EXST7015 Fall2011 Appendix 09

EXST7015 Fall2011 Appendix 09 - Statistical Techniques II...

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Unformatted text preview: Statistical Techniques II Polynomial Regression #1 Appendix 9 Annotated SAS example Page 207 1 dm'log;clear;output;clear'; 2 OPTIONS PS=512 LS=101 NOCENTER NODATE NONUMBER; 3 4 TITLE1 'Appendix09: 10 K race results'; 5 6 filename input 'C:\SAS\Appendix09 MReg-10K Polynomial.DAT'; 7 ODS HTML style=minimal body='C:\SAS\Appendix09 MReg-10K Polynomial.html'; NOTE: Writing HTML Body file: C:\SAS\Appendix09 MReg-10K Polynomial.html 12 13 ***********************************************; 14 *** Finish times in a 10 K race ***; 15 *** Data taken from various sites on the ***; 16 *** internet reporting race results ***; 17 ***********************************************; 18 options ps=256 ls=80 nocenter nodate nonumber; 19 20 data footraces; length hometown $ 23 gender $ 3; infile input 20 ! missover; 21 TITLE1 'EXST7015: Marathon Footrace Example'; 22 input Marathon $ Age gender $ TIME HomeTown $ 35-57; 23 if age eq 99 then age = .; 24 Age2 = age*age; 25 Age3 = age*age*age; 26 Age4 = age*age*age*age; 27 *(apparently 99 represents missing for 5 PA race participants); 28 *---+----1----+----2----+----3----+----4----+----5----+----6; 29 cards; NOTE: The infile INPUT is: File Name=C:\SAS\Appendix09 MReg-10K Polynomial.DAT, RECFM=V,LRECL=256 NOTE: 6150 records were read from the infile INPUT. The minimum record length was 29. The maximum record length was 57. NOTE: Missing values were generated as a result of performing an operation on missing values. Each place is given by: (Number of times) at (Line):(Column). 6 at 24:13 6 at 25:13 6 at 26:13 NOTE: The data set WORK.FOOTRACES has 6150 observations and 8 variables. NOTE: DATA statement used (Total process time): real time 0.01 seconds cpu time 0.01 seconds 29 ! run; 30 ; 31 32 data Vt2002; set footraces; if marathon = 'VT052002'; 33 NOTE: There were 6150 observations read from the data set WORK.FOOTRACES. NOTE: The data set WORK.VT2002 has 1490 observations and 8 variables. NOTE: DATA statement used (Total process time): real time 0.01 seconds cpu time 0.01 seconds 34 proc sort data=Vt2002; by gender; RUN; NOTE: There were 1490 observations read from the data set WORK.VT2002. NOTE: The data set WORK.VT2002 has 1490 observations and 8 variables. NOTE: PROCEDURE SORT used (Total process time): real time 0.00 seconds cpu time 0.00 seconds 35 proc means data=Vt2002; by gender; var age time; run; NOTE: There were 1490 observations read from the data set WORK.VT2002. James P. Geaghan - Copyright 2011 Statistical Techniques II Polynomial Regression #1 Appendix 9 Annotated SAS example Page 208 NOTE: The PROCEDURE MEANS printed page 1. NOTE: PROCEDURE MEANS used (Total process time): real time 0.12 seconds cpu time 0.01 seconds EXST7015: Marathon Footrace Example gender=F The MEANS Procedure Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------------------Age 527 34.4686907 8.6562175 16.0000000 65.0000000 TIME 527 246.7373435 24.4075610 161.3300000 288.4700000 -------------------------------------------------------------------------------gender=M Variable N Mean Std Dev Minimum Maximum -------------------------------------------------------------------------------Age 963 39.9075805 9.3669019 18.0000000 69.0000000 TIME 963 230.7960332 29.3895704 146.4500000 288.3500000 -------------------------------------------------------------------------------- 37 proc glm data=Vt2002; BY gender; 38 TITLE2 'Quartic model - separate by gender'; 39 model time= age age*age age*age*age age*age*age*age; 40 run; NOTE: Interactivity disabled with BY processing. 