regression of yield on x1, x2, x3 1 14:27 Sunday, March 17, 2013 The GLM Procedure Number of Observations Read 33 Number of Observations Used 33 regression of yield on x1, x2, x3 2 14:27 Sunday, March 17, 2013 The GLM Procedure Dependent Variable: y Sum of Source DF Squares Mean Square F Value Model 3 3291.070269 1097.023423 13.99 Error 29 2273.989731 78.413439 Corrected Total 32 5565.060000 Source Pr > F Model <.0001 Error Corrected Total R-Square Coeff Var Root MSE y Mean 0.591381 17.71027 8.855136 50.00000 Source DF Type I SS Mean Square F Value x1 1 3135.275348 3135.275348 39.98 x2 1 138.654195 138.654195 1.77 x3 1 17.140726 17.140726 0.22 Source Pr > F x1 <.0001 x2 0.1940 x3 0.6436 Source DF Type II SS Mean Square F Value x1 1 3052.069582 3052.069582 38.92 x2 1 125.276872 125.276872 1.60 x3 1 17.140726 17.140726 0.22 Source Pr > F x1 <.0001 x2 0.2163 x3 0.6436 regression of yield on x1, x2, x3 3 14:27 Sunday, March 17, 2013 The GLM Procedure Dependent Variable: y Standard Parameter Estimate Error t Value Pr > |t| Intercept 6.486262886 29.06263701 0.22 0.8250 x1 1.011576037 0.16214239 6.24 <.0001 x2 0.480158507 0.37987825 1.26 0.2163 x3 -0.200482880 0.42880312 -0.47 0.6436 Parameter 95% Confidence Limits Intercept -52.95350380 65.926029568 x1 0.679957616 1.343194457 x2 -0.296779748 1.257096762 x3 -1.077483726 0.676517965 regression of yield on x1, x2, x3 4 14:27 Sunday, March 17, 2013 Obs y x1 x2 x3 clml clmu clpl clpu yhat resid 1 34.0 30 17.75 60.2 27.0166 39.5579 14.1216 52.4529 33.2873 0.7127 2 32.9 31 14.76 57.5 25.9009 40.9081 13.8008 53.0082 33.4045 -0.5045 3 43.0 32 27.99 62.3 30.5670 49.0455 19.4749 60.1376 39.8062 3.1938 4 40.0 33 16.76 60.5 30.1798 41.3933 16.8277 54.7453 35.7865 4.2135 5 23.0 34 11.36 69.5 22.1401 42.6617 11.5854 53.2164 32.4009 -9.4009 6 38.4 35 22.71 55.0 34.3171 49.2214 22.1852 61.3533 41.7693 -3.3693 7 20.0 36 17.91 66.2 31.7522 44.7092 18.9960 57.4653 38.2307 -18.2307 8 44.6 37 23.31 61.8 37.0895 48.3450 23.7522 61.6823 42.7172 1.8828 9 46.3 38 18.53 59.5 37.5743 46.2153 23.2758 60.5138 41.8948 4.4052 10 52.2 39 18.56 66.4 35.3396 47.7352 22.3955 60.6793 41.5374 10.6626 11 52.3 40 12.45 58.4 34.3663 48.0719 21.8552 60.5830 41.2191 11.0809 12 51.0 41 16.05 66.0 36.4539 48.4172 23.3625 61.5086 42.4356 8.5644 13 59.9 42 27.10 59.3 42.9597 57.2326 30.6300 69.5622 50.0961 9.8039 14 54.7 43 19.05 57.5 43.1949 52.0117 28.9637 66.2429 47.6033 7.0967 15 52.0 44 20.79 64.6 43.0965 52.9573 29.2570 66.7968 48.0269 3.9731 16 43.5 45 21.88 55.1 45.3712 57.5617 32.3575 70.5754 51.4664 -7.9664 17 56.7 46 20.02 56.5 46.4144 56.1941 32.5450 70.0635 51.3043 5.3957 18 30.5 47 23.17 55.6 47.9181 60.0994 34.9013 73.1163 54.0088 -23.5088 19 60.5 48 19.15 59.2 48.8721 55.8647 33.9232 70.8135 52.3684 8.1316 20 46.1 49 18.28 63.5 47.9936 56.2066 33.5296 70.6706 52.1001 -6.0001 21 48.2 50 18.45 59.8 50.3624 57.5078 35.4753 72.3949 53.9351 -5.7351 22 43.1 51 22.00 62.2 