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ass 3 sol - }00 STAT 350 AM 35W 5TA-7’ 5504Β...

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Unformatted text preview: //}00 , STAT 350% AM 35W 5TA-7’ 5504Β» 4" .7. ,31Β£10f,q5’:27Γ© 04 IQ'VEβ€™β€œβ‚¬"β€˜4 A’Ob/ Fm 5A5 013;, /[?Β§ Ha :MMQ: ’ ,, / Β«h 021: 46:207.. __ 3 mar/@β€œL"1:: STAT 355"Β» A β€˜* _3 fWQK/Lβ€˜ [WLflGβ€”(Mbucflw (JD. ,. _ . V The SAS System 25 Obs speed fitted s ssq it I Lb) 1 1 3.5625 1.09354 1.1958 2 2 5 . 8750 1 .99583 3 .9833 β€™β€œ 3 3 10.6875 3.23973 10.4958 4 4 16. 5625 5.37858 28 .9292 β€œ The SAS System I 34 --------; ------ ._._ --------------------- speeeclzl β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” ,_. , 2. ____ ,,_ β€œFmβ€œ. Plot of resid*obsno. Symbol used is '*'. ti (Ca) resid , 2.438 1 1.433: Β«r β€˜ M. 0.438 β€˜Iβ€˜* at at * . * * I - * -0.563 4 * * . , . -1.563 " * * * \ 1β€˜15β€œfoβ€œffffβ€˜ffffβ€˜ffff"ffffβ€œffffβ€˜ffff".ffffβ€œffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜f 1 2 9 3 4 5 6 7 u 9 . 10 11 12 13 14 15 15 . w....22---._...,_..-.-.___-_._-_.._.__. obsno . -------------------------------------- speec =2 β€”-β€”----β€”β€”---β€”---β€”--------β€”-β€”---β€”---β€”β€”- @ Plot of resid*obsno. Symbol used is β€˜*'. resid , 3.125 * * iiβ€” I [:31 ) 2.125 * n. 1β€˜. DH 1.125 * * * : i- * * 'X' 9.125 H. -0.875 * * ) β€”1.875 β€˜ * * I -2.875 β€˜ * I β€”3.875 * gβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffff’ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜f 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 obsno (.9 -------------------------------------- speedu3 ~------β€”-β€”--β€”-----β€”-------β€”β€”--β€”β€”β€”----- Plot of resid*obsno. Symbol used is '*'. resid 6.313 5.313 4.313 3.313 2 1 0 11))yhu .313 * _313 ~* * x * .313 -9.688 -1.688 -2.688 -3.688 -4.688 * * * )1))71 * gβ€œffffβ€˜ffffβ€˜ffΒ₯fβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffff”ffffβ€˜ffffβ€˜ffffβ€˜ffff'ffffβ€˜ffffβ€˜ffffβ€˜f 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ubsno -------------------------------------- speed 4 --β€”β€”------β€”---------β€”-β€”--------β€”------ Plot of resid*obsno. iymbol used is '*'. resid 8.438 * >s H- 6.438 * 4.438 r 2.438 * H. 9.438 * )\. ~1.563 H. -3.563 * H. β€”5.563 * * H. β€”7.563 * I * Sβ€˜ffff'ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffffβ€˜ffff"ffffβ€˜ffff”ffffβ€˜f 1 2 3 4 5 6 7 8 9 19 11 12 13 14 15 16 ubsno β€”9.563 The UNIVARIAIIβ€˜E Procedure Variable: lny Schematic Plots 3.5 + I I , C I 3 J- +β€”-lβ€”β€”+ it /( I I I I I *_..+__* l I I I 2.5 + *β€”β€”β€”β€”-* + β€”β€”β€”β€”β€” + I I + l l I I l I I + β€”β€”β€”β€”β€” + | 2 + +β€”β€” β€”+ I I l I I I I I I I I I I 1.5 + | + ------ + I * ----- * I I I + I I I + ----- + I l + | I | I l 0 I 0.5 + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” +β€”β€”β€”β€”-β€”β€”β€”β€”β€”β€”+--β€”--~-β€”----β€”-+β€”--β€”β€”-β€”---β€”β€”+-β€”-β€”---β€”-β€”- speed 1 2 3 4 Speed-level statistics for response in Y Obs speed fitted std .' var md 7% El I L j l 1 1.22370 0.10424 1.38629 2 2 1.70387 