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# hw3 - Stat 512 Assignment 3 Due Monday March 29 1 Adapted...

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Stat 512 - Assignment 3 Due Monday, March 29 1. Adapted from Kuehl, Exercise 6.3 . A study was conducted to assess the effect of temperature on the shrinkage of dyed fabric. Four temperatures were ap- plied to four different fabrics in a 4 × 4 crossed design with n = 2 replications per cell. The response variable is the percent shrinkage. The data are shown below. Temperature Fabric 210 F 215 F 220 F 225 F 1 1.8, 2.1 2.0, 2.1 4.6, 5.0 7.5, 7.9 2 2.2, 2.4 4.2, 4.0 5.4, 5.6 9.8, 9.2 3 2.8, 3.2 4.4, 4.8 8.7, 8.4 13.2, 13.0 4 3.2, 3.6 3.3, 3.5 5.7, 5.8 10.9, 11.1 Data for this problem are available in the file FabricShrink.txt . The data can be entered into R by typing > FabricShrink <- read.table("FabricShrink.txt", header=T) at the R command prompt. Then be sure to change the variables fabric and temp into factors. (a) Plot the response variable y versus each factor, and comment on what you see. (b) Fit the two-way ANOVA model using y as the response. Are the effects of the two factors additive? (c) Compute the mean for each level of temp (the ¯ Y · j · ’s) and plot them. Decompose the SS for main effect of temp into independent SS’s corre- spnding to linear, quadratic and cubic contrasts. Which of these trends are significant?

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hw3 - Stat 512 Assignment 3 Due Monday March 29 1 Adapted...

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