41 42 options ls=132 ps=65; NOTE: The PROCEDURE GLM printed pages 2-5. NOTE: PROCEDURE GLM used (Total process time): real time 0.12 seconds cpu time 0.04 seconds EXST7015: Marathon Footrace Example Quartic model - separate by gender gender=F The GLM Procedure Number of Observations Read Number of Observations Used 527 527 Dependent Variable: TIME Source Model Error Corrected Total R-Square 0.027665 Coeff Var 9.791630 Source Age Age*Age Age*Age*Age Age*Age*Age*Age DF 4 522 526 Sum of Squares 8669.0277 304684.4440 313353.4717 Root MSE 24.15961 DF 1 1 1 1 Mean Square 2167.2569 583.6867 F Value 3.71 Pr > F 0.0054 F Value 8.34 6.06 0.45 0.00 Pr > F 0.0040 0.0142 0.5026 0.9597 TIME Mean 246.7373 Type I SS 4869.217307 3535.615012 262.700283 1.495088 Mean Square 4869.217307 3535.615012 262.700283 1.495088 James P. Geaghan - Copyright 2011 Statistical Techniques II Polynomial Regression #1 Appendix 9 Source Age Age*Age Age*Age*Age Age*Age*Age*Age Parameter Intercept Age Age*Age Age*Age*Age Age*Age*Age*Age DF 1 1 1 1 Type III SS 36.90443581 8.38438686 0.05552792 1.49508835 Annotated SAS example Page 209 Mean Square 36.90443581 8.38438686 0.05552792 1.49508835 Standard Error 128.7967390 14.4413269 0.5872016 0.0102639 0.0000652 Estimate 294.5241065 -3.6312529 0.0703774 -0.0001001 -0.0000033 t Value 2.29 -0.25 0.12 -0.01 -0.05 F Value 0.06 0.01 0.00 0.00 Pr > F 0.8016 0.9046 0.9922 0.9597 Pr > |t| 0.0226 0.8016 0.9046 0.9922 0.9597 EXST7015: Marathon Footrace Example Quartic model - separate by gender gender=M Number of Observations Read Number of Observations Used 963 963 Dependent Variable: TIME Source Model Error Corrected Total R-Square 0.038802 DF 4 958 962 Coeff Var 12.51054 Sum of Squares 32241.5904 798682.8797 830924.4700 Root MSE 28.87383 Mean Square 8060.3976 833.6982 F Value 9.67 Pr > F <.0001 TIME Mean 230.7960 Source Age Age*Age Age*Age*Age Age*Age*Age*Age DF 1 1 1 1 Type I SS 18395.26482 13294.83706 170.13913 381.34935 Mean Square 18395.26482 13294.83706 170.13913 381.34935 F Value 22.06 15.95 0.20 0.46 Pr > F <.0001 <.0001 0.6516 0.4990 Source Age Age*Age Age*Age*Age Age*Age*Age*Age DF 1 1 1 1 Type III SS 294.2592048 377.4747067 419.6657057 381.3493517 Mean Square 294.2592048 377.4747067 419.6657057 381.3493517 F Value 0.35 0.45 0.50 0.46 Pr > F 0.5526 0.5012 0.4782 0.4990 Parameter Intercept Age Age*Age Age*Age*Age Age*Age*Age*Age Estimate 163.8853268 8.0557673 -0.3437339 0.0058696 -0.0000329 Standard Error 130.3788678 13.5595824 0.5108377 0.0082729 0.0000487 t Value 1.26 0.59 -0.67 0.71 -0.68 Pr > |t| 0.2091 0.5526 0.5012 0.4782 0.4990 42 ! proc plot data=Vt2002; by gender; plot time*age; 43 TITLE2 'Scatter plot'; run; 44 options ps=256 ls=80; 45 NOTE: There were 1490 observations read from the data set WORK.VT2002. NOTE: The PROCEDURE PLOT printed pages 6-7. NOTE: PROCEDURE PLOT used (Total process time): James P. Geaghan - Copyright 2011 Statistical Techniques II Polynomial Regression #1 Appendix 9 Annotated SAS example Page 210 gender=F Plot of TIME*Age. Legend: A = 1 obs, B = 2 obs, etc. TIME | 300 + | | | | A A A A B A | A A A A A A A A A A A A | B A A B B A A A A B A A A B A 280 + A A A A A A B A A B A A A A A | A A A A A A A A A A A A A | A B A A B B A A A A A A A A | A A C A A A A A A A A A A A | A A A B B A C B B A A A A A A | A A B B A A A A B A A A B A A A A A | A B B B A A A A B A 