0.16280 1.79176 3 3 2.32109 0.10897 2.44140 4 4 2.74986 0.13336 2.80290 Plot of residuals vs fitted Plot of resid*fittad. Symbol used is '*'. (NOTE: 37 obs hidden.) ' resid I 1 + l I , I * * * air . | :9: * * 3L. # lca) I * 3k * * 0 + * * I Jr * * * I * * * I * 9: * I * I * β€”1 + * . ~β€”β€”+ β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” +β€”β€” 1 0 1.5 2 O 2.5 3.0 'the mean, lnyβ€œ Anova Table for Browne-Forsythe Test The ANOVA Procedure Class Level Information Class Levels Values speed 4 1 2 3 4 Number of observations 64 The ANOVA Procedure motβ€œ) Dependent Variable: dij Sum of Source DF Squares Mean Square F Value Pr > F Model 3 0.01931432 0.00643811 l0.lOi/O.9609i Error , 6O 3.94717558 0.06578626 Corrected Total 63 3.96648990 R-Square Coeff Var Root MSE dij Mean 0.004869 96.75837 0.256488 0.265081 Source DF Anova SS Mean Square P Value Pr > F speed 3 0.01931432 0.00643811 0.10 0.9609 Normal Probability plots Plot of resid*nscor:er. Symbol used is '*'. (NOTE: ll obs hidden.) 1.0 + l l I *- 0.5 + l * resid l i 4: 0.0 + I 3.- l I ._O.5 + *- β€”β€”β€”+ β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” +β€”- β€”2 -l 0 1 2 I 13/ , 7 i....,. ....,_,......u_. HJLIWVJ. uacu 4..) " . (NOTE: 8 obs hidden.) f; l(:;) 0.5 + * ' I * I * I * 0.0 + I ~k resid l I ~1- -0.5 + I * l l -1.0 + * --β€”+ β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + ------------- + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” +β€”β€” -2 β€”l 0 l 2 Rank for Variable resid β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” speed=3 ---~β€”β€”β€”----β€”~β€”-β€”β€”β€”β€”β€”β€”β€”-β€”-β€”β€”-β€”β€”β€”β€” Plot of resid*nsccrrer. Symbol used is '*'. (NOTE: 7 obs hidden.) 0.5 + * l I * resid I * I 9: I sl- 0 O + * I u I l | I it -0.5 + * β€”β€”β€”+ β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” +β€”β€” β€”2 β€”l 0 l 2 Rank for Variable resid β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”-β€”β€”: β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” speed=4 β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” β€”β€”β€”β€”β€”β€”β€” Plot of resid*nscorrer. Symbol used is '*β€˜. (NOTE: 2 obs hidden.) 0.5 + (A. I 9: i I V): J: * I * i- 0.0 + * * I i reald l I ~k β€”0.5 + * i I iv 1 β€”l.0 + β€”β€”β€”+ β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” + β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” +-β€” -2 -1 O l 2 Correlations between residuals & normalized residuals β€”β€”-β€”β€”β€”β€”β€”-β€”β€”β€”β€”β€”β€”-β€”β€”β€”β€”f β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” speed=1 β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” The CORR Procedure - ffβ€”l k;}) 2 Variables: resid nscorrer Pearson Correlation Coefficients, N = 16 Prob > Ir under H0: Rho=0 resid nscorrer resid 1.00000 w ,iIl nscorrer 0.99122 1.00000 Rank for Variable resid <.OOOl β€˜ β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” 'β€”β€”β€”--β€”β€”-β€”-β€”β€”-β€”β€”β€”β€”-β€”-β€” speed=2 -β€”-β€”~β€”β€”β€”β€”β€”-β€”-----β€”β€”--β€”---β€”β€”β€”β€”β€”β€”β€” The CCRR Procedure 2 Variables: resid nscorrer