A critical study funded by the National Science Foundation with an additional grant from the American
Military Research Administration measured the deliciousness of various foods cooked for exactly 20
minutes in an array of oven times. This was repeated across three different baked items, namely
cookies, bread rolls, and pretzels.
The data set is located at http://www.uwyo.edu/crawford/Datasets/deliciousness.txt
1) Use the appropriate method (fix any problems) to test whether
oven temperature affects the deliciousness.
a. What is the p-value? 0.651
b. What would you conclude? Based on this analysis we cannot show a relationship
between deliciousness and oventemp
2) Now use a model with deliciousness ~ goods + oventemp.
a. Write the prediction equation for cookies 110.289-.003397*oventemp
b. Write the prediction equation for bread 112.4346-.003397*oventemp
c. Write the prediction equation for pretzels 111.191-.003397*oventemp
d. What is the standard deviation of the residuals for the model? 8.539
e. What do you think of the residual plot? Looks ok
3) Now use a model with goods, oventemp and goods*oventemp to predict deliciousness.
a.
b.
c.
d.
e.
Write the prediction equation for cookies 122.71-.039543*oventemp
Write the prediction equation for bread 113.46-.006277*bread
Write the prediction equation for pretzels 100.866+0.025222*oventemp
What is the standard deviation for the model? 8.263
What do you think of the residual plot? Looks ok
4) Using α=0.05 as the hard cutoff for including a term in the model find the simplest prediction
equation (if something is not significant, then set it to zero)
a. Write the prediction equation for cookies 113.46-.039543*oventemp
b. Write the prediction equation for bread 113.46
c. Write the prediction equation for pretzels 100.866+0.025222*oventemp
5) If you want to maximize deliciousness (within the range of oven temperatures in the study) what
should you do? Either do cookies at a low oven temp, or pretzels at a high oven temp (pretzels
will go higher)
6) For a bake sale I need to bring something with a deliciousness level of 110. What should I do?
Offer 3 possibilities.
Get a new goal
Freeze the cookie dough
Bake pretzels at 362
7) List at least two questions about the validity of this study that you would want to ask before 144
billion humanitarian dollars are spent by the government based on this research?
How are you measuring “deliciousness”?
Do we want to bake these three all at 20 minutes?
What why?
del <read.table("C:\\Users\\scrawfo8\\AppData\\Local\\Temp\\RtmpA9Oy6J\\data1780499d7249",
header=TRUE, quote="\"")
plot(del$deliciousness~del$oventemp)
del[del$goods=="bread",3]<-"Bread"
del[del$goods=="Cookies",2]<-del[del$goods=="Cookies",2]*1000
plot(del$deliciousness~del$oventemp)
summary(lm(deliciousness~oventemp,data=del))
summary(lm(deliciousness~oventemp+goods,data=del))
par(mfrow=c(2,2))
plot(lm(deliciousness~oventemp+goods,data=del))
summary(lm(deliciousness~oventemp*goods,data=del))
plot(lm(deliciousness~oventemp*goods,data=del))
par(mfrow=c(1,1))
hist(del$oventemp)