Chap2

Problem 3

(1)

According to the result above, we can know:

$$
\begin{cases}
\hat{\beta_0}=0.568\\
\hat{\beta_1}=0.102
\end{cases}
\tag{1}
$$

therefore, the relationship between $GPA$ and $ACT$ is:

$$
\hat{GPA}=0.568+0.102*ACT
\tag{2}
$$

It means, the higher ACT is, the higher GPA will be.

The intercept is meaningless here. Generally speaking, students’ $ACT$ won’t be zero.

When the $ACT$ increase 5 points, the $GPA$ will increase $5*0.102=0.51$

(2)

As showed above, we can compute the sum of residuals:

$$
0.08571+0.37912-0.22527+0.17253+0.06813-0.12308-0.42308+0.06593=-1*10^{-5}\approx0
\tag{3}
$$

(3)

$$
GPA=0.568+0.102*20=2.608
\tag{4}
$$

(4)

Because $R^2=0.577$, so 57.7% in the samples can be explained by $x$

(5)

$SER=0.269$, so

$$
\sigma^2=SER^2=0.072
\tag{5}
$$

$$
\hat{\beta_0^2}=0.928^2=0.861
\tag{6}
$$

$$
\hat{\beta_1^2}=0.036^2=0.001
\tag{7}
$$

Problem C2

(3)

The result is showed above.

$$
\log salary=6.505+0.0097*ceoten
\tag{8}
$$

And the predicted percentage increase in salary given one more year as a CEO is 0.97%​