Pearson Correlation Coefficients, N = 16 Prob > Ir] under H0: Rho=0 resid nscorrer resid 1.00000 0.96258 <.OOOl nscorrer 0.96258 1.00000 Rank for Variable resid <.OOOl β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” speed=3 β€”~-~β€”β€”β€”β€”β€”-β€”β€”--β€”--β€”~β€”β€”-β€”-β€”β€”-β€”-Β»β€”- The CORR Procedure 2 Variables: resid nscorrer Pearsonβ€˜Correlatinn Coefficients, N = 16 Prob > [rl under H0: Rho=0 resid nscorrer resid 1.00000 10.97219, ' <.OOOl nscorrer 0.97219 1.00000 Rank for Variable resid <.OOOl β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€”β€” speed=4 ____________1______--___________ The CORR Procedure 2 Variables: resid nscorrer Pearson Correlation Coefficients, N = 16 h Prob > lrl under H0: Rho=0 Β’Β₯I L ) resid nscorrer resid β€˜ 1.00000 [0.97441, <. l nscorrer 0.97441 1.00000 Rank for Variable resid <.0001 The ANOVA Procedure Class Level Information Class Levels Values speed 4 l 2 3 4 Number of observations 64 The AKOVA Procedure Dependent Variable: 1ny #ILA') Sum of Squares Mean Square F Value Pr > F Model 3 21.69169895 7.23056632 156.78}[<.00012 Error Source DF 60 7.64042176 0.12734036 Corrected Total 63 29.33212071 Rβ€”Square Coeff Var Root MSE lny Mean 0.739520 17.84571 0.356848 1.999628 Source , , DF Anova SS Mean Square F Value Pr > E speed 3 21.69169895 7.23056632 56.78 <.0001 The ANOVA Procedure Tukey's Studentized Range (HSD) Test for lny @ NOTE: This test controls the Type I experimentwise error rate. Alpha Error Degrees of Freedom Error Mean Square 0.05 60 0.12734 Critical Value of Studentized Range 3.73709 Minimum Significant Difference IE Comparisons significant at the 0.05 level are indicated by ***. Difference speed Between Comparison Means 0.4288 1.0460 1.5262 β€”0.4288 0.6172 .0974 β€”1.0460 β€”0.6172 0.4802 β€”1.5262 -1.0974 -O.4802 HHHNNNwwwbb-b ll NUblβ€”β€˜UJ-blβ€”β€˜Nnblβ€”JNUJ H Simultaneous 95% Confidence Limits 0.0954 0.7126 1.1928 -O.7622 0.2838 0.7640 -1.3794 -0.9506 0.1468 -l.8596 -1.4308 -0.8l36 The ANOVA Procedure 0.7622 1.3794 1.8596 -0.0954 0.9506 1.4308 -0.7126 ~0.2838 0.8136 -l.1928 -O.764O -O.1468 Bonferroni (Dunn) t Tests for lny *** *** *β€˜ki' *** Julβ€”i- *** *** *** *** *** *** **~k # (7) NOTE: This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than Tukey's for all pairwise comparisons. Alpha Error Degrees of Freedom Error Mean Square Critical Value of t Minimum significant Difference ! 0.3442 Z 0.05 60 0.12734 2.72855 Comparisons significant at the 0.05 level are indicated-by ***. Difference speed Between Comparison Means 4 - 3 0.4288 4 - 2 1.C460 4 - 1 1.5262 3 - 4 β€”0.4288 3 β€” 2 0.6172 3 - 1 1.0974 2 - 4 β€”l.0460 2 β€” 3 β€”0.6172 2 - 1 0.4802 1 - 4 -1.5262 1 - 3 β€”l.0974 1 - 2 β€”0.4002 Simultaneous 95% Confidence Limits 0.0845 0.7017 1.1819 -O.7730 0.2730 0.7531 -l.3902 β€”0.9615 0.1359 -1.8704 β€”1.4416 -0.8244 0.7730 1.3902 1.8704 β€”0.0845 0.9615 1.4416 -O.7017 -0.2730 0.8244 -1.1819 A "1:51 β€˜U. IJJJ. -0.1359 ii IV] dm output 'clear'; options linesize=85 pagesize=35; footnote ' '; data threads; infile 'z:\STAT3504A\chl 