Example: Choosing Between the Full and Reduced Models Litters ...
Example: Choosing Between the Full and Reduced Models Litters ...
Example: Choosing Between the Full and Reduced Models Litters ...
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<strong>Example</strong>: <strong>Choosing</strong> <strong>Between</strong> <strong>the</strong> <strong>Full</strong> <strong>and</strong> <strong>Reduced</strong> <strong>Models</strong><br />
<strong>Litters</strong> Data: We are interested in <strong>the</strong> relationship between brain size<br />
<strong>and</strong> litter size, after taking body weight into account<br />
<strong>Reduced</strong> Model: brain weight ∼ body weight<br />
<strong>Full</strong> Model: brain weight ∼ body weight + litter size<br />
n = 20, p = 3 (for full model)<br />
r = 1<br />
The partial F test here will be on 1 <strong>and</strong> 17 degrees of freedom<br />
1
<strong>Full</strong> Model Analysis<br />
litters.lm
Conducting <strong>the</strong> Partial F Test<br />
> anova(littersred.lm, litters.lm)<br />
Analysis of Variance Table<br />
Model 1: brainwt ˜ bodywt<br />
Model 2: brainwt ˜ lsize + bodywt<br />
Res.Df RSS Df Sum of Sq F Pr(>F)<br />
1 18 0.0030806<br />
2 17 0.0024287 1 0.00065186 4.5628 0.04751 *<br />
---<br />
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1<br />
Conclusion: After accounting for body weight, we have evidence<br />
that litter size <strong>and</strong> brain weight are related<br />
Note: p-value for this test matches <strong>the</strong> p-value for <strong>the</strong> test of<br />
H 0 : β 2 = 0. Why?<br />
3
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