boxplot 1 0 1 | 0 68889 5 +-----+ 0 02224 5 *--+--* -0 4422 4 | | -0 98765 5 +-----+ -1 0 1 | ----+----+----+----+ Multiply Stem.Leaf by 10**+3 Normal Probability Plot 1250+ ++++++++ | * *+*+*+*+ * | ***+**++ | ++**+** | * +*+*+*+* * -1250+ ++++++++ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 11 15:45 Thursday, June 28, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y3 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 2 37790573 18895286 506.53 <.0001 Error 18 671456 37303 Corrected Total 20 38462029 Root MSE 193.14013 R-Square 0.9825 Dependent Mean 3524.61905 Adj R-Sq 0.9806 Coeff Var 5.47974 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Intercept 1 -816.64197 167.06215 -4.89 0.0001 260881728 X 1 90.96909 4.53168 20.07 <.0001 30305600 X2 1 -0.37279 0.02632 -14.17 <.0001 7484973 Parameter Estimates Variable DF Type II SS Intercept 1 891358 X 1 15031891 X2 1 7484973 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 12 15:45 Thursday, June 28, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y3 Output Statistics Dep Var Predicted Std Error Std Error Student Obs Y3 Value Mean Predict Residual Residual Residual 1 590.0000 383.8594 115.2864 206.1406 155.0 1.330 2 910.0000 929.3107 94.7035 -19.3107 168.3 -0.115 3 1305 1438 78.2255 -133.2290 176.6 -0.754 4 1730 1911 66.3560 -180.6144 181.4 -0.996 5 2140 2346 59.3390 -206.4668 183.8 -1.123 6 2725 2746 56.6905 -20.7863 184.6 -0.113 7 2890 3109 57.1114 -218.5729 184.5 -1.185 8 3685 3435 59.0356 250.1735 183.9 1.360 9 3920 3725 61.1932 195.4528 183.2 1.067 10 4325 3978 62.7708 347.2651 182.7 1.901 11 4410 4194 63.3404 215.6103 182.5 1.182 12 4485 4375 62.7708 110.4885 182.7 0.605 13 4515 4518 61.1932 -3.1004 183.2 -0.0169 14 4480 4625 59.0356 -145.1564 183.9 -0.789 15 4520 4696 57.1114 -175.6794 184.5 -0.952 16 4545 4730 56.6905 -184.6694 184.6 -1.000 17 4525 4727 59.3390 -202.1266 183.8 -1.100 18 4560 4688 66.3560 -128.0507 181.4 -0.706 19 4565 4612 78.2255 -47.4420 176.6 -0.269 20 4626 4500 94.7035 125.6997 168.3 0.747 21 4566 4352 115.2864 214.3744 155.0 1.383 Output Statistics Cook's Obs -2-1 0 1 2 D 1 | |** | 0.327 2 | | | 0.001 3 | *| | 0.037 4 | *| | 0.044 5 | **| | 0.044 6 | | | 0.000 7 | **| | 0.045 8 | |** | 0.064 9 | |** | 0.042 10 | |*** | 0.142 11 | |** | 0.056 12 | |* | 0.014 13 | | | 0.000 14 | *| | 0.021 15 | *| | 0.029 16 | **| | 0.031 17 | **| | 0.042 18 | *| | 0.022 19 | | | 0.005 20 | |* | 0.059 21 | |** | 0.353 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 13 15:45 Thursday, June 28, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y3 Sum of Residuals 0 Sum of Squared Residuals 671456 Predicted Residual SS (PRESS) 944103 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 14 15:45 Thursday, June 28, 2001 Plot of YRES*YPRED. Legend: A = 1 obs, B = 2 obs, etc. | | 400 + | | | A | | 300 + | | | A | | A A 200 + A A | | | | A R | A e 100 + s | i | d | u | a | l 0 + A | A A | | A | | -100 + | | A A | A | | A AA -200 + A A | A | | | | -300 + | --+-----------+-----------+-----------+-----------+-----------+-- 0 1000 2000 3000 4000 5000 Predicted Value of Y3 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 15 15:45 Thursday, June 28, 2001 Plot of YRES*X. Legend: A = 1 obs, B = 2 obs, etc. | | 400 + | | | A | | 300 + | | | A | | A A 200 + A A | | | | A R | A e 100 + s | i | d | u | a | l 0 + A | A A | | A | | -100 + | | A A | A | | A A A -200 + A A | A | | | | -300 + | ---+---------+---------+---------+---------+---------+-- 0 35 70 105 140 175 X 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 16 15:45 Thursday, June 28, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Moments N 21 Sum Weights 21 Mean 0 Sum Observations 0 Std Deviation 183.228815 Variance 33572.7985 Skewness 0.3971926 Kurtosis -1.3287841 Uncorrected SS 671455.969 Corrected SS 671455.969 Coeff Variation . Std Error Mean 39.9838053 