ࡱ> RTMNOPQq` FbjbjqPqP Ė::Y=B@@@@@@@DbbbLcDc~:ddeeeeTreDe$>~@~@~@~@~@~@~$had~@leelld~@@eey~zzzl@e@e>~zl>~zz@@zed ZIbrz2{ ~0~zVxz@zdeglzDi$hjeeed~d~pz^eee~llll6:D(:@@@@@@ Transformations Using SAS /*Use the permanent SAS baseball data set*/ libname sasdata2 "d:\sasdata2"; title "Baseball Data Set"; proc means data=sasdata2.baseball; run; Baseball Data Set The MEANS Procedure Variable Label N Mean Std Dev Minimum --------------------------------------------------------------------------------------------- no_atbat Times at Bat in 1986 322 390.0745342 143.5958352 127.0000000 no_hits Hits in 1986 322 103.3975155 44.1795091 31.0000000 no_home Home Runs in 1986 322 11.1024845 8.6987696 0 no_runs Runs in 1986 322 52.2173913 25.0573661 12.0000000 no_rbi RBIs in 1986 322 49.3726708 25.5011624 8.0000000 no_bb Walks in 1986 322 39.8571429 21.0959408 3.0000000 yr_major Years in the Major Leagues 322 7.6801242 4.9697066 1.0000000 cr_atbat Career times at bat 322 2763.08 2328.48 166.0000000 cr_hits Career Hits 322 747.6863354 654.7876194 34.0000000 cr_home Career Home Runs 322 74.0900621 90.0651268 0 cr_runs Career Runs 322 374.2857143 336.4250377 18.0000000 cr_rbi Career RBIs 322 347.6149068 338.7903452 9.0000000 cr_bb Career Walks 322 273.3944099 273.6253716 8.0000000 no_outs Put Outs in 1986 322 288.9937888 280.6566732 0 no_assts Assists in 1986 322 106.9161491 136.8524541 0 no_error Errors in 1986 322 8.0403727 6.3683591 0 salary 1987 Salary in $ Thousands 263 535.9258821 451.1186807 67.5000000 --------------------------------------------------------------------------------------------- Variable Label Maximum ------------------------------------------------------ no_atbat Times at Bat in 1986 687.0000000 no_hits Hits in 1986 238.0000000 no_home Home Runs in 1986 40.0000000 no_runs Runs in 1986 130.0000000 no_rbi RBIs in 1986 121.0000000 no_bb Walks in 1986 105.0000000 yr_major Years in the Major Leagues 24.0000000 cr_atbat Career times at bat 14053.00 cr_hits Career Hits 4256.00 cr_home Career Home Runs 548.0000000 cr_runs Career Runs 2165.00 cr_rbi Career RBIs 1659.00 cr_bb Career Walks 1566.00 no_outs Put Outs in 1986 1378.00 no_assts Assists in 1986 492.0000000 no_error Errors in 1986 32.0000000 salary 1987 Salary in $ Thousands 2460.00 ------------------------------------------------------ proc freq data=sasdata2.baseball; tables team league division; run; Baseball Data Set The FREQ Procedure Team at the end of 1986 Cumulative Cumulative team Frequency Percent Frequency Percent ----------------------------------------------------------------- Atlanta 11 3.42 11 3.42 Baltimore 15 4.66 26 8.07 Boston 10 3.11 36 11.18 California 13 4.04 49 15.22 Chicago 24 7.45 73 22.67 Cincinnati 12 3.73 85 26.40 Cleveland 12 3.73 97 30.12 Detroit 12 3.73 109 33.85 Houston 11 3.42 120 37.27 KansasCity 14 4.35 134 41.61 LosAngeles 14 4.35 148 45.96 Milwaukee 14 4.35 162 50.31 Minneapolis 13 4.04 175 54.35 Montreal 14 4.35 189 58.70 NewYork 24 7.45 213 66.15 Oakland 12 3.73 225 69.88 Philadelphia 12 3.73 237 73.60 Pittsburgh 11 3.42 248 77.02 SanDiego 13 4.04 261 81.06 SanFrancisco 14 4.35 275 85.40 Seattle 12 3.73 287 89.13 StLouis 11 3.42 298 92.55 Texas 13 4.04 311 96.58 Toronto 11 3.42 322 100.00 League at the end of 1986 Cumulative Cumulative league Frequency Percent Frequency Percent ------------------------------------------------------------- American 175 54.35 175 54.35 National 147 45.65 322 100.00 Division at the end of 1986 Cumulative Cumulative division Frequency Percent Frequency Percent ------------------------------------------------------------- East 157 48.76 157 48.76 West 165 51.24 322 100.00 proc univariate data=sasdata2.baseball; var salary; histogram; qqplot / normal(mu=est sigma=est); run;   goptions reset=all; goptions device=win target=winprtm; symbol1 color=black value=dot height=.5 interpol=rl; title "Salary vs. Number of Hits in Previous Year"; proc gplot data=sasdata2.baseball; plot salary * no_hits; run; quit;  proc reg data=sasdata2.baseball; model salary = no_hits; plot rstudent.