260 + B A B A C C B A A A A A B A A A | A A A B A A C A A A A A A A A A A | A A B A A A A A A A A A A C B A A A | A A A B A C B B A A A A A A | C A A A B A A A A A A A | A B A A A B A B A C B B B A A A A A | A B A B A A C B C B C A A A A A 240 + A A C B A C C A C B A A A B | B A B B B B A C B A A B D A B A A | B B B B B A A A A C A | A A A B B A A B A A C | A A B B A B B A A A A B A | A A A A B B A A B A A A | A A A A A A A A A A A 220 + A A A B A A A A A B A A | A A A A A A B A A A A A B A | A A A A A A A A A A | B A B A A | A A A A A A | C A A A A A | A A A 200 + A A | B A | A A | A A | A | A A | A 180 + A | A | A | | A | | A 160 + A | ---+---------+---------+---------+---------+---------+---------+---------+---------+---------+---------+-15 20 25 30 35 40 45 50 55 60 65 Age gender=M Plot of TIME*Age. Legend: A = 1 obs, B = 2 obs, etc. TIME | | 300 + | | | A | A A A A A B A B A A A A | A A A A A A A A B A A A A A D A B A 280 + B A A A A A A A C A A A A A A A | A A A A A A A A A B A A A C A A A A A A A | A A A B A A A A C A | A A A B B A A A A A A A A | B B A A B B B B C A A A B C B A A A A A B A | A A A A B C A B A A A B B A A B A B A A 260 + A A A A B A B A B B A B A A A B A | B A A A A A A B B C A C A B C A B B A A A A A B | B A C B A A C A B A B A B C B C A A A A A A A | A A B B A A B A B B B B A A A B B A A | A A A A B A D A A C A A A A C | A A C B A A A B A B A A A A B A 240 + A A A A A A B A B A A A C C A A B A A A | A A A C C A B A B C C A A C A B C B D B C A A B A A | A A A A B A A B A A A C B B A A B B A A C B A A A A | A A D B A A B B A C A B B A E A C B B A A C B A B A B A | A B B C A A B A A B C B B A A C B A B A B | A A A A A A B C A C A C C B A E B B A A A B A 220 + B A A A A B C A B D A A B A B A A A B A B A A A A | A A A A C A A A C A C A A B A B C B A B A A A B A | A B A B C C A A A A A B A A A A A B A A A A B A A | A A A A B B A B C B D C A C B A C A C B A B B A | A A B A A B B A A A A B B A B C A A A B A B B A A | B A A A A D A A B D A A A B B B B A 200 + A A A A A A A C A A B D B C A B | A A A D A B A A C E A A B B A B A A | A B A C B A A B A A A | A A A B B B A D A A A A | A A A A A A A A A A | A A A B A B A A A 180 + A B A A A A A B C A A A A | A A A A A B A A | A A A A A A | A A A A A A | A A | A A A 160 + A | A | A | B | A | 140 + | ---+----------+----------+----------+----------+----------+----------+----------+----------+----------+----------+----------+-15 20 25 30 35 40 45 50 55 60 65 70 Age 46 proc glm data=Vt2002; BY gender; 47 TITLE2 'Quadratic model - separate by gender'; 48 model time= age age*age; 49 output out=resid p=pred r=resid; 50 run; NOTE: Interactivity disabled with BY processing. 51 James P. Geaghan - Copyright 2011 Statistical Techniques II Polynomial Regression #1 Appendix 9 Annotated SAS example Page 211 NOTE: The data set WORK.RESID has 1490 observations and 10 variables. NOTE: The PROCEDURE GLM printed pages 8-11. NOTE: PROCEDURE GLM used (Total process time): real time 0.09 seconds cpu time 0.01 seconds EXST7015: Marathon Footrace Example Quadratic model - separate by gender gender=F The GLM Procedure Number of Observations Read Number of Observations Used 527 527 Dependent Variable: TIME Source Model Error Corrected Total R-Square 0.026822 DF 2 524 526 Coeff Var 9.777162 Sum of Squares 8404.8323 304948.6394 313353.4717 Root MSE 24.12391 Mean Square 4202.4162 581.9631 F Value 7.22 Pr > F 0.0008 TIME Mean 246.7373 Source Age Age*Age DF 1 1 Type I SS 4869.217307 3535.615012 Mean Square 4869.217307 3535.615012 F Value 8.37 