Note that this t test depends on the other variables that are in the regression

# Note that this t test depends on the other variables

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(d) (20 points) Now typeanova( fuel.fit2, fuel.fit )Corresponding to this anova command, write down your null and alternative hypotheses, the theoretical test statisticand its distribution under the null hypothesis, the critical value for the test and your decision rule if using significancelevel 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{(xi, yi) :i= 1, . . . ,11}are as plotted in the left panel of Figure 3. Suppose that the modelYi=α+βxi+iis fitted, whereiiidN(0, σ2). The center panel of Figure 3 shows the diagonals of the hat matrix, andthe right panel shows the ordinary residuals from the fitted model ({yi-ˆyi:i= 1, . . . ,11}). In each of the three panels,the point corresponding toi= 11is indicated by a solid square.(a) (5 points) Explain why the absolute value of the magnitude of the residual corresponding toi= 11is relatively small.

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