8pr17.dat'; input breaks speed obsno; run; proc univariate noprint; var breaks; output out=stats mean=fitted std=s var=ssq; by speed; run; proc print; run; data diagnose; merge threads stats; by speed; resid=breaks—fitted; run; proc plot data=diagnose; plot resid*obsno='*'; by speed; quit; data transform; set threads; lny=iog(breaks); run; ods select ssplots; proc univariate plot; var lny; output out=stat52 mean=fitted std=s var=ssq median=md; by speed; run; proc print; run; data diagnose]; merge transform statsZ; by speed; resid=lny-fitted; dij=abs(lny-md); run; proc plot; plot resid*fitted='*'; quit; proc anova; class speed; model dij=speed; quit; proc rank normal=blom; var resid; ranks nscorerr; by speed; run; proc plot; plot resid*nscorerr='*'; by speed; quit; proc corr nosimple; var resid nscorerr; by speed; run; proc anova data=transform; class speed; model lny=speed; means speed/hon tukey cldiff; quit; dm output 'clear'; options linesize=85; footnote ' '; data firms; infile 'z:\stat3504a\ch1 6pr07 .dat'; input improve expend; V run; proc means noprint; var improve; output out=stats mean=fitted; by expend; run; data diagnose; merge firms stats; by expend; residsa'mprove-fitted; run; A proc rank normal=blom; var resids; ranks nscorerr; run; proc plot; β€˜ . β€˜ β€œ plot resids *nscorerr=’* '; quit; proc corr nosimple; var resids nscorerr; run; The SAS System Plot of residsβ€˜nscorrer. Symbol used is '*'. The SAS System The CORR Procedure 2 Variables: resids nscorrer Pearson Correlation Coefficients, N = 27 Prob > [II under H0: Rho=0 resids nscorrer # Z b (I, ) resids - 1.00000 (0.99197. <. nscorrer 0.99197 1.00000 Rank for Variable resids <.0001 dm output 'clear'; options linesize=85; data employees; input business [email protected]@; cards; 110135014126115110611812316218 2 244 2293 2 3532 2207 2 326 2 533 2 304 2192 2143 2199 317 3149338 35 310131312 3233 331339 run; proc nparlway Wilcoxon; class business; I run; proc rank; var employee; ranks rankemploy; run; proc anova; class business; model rankemploy=business; quit; The SAS System 1 The NPAR1 WAY Procedure Wilcoxon Scores (Rank Sums) for Variable errployee Classified by Variable business Sum of Expected Std De\ Mean business N Scores Under HO Under H21 Score 1 10 108.0 155.0 22.730303 10.80 2 10 242.0 155.0 22.730303; 24.20 10 115.0 155.0 22.730303: 11.50 Kruskal-Wallis Test Chi-Square Β£14.6813 ? DF 2 Pr> Chi-Square [0.0006 l The SAS System The ANOVA Procedure Class Level information Class Levels Values business 3 1 2 3 Number of Observations Read Number of Observations Used The SAS System The ANOVA Procedure 30 30 Dependent Variable: rankemploy Rank for Variable employee Source Model Error Sum of BF Squares Mean Square F Value Pr > F 2 1137.800000 568.900000 113.84 a {.0001 I 27 1109.700000 41.100000 Corrected Total 29 2247.500000 R-Square Coeff Var Root MSE 0.506251 41.36083 6.410928 Source business rankemp oy Mean 1 5.50000 DF Anova SS Mean Square F Value Pr > F 2 1137.800000 568.900000 13.84 <.0001 10 ...
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