logistic_guy
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A study was conducted at Virginia Tech to determine if certain static arm-strength measures have an influence on the “dynamic lift” characteristics of an individual. Twenty-five individuals were subjected to strength tests and then were asked to perform a weightlifting test in which weight was dynamically lifted overhead. The data are given here.
\(\displaystyle \bold{(a)}\) Estimate \(\displaystyle \beta_0\) and \(\displaystyle \beta_1\) for the linear regression curve \(\displaystyle \mu_Y|_x = \beta_0 + \beta_1x\).
\(\displaystyle \bold{(b)}\) Find a point estimate of \(\displaystyle \mu_Y|_{30}\).
\(\displaystyle \bold{(c)}\) Plot the residuals versus \(\displaystyle x'\)s (arm strength). Comment.
Individual | Arm Strength, \(\displaystyle x\) | Dynamic Lift, \(\displaystyle y\) |
|---|---|---|
1 | 17.3 | 71.7 |
2 | 19.3 | 48.3 |
3 | 19.5 | 88.3 |
4 | 19.7 | 75.0 |
5 | 22.9 | 91.7 |
6 | 23.1 | 100.0 |
7 | 26.4 | 73.3 |
8 | 26.8 | 65.0 |
9 | 27.6 | 75.0 |
10 | 28.1 | 88.3 |
11 | 28.2 | 68.3 |
12 | 28.7 | 96.7 |
13 | 29.0 | 76.7 |
14 | 29.6 | 78.3 |
15 | 29.9 | 60.0 |
16 | 29.9 | 71.7 |
17 | 30.3 | 85.0 |
18 | 31.3 | 85.0 |
19 | 36.0 | 88.3 |
20 | 39.5 | 100.0 |
21 | 40.4 | 100.0 |
22 | 44.3 | 100.0 |
23 | 44.6 | 91.7 |
24 | 50.4 | 100.0 |
25 | 55.9 | 71.7 |
\(\displaystyle \bold{(a)}\) Estimate \(\displaystyle \beta_0\) and \(\displaystyle \beta_1\) for the linear regression curve \(\displaystyle \mu_Y|_x = \beta_0 + \beta_1x\).
\(\displaystyle \bold{(b)}\) Find a point estimate of \(\displaystyle \mu_Y|_{30}\).
\(\displaystyle \bold{(c)}\) Plot the residuals versus \(\displaystyle x'\)s (arm strength). Comment.