6.08 Pr > F 0.0040 0.0140 Source Age Age*Age DF 1 1 Type III SS 2411.409218 3535.615012 Mean Square 2411.409218 3535.615012 F Value 4.14 6.08 Pr > F 0.0423 0.0140 Parameter Intercept Age Age*Age Standard Error 15.35406824 0.86794473 0.01178890 Estimate 270.9394749 -1.7667692 0.0290575 t Value 17.65 -2.04 2.46 Pr > |t| <.0001 0.0423 0.0140 gender=M The GLM Procedure Number of Observations Read Number of Observations Used 963 963 Dependent Variable: TIME Source Model Error Corrected Total R-Square 0.038138 Source Age Age*Age Coeff Var 12.50182 DF 2 960 962 Sum of Squares 31690.1019 799234.3682 830924.4700 Root MSE 28.85370 DF 1 1 Mean Square 15845.0509 832.5358 F Value 19.03 Pr > F <.0001 F Value 22.10 15.97 Pr > F <.0001 <.0001 TIME Mean 230.7960 Type I SS 18395.26482 13294.83706 Mean Square 18395.26482 13294.83706 James P. Geaghan - Copyright 2011 Statistical Techniques II Polynomial Regression #1 Appendix 9 Source Age Age*Age Parameter Intercept Age Age*Age DF 1 1 Estimate 265.6026299 -2.3002662 0.0339182 Type III SS 9002.09673 13294.83706 Standard Error 13.97817068 0.69953221 0.00848775 Annotated SAS example Page 212 Mean Square 9002.09673 13294.83706 t Value 19.00 -3.29 4.00 F Value 10.81 15.97 Pr > F 0.0010 <.0001 Pr > |t| <.0001 0.0010 <.0001 EXST7015: Marathon Footrace Example Quadratic model - separate by gender gender=F The UNIVARIATE Procedure Variable: resid Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 527 0 24.0780038 -0.4309211 304948.639 . Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean 527 0 579.750265 0.01054677 304948.639 1.04885432 Basic Statistical Measures Location Variability Mean 0.00000 Std Deviation 24.07800 Median -0.02799 Variance 579.75026 Mode -5.17259 Range 127.23008 Interquartile Range 33.63303 NOTE: The mode displayed is the smallest of 2 modes with a count of 2. Tests for Location: Mu0=0 Test -StatisticStudent's t t 0 Sign M -0.5 Signed Rank S 2274 Tests for Normality Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling -----p Value-----Pr > |t| 1.0000 Pr >= |M| 1.0000 Pr >= |S| 0.5161 --Statistic--W 0.978409 D 0.048239 W-Sq 0.209919 A-Sq 1.808508 -----p Value-----Pr < W <0.0001 Pr > D <0.0100 Pr > W-Sq <0.0050 Pr > A-Sq <0.0050 Quantiles (Definition 5) Quantile Estimate 100% Max 44.1002947 99% 41.2680712 95% 36.7724101 90% 31.6869738 75% Q3 19.3687293 50% Median -0.0279864 25% Q1 -14.2642995 10% -31.3097884 5% -39.3543808 1% -65.5097053 James P. Geaghan - Copyright 2011 Statistical Techniques II Polynomial Regression #1 0% Min Appendix 9 Annotated SAS example Page 213 -83.1297884 Extreme Observations ------Lowest----Value Obs -83.1298 1 -81.7112 2 -79.5176 3 -69.7239 4 -66.1496 5 -----Highest----Value Obs 41.3237 519 41.7093 526 41.8988 523 43.0561 522 44.1003 525 Histogram Boxplot 42.5+**** .*************** .************** .*************** .*************** 17.5+******************* .*************** .**************** .********************* .********************** -7.5+**************************** .****************** .************ .********** .************** -32.5+*********** .****** .***** .** .*** -57.5+* .* .** . .