Basic Statistical Measures Location Variability Mean 0.0000 Std Deviation 183.22881 Median -20.7863 Variance 33573 Mode . Range 565.83799 Interquartile Range 371.13221 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M -2.5 Pr >= |M| 0.3833 Signed Rank S -0.5 Pr >= |S| 0.9866 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.894684 Pr < W 0.0276 Kolmogorov-Smirnov D 0.186251 Pr > D 0.0558 Cramer-von Mises W-Sq 0.136443 Pr > W-Sq 0.0344 Anderson-Darling A-Sq 0.847874 Pr > A-Sq 0.0241 Quantiles (Definition 5) Quantile Estimate 100% Max 347.2651 99% 347.2651 95% 250.1735 90% 215.6103 75% Q3 195.4528 50% Median -20.7863 25% Q1 -175.6794 10% -202.1266 5% -206.4668 1% -218.5729 0% Min -218.5729 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 17 15:45 Thursday, June 28, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Extreme Observations ------Lowest----- -----Highest----- Value Obs Value Obs -218.573 7 206.141 1 -206.467 5 214.374 21 -202.127 17 215.610 11 -184.669 16 250.174 8 -180.614 4 347.265 10 Frequency Counts Percents Percents Value Count Cell Cum Value Count Cell Cum -218.57287884 1 4.8 4.8 -19.31067194 1 4.8 57.1 -206.46682517 1 4.8 9.5 -3.10040714 1 4.8 61.9 -202.12656543 1 4.8 14.3 110.48849000 1 4.8 66.7 -184.66944040 1 4.8 19.0 125.69971767 1 4.8 71.4 -180.61438379 1 4.8 23.8 195.45283961 1 4.8 76.2 -175.67937234 1 4.8 28.6 206.14059853 1 4.8 81.0 -145.15636126 1 4.8 33.3 214.37436477 1 4.8 85.7 -133.22899938 1 4.8 38.1 215.61033017 1 4.8 90.5 -128.05074742 1 4.8 42.9 250.17350887 1 4.8 95.2 -47.44198639 1 4.8 47.6 347.26511338 1 4.8 100.0 -20.78632352 1 4.8 52.4 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 18 15:45 Thursday, June 28, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Stem Leaf # Boxplot 3 5 1 | 2 01125 5 +-----+ 1 13 2 | | 0 | + | -0 5220 4 *-----* -1 888533 6 +-----+ -2 210 3 | ----+----+----+----+ Multiply Stem.Leaf by 10**+2 Normal Probability Plot 350+ ++*++ | * *+*+*++ | ***++++ 50+ ++++++ | ++++**** | *+*+*** * -250+ * ++*+*+ +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 19 15:45 Thursday, June 28, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y3 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 37825069 12608356 336.51 <.0001 Error 17 636960 37468 Corrected Total 20 38462029 Root MSE 193.56712 R-Square 0.9834 Dependent Mean 3524.61905 Adj R-Sq 0.9805 Coeff Var 5.49186 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Intercept 1 -1037.45941 284.59581 -3.65 0.0020 260881728 X 1 103.27931 13.60974 7.59 <.0001 30305600 X2 1 -0.54567 0.18210 -3.00 0.0081 7484973 X3 1 0.00068604 0.00071499 0.96 0.3507 34496 Parameter Estimates Variable DF Type II SS Intercept 1 497907 X 1 2157695 X2 1 336446 X3 1 34496 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 20 15:45 Thursday, June 28, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y3 Output Statistics Dep Var Predicted Std Error Std Error Student Obs Y3 Value Mean Predict Residual Residual Residual 1 590.0000 303.3825 142.7737 286.6175 130.7 2.193 2 910.0000 897.1199 100.6677 12.8801 165.3 0.0779 3 1305 1442 78.4779 -136.6175 176.9 -0.772 4 1730 1938 72.4870 -208.2872 179.5 -1.160 5 2140 2389 73.8880 -248.5407 178.9 -1.389 6 2725 2794 75.7030 -68.7901 178.1 -0.386 7 2890 3155 75.2506 -265.4472 178.3 -1.488 8 3685 3475 72.4358 210.0762 179.5 1.170 9 3920 3754 68.4104 166.3682 181.1 0.919 10 4325 3993 64.8857 332.0169 182.4 1.821 11 4410 4194 63.4804 215.6103 182.9 1.179 12 4485 4359 64.8857 125.7368 182.4 0.689 13 4515 4489 68.4104 25.9842 181.1 0.143 14 4480 4585 72.4358 -105.0591 179.5 -0.585 15 4520 4649 75.2506 -128.8051 178.3 -0.722 16 4545 4682 75.7030 -136.6656 178.1 -0.767 17 4525 4685 73.8880 -160.0527 178.9 -0.895 18 4560 4660 72.4870 -100.3780 179.5 -0.559 19 4565 4609 78.4779 -44.0535 176.9 -0.249 20 4626 4532 100.6677 93.5089 165.3 0.566 21 4566 4432 142.7737 133.8974 