Solutions to even numbered problems in the suggested homeworks :
Chapter 12
12.12a. Since the correlation coeﬃcient of height (with weight) is highest compared to that between
(%BF, weight) and (age, weight), we conclude that height is the best predictor of weight. Here we can
directly compare the correlations because r (correlation coeﬃcient) doesnot depend on units.
b. This is because, if we add a new explanatory variable to a regression, the
R
2
value either gets larger
or at worst, stays the same (if the new explanatory variable is useless).
c. No, age doesnot help us in predicting weight because on adding it,
R
2
increases by only 1%(66% to
67%) (i.e the prediction error decreases by only 1%) which is negligible.
12.22a. The steps for the signiﬁcance test are as follows :
1. Assumptions : Please see my notes. Is the sample random or convenience ?
2. Hypotheses :
H
0
:
β
2
= 0 vs
H
a
:
β
2
6
= 0
3. Test Statistic : t = 1.39
4. P  value : 0.17
5. Conclusion: If the null hypotheses were true, the probability would have been 0.17 of getting a
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 Spring '08
 TA
 Statistics, Correlation, 1%, $1,000, 67%, 66%, 60pound

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