Statistics 371 Assignment 12 Supplement Fall 2002 This document describes how to use R to carry out parts of Exercises 11 31 35 on pages 497 498 in the textbook Carry out all of the steps but include in your homework write up only answers to questions 1 Download the data set in 11 31 txt to a textfile 2 Read this data into R Attach the data set so that individual variables may be referred to by name Under Windows you may need to specify a complete path name for the data set something like C My Documents 11 31 txt if you put the downloaded text file in that location beans read table 11 31 txt header T attach beans 3 Make side by side boxplots by group which is the result of a two way classification boxplot split yield group Question 1 Do the groups have similar centers Do the groups have similar amounts of variability 4 Calculate sample sizes sample means and standard deviations for each group The function split partitions the first variable by the categorical levels of the second variable and stores the results in a list The function lapply applies a function to each element of a list lapply split yield group length lapply split yield group mean lapply split yield group sd Question 2 Record these values in a table 5 Carry out a one way ANOVA with yield as the response variable and group as the explanatory variable Show the ANOVA table The command lm fits a linear model of which ANOVA is an example fit1 lm yield group data beans anova fit1 Question 3 Summarize the results of this test in the context of the problem Is the test significant at the 0 05 level 6 Make a plot of the residuals versus the fitted values plot fit1 fitted fit1 resid xlab Fitted Values ylab Residuals abline h 0 Question 4 Refer to the boxplots made previously Does this plot indicate that the assumption of normality might be suspect Does this plot indicate that the assumption of equal variances might be suspect Question 5 Refer to the residual plot Does this plot indicate that variability is related to the mean value 7 Make a normal probability plot of the residuals qqnorm fit1 resid Question 6 Do the residuals look normally distributed 8 Transformations of the response variable often fit the assumption better than data in the original scale Two common transformations that help when the variance seems to be a function of the mean with larger spread in populations with larger means are logarithms and square roots Exercise 11 35 refers to a reciprocal transformation which can make sense in some settings Carry out a one way ANOVA with log yield as the response variable fit2 lm log yield group data beans anova fit2 Bret Larget November 20 2002 Statistics 371 Assignment 12 Supplement Fall 2002 9 Make a plot of the residuals versus fitted values side by side boxplots of log yield and normal probability plots of the residuals plot fit2 fitted fit2 resid xlab Fitted Values ylab Residuals abline h 0 boxplot split log yield group qqnorm fit2 resid Question 7 Do these plots indicate that the variablity within each sample are more equal for the transformed data Bret Larget November 20 2002
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