1. Suppose you’ve planted 30 tomato plants in your garden, 10 each of three different varieties (labeled
A, B, C), and you want to compare the varieties in terms of the weight of their fruits. However, you
also want to consider the height of the plants. So you weigh (in ounces) one ripe tomato from each
plant, as well as the height of the plant (in meters). Below are the results from a general linear
model on your data:
!
Table 1 – Regression Results
!
Estimate
St. Error
t-statistic
p-value
Intercept
2.98
0.51
5.84
< 0.01
Var_A
-0.78
0.21
-3.71
< 0.01
Var_B
0.41
0.26
1.58
0.13
Height
0.20
0.09
2.22
0.04
!
Here is how you dummy coded your categorical variable (variety of tomato plant):
!
Variable Name!
Var_A
Var_B
Plant A
1
0
Plant B
0
1
Plant C
0
0
!
!
a. Write your overall regression equation predicting fruit weight from tomato variety and height. (4 pts)
!
b. Which assumption would you have failed if you had weighed two fruits from each plant? (1pt)
!
c. Suppose a fruit from a variety A plant that was 0.9 m tall weighed 2.09 oz. What is this tomato’s
residual? (3pt)
!
d. Which variety had the highest mean fruit weight, while controlling for height? (2pts)
2. As part of a larger study to investigate symptoms that mountain climbers experience at high
altitudes, researchers studied the skeletal muscle tissue of a random sample of climbers. The
climbers trained for four weeks on a bicycle, either at a normal oxygen supply or under hypoxic
conditions corresponding to an altitude of 13,000 ft, and trained either at a high or low level of
energy expenditure. The percent change in vascular endothelial growth factor mRNA was measured
for each subject, and all relevant assumptions were met.
!
!
a. Fill in the ANOVA table below. Use either p<0.05 or p>0.05 for the p-values column. (4pt)
Source
df
SS
Oxygen Supply
F
p-value
3,588.6
Energy Expenditure
MS
1,134.6
Interaction
Error
!
Total
10,991.0
59
15,875.3
b. Summarize the results of both main effects and the interaction term, based on the ANOVA table
above. (3pt)
!
!
c. Below is an interaction plot for this analysis. For the main effect of each explanatory variable,
comment on the direct of the relationship with the response variable. (2pt)
Figure 1
Interaction between Oxygen Supply and Energy Expenditure
!
d. Explain how the plot above confirms the results for the interaction term in the ANOVA
table. (1pt)