* -82.5+* ----+----+----+----+----+--* may represent up to 2 counts 7 30 27 29 30 38 29 31 42 44 56 35 23 20 28 21 11 9 3 5 1 2 3 1 2 | | | | | +-----+ | | | | | + | *-----* | | +-----+ | | | | | | | | | | 0 0 0 Normal Probability Plot 42.5+ ++ **** | ******** | **** | **** | ***+ 17.5+ ***+ | **+ | *** | *** | *** -7.5+ **** | *** | ** | *** | *** -32.5+ **** | ** | ** | +* | +*** -57.5+ ++ * |+ * |*** | |* -82.5+* +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 James P. Geaghan - Copyright 2011 Statistical Techniques II Polynomial Regression #1 Appendix 9 Annotated SAS example Page 214 54 proc glm data=Vt2002; 55 TITLE2 'Quadratic model - combined for gender'; 56 model time= age age*age; 57 run; 58 NOTE: The PROCEDURE GLM printed pages 15-16. NOTE: PROCEDURE GLM used (Total process time): real time 0.12 seconds cpu time 0.06 seconds NOTE: SAS Institute Inc., SAS Campus Drive, Cary, NC USA 27513-2414 NOTE: The SAS System used: real time 2.04 seconds cpu time 0.93 seconds EXST7015: Marathon Footrace Example Quadratic model - separate by gender gender=M The UNIVARIATE Procedure Variable: resid Moments N Mean Std Deviation Skewness Uncorrected SS Coeff Variation 963 0 28.8236874 -0.0312121 799234.368 . Sum Weights Sum Observations Variance Kurtosis Corrected SS Std Error Mean Basic Statistical Measures Location Variability Mean 0.0000 Std Deviation Median -0.2431 Variance Mode -30.4263 Range Interquartile Range 963 0 830.804957 -0.5945171 799234.368 0.92883035 28.82369 830.80496 140.51558 43.82228 NOTE: The mode displayed is the smallest of 4 modes with a count of 2. Tests for Location: Mu0=0 Test -StatisticStudent's t t 0 Sign M -1.5 Signed Rank S 40 Tests for Normality Test Shapiro-Wilk Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling -----p Value-----Pr > |t| 1.0000 Pr >= |M| 0.9486 Pr >= |S| 0.9963 --Statistic--W 0.990265 D 0.034784 W-Sq 0.243216 A-Sq 1.807209 Quantiles (Definition 5) Quantile Estimate 100% Max 60.239251 99% 56.676872 95% 48.261815 90% 39.982967 75% Q3 22.314093 -----p Value-----Pr < W <0.0001 Pr > D <0.0100 Pr > W-Sq <0.0050 Pr > A-Sq <0.0050 50% Median 25% Q1 10% 5% 1% 0% Min -0.243128 -21.508185 -36.054976 -48.319754 -63.901010 -80.276333 James P. Geaghan - Copyright 2011 Statistical Techniques II Polynomial Regression #1 Extreme Observations ------Lowest----Value Obs -80.2763 528 -77.5063 529 -77.3648 531 -75.5563 530 -71.2263 532 Appendix 9 Annotated SAS example Page 215 -----Highest----Value Obs 59.2996 1481 59.3902 1485 60.0418 1490 60.1537 1480 60.2393 1489 Histogram Boxplot 65+* .************* .******************* 35+************************ .********************************* .**************************** 5+******************************************** .*************************************** .*************************************** -25+*********************************** .************************ .************ -55+********** .*** .** -85+* ----+----+----+----+----+----+----+----+---* may represent up to 3 counts 3 37 56 72 97 83 132 115 116 105 71 34 30 7 4 1 | | | | +-----+ | | | + | *-----* | | +-----+ | | | | | | Normal Probability Plot 65+ ++++* | ********* | ***** 35+ ***** | ****+ | *** 5+ ***** | **** | **** -25+ ***** | ***** | **** -55+ ****** |***++ |* -85+* +----+----+----+----+----+----+----+----+----+----+ -2 -1 0 +1 +2 EXST7015: Marathon Footrace Example Quadratic model - combined for gender The GLM Procedure Number of Observations Read Number of Observations Used 1490 1490 James P. Geaghan - Copyright 2011 Statistical Techniques II Polynomial Regression #1 Appendix 9 Annotated SAS example Page 216 Dependent Variable: TIME Source Model Error Corrected Total R-Square 0.020147 DF 2 1487 1489 Coeff Var 12.04521 Sum of Squares 24797.393 1206036.845 1230834.237 Root MSE 28.47900 Mean Square 12398.696 811.054 F Value 15.29 Pr > F <.0001 TIME Mean 236.4343 Source Age Age*Age DF 1 1 Type I SS 4204.04870 20593.34390 Mean Square 