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HW 9 SOLUTIONS
Regression and Correlation
1. 12.41. The three residual plots, (i), (ii), and (iii), were generated after fitting regression lines to the three
scatterplots, (a), (b), and (c). Which residual plot goes with which scatterplot? How do you know?
Correct:
Scatterplot (b) shows curvature, so it goes with residual plot (ii). In scatterplot (a), the points fan out as X
increases, so this scatterplot goes with residual plot (iii). Finally, there are no unusual features in scatterplot (c),
which goes with residual plot (i).
2. 12.5(modified). Twenty plots, each 10 x 4 meters were randomly chosen in a large field of corn. For each
plot, the plant density (number of plants in the plot) and the mean cob weight (g of grain per cob) were
observed. The results are given in the table.
Plant Density
X
Cob Weight
Y
Plant Density
X
Cob Weight
Y
137
212
173
194
107
241
124
241
132
215
157
196
135
225
184
193
115
250
112
224
103
241
80
257
102
237
165
200
65
282
160
190
149
206
157
208
85
246
119
224
a. Calculate the linear regression of
Y
on
X
.
Correct:
TI84
After entering x’s in L1 and y’s in L2>STAT>TESTS and LinRegTTest>ENTER>Xlist: L1 Ylist: L2
Calculate>ENTER yields Y = 316.376 – 0.7206X
b. Calculate s
Y
and specify the units.
TI84
STAT>CALC>ENTER>L2>ENTER yields s
= 24.954 g
c. Calculate the value of s
YX
and specify the units.
Correct:
TI84
From LinRegTTest output we find S
YX
= 8.619254138 = 8.619 g
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View Full Documentd. Interpret the value of s
YX
in the context of this setting.
Correct:
Predictions of cob weight based on the regression model tend to be off by 8.6 g, on average.
e. Calculate the value of r
2
Correct:
TI84
From LinRegTTest output, we find r
2
= 0.887
f. Interpret the value of r
2
in the context of the setting.
Correct:
88.7% of the variability in grams of grain per cob is explained by variability in the number of plants per plot
g. Now, using the QQplot of the residuals and a residual vs. predicted (fitted) values plot. Use these plots to
comment on the assumptions (that can be checked here).
Correct:
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 Fall '09
 Hendrix
 Correlation

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