Note that this t test depends on the other variables

(d) (20 points) Now type
anova( fuel.fit2, fuel.fit )
Corresponding to this anova command, write down your null and alternative hypotheses, the theoretical test statistic
and its distribution under the null hypothesis, the critical value for the test and your decision rule if using significance
level 0.05, followed by the observed value of your test statistic, and your decision if using significance level 0.05.
8

4. (10 points) Suppose that data { ( x
i
, y
i
) : i = 1 , . . . , 11 } are as plotted in the left panel of Figure 3. Suppose that the model
Y
i
= α + βx
i
+
i
is fitted, where
i
∼
iid
N (0 , σ
2
) . The center panel of Figure 3 shows the diagonals of the hat matrix, and
the right panel shows the ordinary residuals from the fitted model ( { y
i
- ˆ y
i
: i = 1 , . . . , 11 } ). In each of the three panels,
the point corresponding to i = 11 is indicated by a solid square.
(a) (5 points) Explain why the absolute value of the magnitude of the residual corresponding to i = 11 is relatively small.