130.7 1.024 Output Statistics Cook's Obs -2-1 0 1 2 D 1 | |**** | 1.434 2 | | | 0.001 3 | *| | 0.029 4 | **| | 0.055 5 | **| | 0.082 6 | | | 0.007 7 | **| | 0.099 8 | |** | 0.056 9 | |* | 0.030 10 | |*** | 0.105 11 | |** | 0.042 12 | |* | 0.015 13 | | | 0.001 14 | *| | 0.014 15 | *| | 0.023 16 | *| | 0.027 17 | *| | 0.034 18 | *| | 0.013 19 | | | 0.003 20 | |* | 0.030 21 | |** | 0.313 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 21 15:45 Thursday, June 28, 2001 The REG Procedure Model: MODEL1 Dependent Variable: Y3 Sum of Residuals 0 Sum of Squared Residuals 636960 Predicted Residual SS (PRESS) 1203103 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 22 15:45 Thursday, June 28, 2001 Plot of YRES*YPRED. Legend: A = 1 obs, B = 2 obs, etc. | | 400 + | | | | A | 300 + | A | | | | A A 200 + | | A | | AA R | e 100 + A s | i | d | u | A a | A l 0 + | | | A | A | -100 + AA | | A B | | A | -200 + A | | | A | A | -300 + | --+-----------+-----------+-----------+-----------+-----------+-- 0 1000 2000 3000 4000 5000 Predicted Value of Y3 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 23 15:45 Thursday, June 28, 2001 Plot of YRES*X. Legend: A = 1 obs, B = 2 obs, etc. | | 400 + | | | | A | 300 + | A | | | | A A 200 + | | A | | A A R | e 100 + A s | i | d | u | A a | A l 0 + | | | A | A | -100 + A A | | A A A | | A | -200 + A | | | A | A | -300 + | ---+---------+---------+---------+---------+---------+-- 0 35 70 105 140 175 X 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 24 15:45 Thursday, June 28, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Moments N 21 Sum Weights 21 Mean 0 Sum Observations 0 Std Deviation 178.460063 Variance 31847.994 Skewness 0.31363118 Kurtosis -1.0472272 Uncorrected SS 636959.88 Corrected SS 636959.88 Coeff Variation . Std Error Mean 38.9431784 Basic Statistical Measures Location Variability Mean 0.0000 Std Deviation 178.46006 Median -44.0535 Variance 31848 Mode . Range 597.46402 Interquartile Range 270.51492 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M -0.5 Pr >= |M| 1.0000 Signed Rank S -1.5 Pr >= |S| 0.9599 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.950488 Pr < W 0.3480 Kolmogorov-Smirnov D 0.141673 Pr > D >0.1500 Cramer-von Mises W-Sq 0.06884 Pr > W-Sq >0.2500 Anderson-Darling A-Sq 0.391873 Pr > A-Sq >0.2500 Quantiles (Definition 5) Quantile Estimate 100% Max 332.0169 99% 332.0169 95% 286.6175 90% 215.6103 75% Q3 133.8974 50% Median -44.0535 25% Q1 -136.6175 10% -208.2872 5% -248.5407 1% -265.4472 0% Min -265.4472 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 25 15:45 Thursday, June 28, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Extreme Observations ------Lowest----- -----Highest----- Value Obs Value Obs -265.447 7 166.368 9 -248.541 5 210.076 8 -208.287 4 215.610 11 -160.053 17 286.618 1 -136.666 16 332.017 10 Frequency Counts Percents Percents Value Count Cell Cum Value Count Cell Cum -265.4471686 1 4.8 4.8 12.8801054 1 4.8 57.1 -248.5407359 1 4.8 9.5 25.9842426 1 4.8 61.9 -208.2871573 1 4.8 14.3 93.5089403 1 4.8 66.7 -160.0526547 1 4.8 19.0 125.7367529 1 4.8 71.4 -136.6656496 1 4.8 23.8 133.8974214 1 4.8 76.2 -136.6175023 1 4.8 28.6 166.3681899 1 4.8 81.0 -128.8050825 1 4.8 33.3 210.0762248 1 4.8 85.7 -105.0590772 1 4.8 38.1 215.6103302 1 4.8 90.5 -100.3779739 1 4.8 42.9 286.6175419 1 4.8 95.2 -68.7901143 1 4.8 47.6 332.0168504 1 4.8 100.0 -44.0534835 1 4.8 52.4 1 EXAMPLE 9. POLYNOMIAL REGRESSION: FISH LENGTH DATA 26 15:45 Thursday, June 28, 2001 The UNIVARIATE Procedure Variable: YRES (Residual) Stem Leaf # Boxplot 3 3 1 | 2 129 3 | 1 337 3 +-----+ 0 139 3 | + | -0 74 2 *-----* -1 644310 6 +-----+ -2 751 3 | ----+----+----+----+ Multiply Stem.Leaf by 10**+2 Normal Probability Plot 350+ ++*+++ | * *+*++ | **+*+++ 50+ +**+*+ | ++++** | +*+*+*** * -250+ * ++*+* +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2