4204.04870 20593.34390 F Value 5.18 25.39 Pr > F 0.0229 <.0001 Source Age Age*Age DF 1 1 Type III SS 17577.43790 20593.34390 Mean Square 17577.43790 20593.34390 F Value 21.67 25.39 Pr > F <.0001 <.0001 Parameter Intercept Age Age*Age Estimate 279.1882715 -2.4976510 0.0340045 Standard Error 10.28225940 0.53651116 0.00674835 t Value 27.15 -4.66 5.04 Pr > |t| <.0001 <.0001 <.0001 General linear hypothesis test of the need for separate models for the two genders. The test compares models separated by gender (6 parameter full model) versus a model with gender combined (3 parameter reduced model). Source d.f. SSE MSE F P>F Reduced model 1487 1206036.85 Full model 1484 1104183.01 Difference 3 101853.84 33951.2791 45.6298 3.320764E-28 Full model 1484 1104183.01 744.0586 45 GOPTIONS DEVICE=CGMflwa GSFMODE=REPLACE GSFNAME=OUT NOPROMPT noROTATE 46 ftext='TimesRoman' ftitle='TimesRoman' htext=1 htitle=1 ctitle=black ctext=black; 47 48 GOPTIONS GSFNAME=OUT1; 49 FILENAME OUT1 'C:\SAS\MarathonReg1VT.CGM'; 50 PROC GPLOT DATA=TWO; BY SEX; 51 TITLE1 font='TimesRoman' H=1 'Polynomial Regression Example'; 52 TITLE2 font='TimesRoman' H=1 'Marathon race'; 53 PLOT TIME*AGE=1 TIME*AGE=2 TIME*AGE=3 / overlay HAXIS=AXIS1 VAXIS=AXIS2; 54 AXIS1 LABEL=(font='TimesRoman' H=1 'Age (years)') WIDTH=1 MINOR=(N=1) 55 VALUE=(font='TimesRoman' H=1) color=black ORDER=10 TO 70 BY 10; 56 AXIS2 LABEL=(ANGLE=90 font='TimesRoman' H=1 'Time to run marathon (min)') 57 WIDTH=1 VALUE=(font='TimesRoman' H=1) MINOR=(N=5) color=black 58 ORDER=125 TO 325 BY 25; 59 SYMBOL1 color=red V=None I=RQclm95 L=1 MODE=INCLUDE; 60 SYMBOL2 color=green V=None I=RQcli95 L=1 MODE=INCLUDE; 61 SYMBOL3 color=blue V=dot I=None L=1 MODE=INCLUDE; RUN; NOTE: Regression equation : TIME = 270.9395 - 1.766769*Age + 0.029057*Age^2. NOTE: Regression equation : TIME = 270.9395 - 1.766769*Age + 0.029057*Age^2. NOTE: Foreground color BLACK same as background. Part of your graph may not be visible. James P. Geaghan - Copyright 2011 Statistical Techniques II Polynomial Regression #1 Appendix 9 Annotated SAS example Page 217 NOTE: 404 RECORDS WRITTEN TO C:\SAS\MarathonReg1VT.CGM NOTE: Regression equation : TIME = 265.6026 - 2.300266*Age + 0.033918*Age^2. NOTE: Regression equation : TIME = 265.6026 - 2.300266*Age + 0.033918*Age^2. NOTE: Foreground color BLACK same as background. Part of your graph may not be visible. NOTE: 713 RECORDS WRITTEN TO C:\SAS\MarathonReg1VT.CGM 62 63 64 65 66 67 68 69 **** V = "dot" would place a dot for each point; **** I = for regression: R requests fitted regression line, L, Q or C requests Linear, Quadraatic or cubic, CLM or CLI requests corresponding confidence interval and 95 specifies alpha level for CI (any value from 50 to 99); **** I = for categories: requests STD (std dev) 1 (1 width, 2 or 3) M (of mean=std err) J (join means of bars) t (add top & bottom hash) p (use pooled variance); **** Other options for categories: omit M=std dev, use B to get bar for min/max; RUN: 300 275 250 225 200 Marathon race sex=F 175 150 Polynomial Regression Example 125 10 20 325 Time to run marathon (min) Time to run marathon (min) 325 30 40 Age (years) 50 60 70 Polynomial Regression Example 300 275 250 225 200 175 Marathon race 150 sex=M 125 10 20 30 40 Age (years) 50 60 70 James P. Geaghan - Copyright 2011 ...
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This note was uploaded on 12/29/2011 for the course EXST 7015 taught by Professor Wang,j during the Fall '08 term at LSU.

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