Pumpkin Example: Flaws in Diagnostics: Correcting Models
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1 Math Treibergs Pumpkin Example: Flaws in Diagnostics: Correcting Models Name: Example March, 204 From Levine Ramsey & Smidt, Applied Statistics for Engineers and Scientists, Prentice Hall, Upper Saddle River, NJ, 200. The circumference (in cms) and weight (in grams) is recorded for 22 pumpkins. Can one predict the weight from circumference? Data Set Used in this Analysis : # Math Pumpkin Data March, 204 # Treibergs # # From Levine Ramsey & Smidt, Applied Statistics for Engneers and # Scientists, Prentice Hall, Upper saddle River, NJ, 200. # The circumference (in cms) and weight (in grams) is recorded # for 22 pumpkins. Can one predict the weight from circumference? # "Circ" "Weight"
2 R Session: R version 2.3. ( ) Copyright (C) 20 The R Foundation for Statistical Computing ISBN Platform: i38-apple-darwin9.8.0/i38 (32-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type license() or licence() for distribution details. Natural language support but running in an English locale R is a collaborative project with many contributors. Type contributors() for more information and citation() on how to cite R or R packages in publications. Type demo() for some demos, help() for on-line help, or help.start() for an HTML browser interface to help. Type q() to quit R. [R.app GUI.4 (5874) i38-apple-darwin9.8.0] [History restored from /Users/andrejstreibergs/.Rapp.history] > tt=read.table("m3082datapumpkin.txt",header=t) > attach(tt) > names(tt) [] "Circ" "Weight" > ############## SCATTERPLOT OF WEIGHT VS CIRC WITH REGRESSION LINE ###### > f=lm(weight~circ) > abline(f,col=2) > plot(weight~circ, main="scatter Plot of Pumpkin Weight vs. Circumference") > abline(f,col=2) > ############### DIAGNOSTIC PLOTS OF LINEAR MODEL ####################### > layout(matrix(c(,3,2,4),nrow=2)) > plot(f) > ####################### SUMMARY AND ANOVA TABLE FOR LINEAR MODEL ##### > summary(f); anova(f) Call: lm(formula = Weight ~ Circ) Residuals: Min Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) e-09 *** Circ e-4 *** 2
3 --- Signif. codes: 0 *** 0.00 ** 0.0 * Residual standard error: on 2 degrees of freedom Multiple R-squared: ,Adjusted R-squared: F-statistic: 33.7 on and 2 DF, p-value: 4.203e-4 Analysis of Variance Table Response: Weight Df Sum Sq Mean Sq F value Pr(>F) Circ e-4 *** Residuals Signif. codes: 0 *** 0.00 ** 0.0 * > layout() > ############## REGRESSION LOG(WEIGHT) VS LOG(CIRC) ################# > f2=lm(log(weight)~log(circ)) > summary(f2); anova(f2) Call: lm(formula = log(weight) ~ log(circ)) Residuals: Min Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) *** log(circ) e-4 *** --- Signif. codes: 0 *** 0.00 ** 0.0 * Residual standard error: on 2 degrees of freedom Multiple R-squared: ,Adjusted R-squared: F-statistic: 355 on and 2 DF, p-value:.23e-4 Analysis of Variance Table Response: log(weight) Df Sum Sq Mean Sq F value Pr(>F) log(circ) e-4 *** Residuals Signif. codes: 0 *** 0.00 ** 0.0 * > ########### SCATTERPLOT WITH FITTED POWER CURVE ########################## > plot(weight~circ,main="scatter Plot of Pumpkin Weight vs. Circumference") > curve(exp(f2$coefficients[]+f2$coefficients[2]*log(x)),30,8,col=4, add=t) 3
4 > > ############# DIAGNOSTIC PLOT OF LOG-LOG REGRESSION ##################### > layout(matrix(c(,3,2,4),nrow=2)) > plot(f2) > > ################ REMOVE OBSERVATIONS 5 AND FROM DATA ################## > W=Weight[-:-5]; C=Circ[-:-5] > f3=lm(log(w)~log(c)) > summary(f3); anova(f3) Call: lm(formula = log(w) ~ log(c)) Residuals: Min Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) e-05 *** log(c) < 2e- *** --- Signif. codes: 0 *** 0.00 ** 0.0 * Residual standard error: on 9 degrees of freedom Multiple R-squared: 0.978,Adjusted R-squared: F-statistic: on and 9 DF, p-value: < 2.2e- Analysis of Variance Table Response: log(w) Df Sum Sq Mean Sq F value Pr(>F) log(c) < 2.2e- *** Residuals Signif. codes: 0 *** 0.00 ** 0.0 * > > ############### SCATTERPLOT OF DATA WITHOUT OBS 5 AND ############## > layout() > plot(w~c,main="scatter Plot of Pumpkin Wt vs. Circ Omitting Obs 5,") > curve(exp(f3$coefficients[]+f3$coefficients[2]*log(x)),30,8,col=4, add=t) > > ############### DIAGNOSTICS FOR REGRESSION WITHOUT POINTS 5 AND #### > layout(matrix(c(,3,2,4),nrow=2)) > plot(f3) > 4
5 Scatter Plot of Pumpkin Weight vs. Circumference Weight Circ 5
6 Residuals Residuals vs Fitted Normal Q-Q Theoretical Quantiles Scale-Location Residuals vs Leverage Cook's distance Leverage
7 Scatter Plot of Pumpkin Weight vs. Circumference Weight Circ 7
8 Residuals vs Fitted Normal Q-Q Residuals Theoretical Quantiles Scale-Location Residuals vs Leverage Cook's distance Leverage 8
9 Scatter Plot of Pumpkin Wt vs. Circ Omitting Obs 5, W C 9
10 Residuals vs Fitted Normal Q-Q Residuals Theoretical Quantiles Scale-Location Residuals vs Leverage 9 9 Cook's distance Leverage 0
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