51.7129 60.6273 37.5189 74.8213 56.1701 -13.0701 23 62.2 52 19.05 59.6 52.4338 60.1391 37.7704 74.8025 56.2865 5.9135 24 52.9 53 15.67 60.0 50.7291 60.4607 36.8419 74.3479 55.5949 -2.6949 25 53.9 54 15.92 55.6 50.8217 64.3956 38.2679 76.9494 57.6086 -3.7086 26 48.4 55 16.75 63.6 52.1114 62.7184 38.5436 76.2862 57.4149 -9.0149 27 52.8 56 12.34 62.4 49.4522 63.6469 37.0977 76.0014 56.5495 -3.7495 28 62.1 57 15.82 59.0 54.1316 65.6958 40.9023 78.9251 59.9137 2.1863 29 66.0 58 15.24 62.5 53.8401 66.0501 40.8330 79.0572 59.9451 6.0549 30 64.2 59 21.72 62.8 57.9634 70.0526 44.9151 83.1008 64.0080 0.1920 31 63.2 60 25.08 59.7 60.1146 74.3942 47.7870 86.7217 67.2544 -4.0544 32 75.4 61 17.79 57.4 58.5494 71.9040 45.9242 84.5292 65.2267 10.1733 33 76.0 62 26.61 66.6 58.3884 78.8692 47.8234 89.4343 68.6288 7.3712 residual plots: regression of y on x1, x2, and x3 5 14:27 Sunday, March 17, 2013 Plot of resid*yhat. Legend: A = 1 obs, B = 2 obs, etc. 15 + | | | | | B 10 + A A | | A A | A A | | A A 5 + A | A A A | A resid | A | A | A 0 +----------------------------------------------A---------- | A | | A | A AA | A -5 + | A A | | | A | A A -10 + | | | | A | -15 + | | | | A | -20 + | | | | A | -25 + ---+------------+------------+------------+------------+-- 30 40 50 60 70 yhat residual plots: regression of y on x1, x2, and x3 6 14:27 Sunday, March 17, 2013 Plot of resid*x1. Legend: A = 1 obs, B = 2 obs, etc. 15 + | | | | | AA 10 + A A | | A A | A A | | A A 5 + A | A A A | A resid | A | A | A 0 +-------------------------------A------------- | A | | A | A A A | A -5 + | AA | | | A | A A -10 + | | | | A | -15 + | | | | A | -20 + | | | | A | -25 + ---+---------+---------+---------+---------+-- 30 40 50 60 70 x1 residual plots: regression of y on x1, x2, and x3 7 14:27 Sunday, March 17, 2013 Plot of resid*x2. Legend: A = 1 obs, B = 2 obs, etc. 15 + | | | | | A A 10 + A A | | A A | A A | | A A 5 + A | A A A | A resid | A | A | A 0 +--------------------------------A------------------------ | A | | A | A A A | A -5 + | B | | | A | A A -10 + | | | | A | -15 + | | | | A | -20 + | | | | A | -25 + ---+------------+------------+------------+------------+-- 10 15 20 25 30 x2 residual plots: regression of y on x1, x2, and x3 8 14:27 Sunday, March 17, 2013 Plot of resid*x3. Legend: A = 1 obs, B = 2 obs, etc. 15 + | | | | | A A 10 + A A | | A A | A A | | A A 5 + A | A A A | A resid | A | A | A 0 +---------------------------------A------------------------------- | A | | A | A A A | A -5 + | A A | | | A | A A -10 + | | | | A | -15 + | | | | A | -20 + | | | | A | -25 + ---+---------+---------+---------+---------+---------+---------+-- 55.0 57.5 60.0 62.5 65.0 67.5 70.0 x3 residual plots: regression of y on x1, x2, and x3 9 14:27 Sunday, March 17, 2013 Plot of nscore*resid. Legend: A = 1 obs, B = 2 obs, etc. | | 2.5 + | | | A 2.0 + | | | A R 1.5 + a | A n | A k | A 1.0 + A f | A o | A r | A 0.5 + AA V | A a | B r | AA i 0.0 + A a | AA b | A A l | A e -0.5 + B | A r | A e | A s -1.0 + A i | A d | A | A -1.5 + | A | | -2.0 + | A | | -2.5 + | --+-----------+-----------+-----------+-----------+-----------+-- -30 -20 -10 0 10 20 resid residual plots: regression of y on x1, x2, and x3 10 14:27 Sunday, March 17, 2013 The UNIVARIATE Procedure Variable: resid Moments N 33 Sum Weights 33 Mean 0 Sum Observations 0 Std Deviation 8.42983862 Variance 71.0621791 Skewness -0.9238005 Kurtosis 0.68675409 Uncorrected SS 2273.98973 Corrected SS 2273.98973 Coeff Variation . Std Error Mean 1.46744655 Basic Statistical Measures Location Variability Mean 0.000000 Std Deviation 8.42984 Median 1.882771 Variance 71.06218 Mode . Range 34.58968 Interquartile Range 10.10926 Tests for Location: Mu0=0 Test -Statistic- -----p Value------ Student's t t 0 Pr > |t| 1.0000 Sign M 2.5 Pr >= |M| 0.4869 Signed Rank S 30.5 Pr >= |S| 0.5936 Tests for Normality Test --Statistic--- -----p Value------ Shapiro-Wilk W 0.934012 Pr < W 0.0456 Kolmogorov-Smirnov D 0.105534 Pr > D >0.1500 Cramer-von Mises W-Sq 0.079536 Pr > W-Sq 0.2103 Anderson-Darling A-Sq 0.56232 Pr > A-Sq 0.1391 Quantiles (Definition 5) Quantile Estimate 100% Max 11.08092 99% 11.08092 95% 10.66259 90% 9.80388 75% Q3 6.05489 50% Median 1.88277 25% Q1 -4.05437 10% -9.40089 5% -18.23067 1% -23.50876 0% Min -23.50876 residual plots: regression of y on x1, x2, and x3 11 14:27 Sunday, March 17, 2013 The UNIVARIATE Procedure Variable: resid Extreme Observations ------Lowest------ ------Highest----- Value Obs Value Obs -23.50876 18 8.56445 12 -18.23067 7 9.80388 13 -13.07009 22 10.17330 32 -9.40089 5 10.66259 10 -9.01489 26 11.08092 11 Stem Leaf # Boxplot 1 0011 4 | 0 5667789 7 +-----+ 0 01223444 8 *--+--* -0 444331 6 +-----+ -0 99866 5 | -1 3 1 | -1 8 1 | -2 4 1 0 ----+----+----+----+ Multiply Stem.Leaf by 10**+1 Normal Probability Plot 12.5+ ++*++* * | ****+*** | *******+ | *****+ | ***+**+ | +++*++ | ++++++* -22.5+++ * +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 regressions with sequential coefficients 12 14:27 Sunday, March 17, 2013 The REG Procedure Model: MODEL1 Dependent Variable: y Number of Observations Read 33 Number of Observations Used 33 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 3 3291.07027 1097.02342 13.99 <.0001 Error 29 2273.98973 78.41344 Corrected Total 32 5565.06000 Root MSE 8.85514 R-Square 0.5914 Dependent Mean 50.00000 Adj R-Sq 0.5491 Coeff Var 17.71027 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Type I SS Intercept 1 6.48626 29.06264 0.22 0.8250 82500 x1 1 1.01158 0.16214 6.24 <.0001 3135.27535 x2 1 0.48016 0.37988 1.26 0.2163 138.65419 x3 1 -0.20048 0.42880 -0.47 0.6436 17.14073 Parameter Estimates Variable DF Type II SS Intercept 1 3.90580 x1 1 3052.06958 x2 1 125.27687 x3 1 17.14073 Sequential Parameter Estimates Intercept x1 x2 x3 50.000000 0 0 0 2.911497 1.023663 0 0 -6.228448 1.014223 0.501488 0 6.486263 1.011576 0.480159 -0.200483