*predicted.; output out=regdata1 p=predict r=resid rstudent=rstudent; run; quit; Salary vs. Number of Hits in Previous Year The REG Procedure Model: MODEL1 Dependent Variable: salary 1987 Salary in $ Thousands Number of Observations Read 322 Number of Observations Used 263 Number of Observations with Missing Values 59 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 13402507 13402507 87.63 <.0001 Error 261 39916605 152937 Corrected Total 262 53319113 Root MSE 391.07184 R-Square 0.2514 Dependent Mean 535.92588 Adj R-Sq 0.2485 Coeff Var 72.97125 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Pr > |t| Intercept Intercept 1 -25.27489 64.61726 -0.39 0.6960 no_hits Hits in 1986 1 5.14110 0.54919 9.36 <.0001  proc univariate data=regdata1; var rstudent; histogram; qqplot / normal(mu=est sigma=est); run;   /*Natural Log Transformation is indicated (Lambda = 0)*/ title "Use Proc Transreg to decide on a transformation of Y"; proc transreg data=sasdata2.baseball; model boxcox(salary/geo) = linear (no_hits); run; Use Proc Transreg to decide on a transformation of Y The TRANSREG Procedure Transformation Information for BoxCox(salary) Lambda R-Square Log Like -3.00 0.11 -2181.74 -2.75 0.11 -2098.39 -2.50 0.12 -2017.58 -2.25 0.12 -1939.68 -2.00 0.13 -1865.19 -1.75 0.14 -1794.69 -1.50 0.15 -1728.90 -1.25 0.16 -1668.67 -1.00 0.17 -1615.03 -0.75 0.19 -1569.17 -0.50 0.21 -1532.43 -0.25 0.23 -1506.23 0.00 + 0.24 -1491.97 * 0.25 0.25 -1490.84 < 0.50 0.26 -1503.56 0.75 0.26 -1530.13 1.00 0.25 -1569.82 1.25 0.24 -1621.22 1.50 0.22 -1682.60 1.75 0.20 -1752.22 2.00 0.18 -1828.50 2.25 0.16 -1910.17 2.50 0.15 -1996.19 2.75 0.13 -2085.81 3.00 0.12 -2178.41 < - Best Lambda * - Confidence Interval + - Convenient Lambda TRANSREG MORALS Algorithm Iteration History for BoxCox(salary) Iteration Average Maximum Criterion Number Change Change R-Square Change Note ------------------------------------------------------------------------- 1 0.24731 3.25531 0.20621 2 0.00000 0.00000 0.39688 0.19067 Converged Algorithm converged. /*Create the natural log of salary*/ data baseball2; set sasdata2.baseball; log_salary = log(salary+1); run; goptions reset=all; goptions device=win target=winprtm; symbol1 color=black value=dot height=.5 interpol=rl; title "Log of Salary vs. Number of Hits"; proc gplot data=baseball2; plot log_salary * no_hits; run; quit;  proc reg data=baseball2; model log_salary = no_hits; plot rstudent.*predicted.; output out=regdata2 p=predict r=resid rstudent=rstudent; run; quit; Log of Salary vs. Number of Hits The REG Procedure Model: MODEL1 Dependent Variable: log_salary Number of Observations Read 322 Number of Observations Used 263 Number of Observations with Missing Values 59 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 49.86811 49.86811 83.57 <.0001 Error 261 155.74398 0.59672 Corrected Total 262 205.61209 Root MSE 0.77248 R-Square 0.2425 Dependent Mean 5.93114 Adj R-Sq 0.2396 Coeff Var 13.02408 Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Pr > |t| Intercept Intercept 1 4.84862 0.12764 37.99 <.0001 no_hits Hits in 1986 1 0.00992 0.00108 9.14 <.0001 proc univariate data=regdata2; var rstudent; histogram; qqplot / normal(mu=est sigma=est); run;   /*Try to understand the bimodal residuals ODS or INSIGHT*/ ods graphics; ods rtf file="d:\salary_regression.rtf"; title "Log Salary vs Number of Hits and Years in Majors"; proc reg data=baseball2; model log_salary = no_hits yr_major / partial; plot rstudent.*predicted.; output out=regdata3 p=predict r=resid rstudent=rstudent; run; quit; ods rtf close; tc "Reg " \f C \l 1tc "MODEL1 " \f C \l 2tc "Fit " \f C \l 3tc " " \f C \l 4tc "Number of Observations " \f C \l 5Number of Observations Read322Number of Observations Used263Number of Observations with Missing Values59 tc "Analysis of Variance " \f C \l 5Analysis of VarianceSourceDFSumof SquaresMean SquareF ValuePr>FModel2115.4241357.71206166.38<.0001Error26090.187970.34688Corrected Total262205.61209 tc "Fit Statistics " \f C \l 5Root MSE0.58896R-Square0.5614Dependent Mean5.93114Adj R-Sq0.5580Coeff Var9.93000 tc "Parameter Estimates " \f C \l 5Parameter EstimatesVariableLabelDFParameter EstimateStandard ErrortValuePr>|t|InterceptIntercept14.075600.1123936.26<.0001no_hitsHits in 198610.009930.0008270912.00<.0001yr_majorYears in the Major Leagues10.104420.0076013.75<.0001 tc "Observation-wise Statistics " \f C \l 3tc " " \f C \l 4tc "Diagnostic Plots " \f C \l 5tc "Fit Diagnostics " \f C \l 6 tc "Residual Plots " \f C \l 6 tc "Partial Residual Plots " \f C \l 3tc "log_salary " \f C \l 4tc "Panel 1 " \f C \l 5 tc "Plots " \f C \l 3tc "RSTUDENT*PRED " \f C \l 4      DATE \@ "hh:mm dddd, MMMM dd, yyyy " 08:07 Tuesday, February 06, 2007  PAGE 9  DATE \@ "hh:mm dddd, MMMM dd, yyyy " 08:07 Tuesday, February 06, 2007  PAGE 11   DATE \@ 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