Chap2

Problem 3

(1)

According to the result above, we can know:

$$\begin{array}{}\text{(1)}& \{\begin{array}{l}\widehat{{\beta }_0}=0.568\\ \widehat{{\beta }_1}=0.102\end{array}\end{array}$$

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

$$\begin{array}{}\text{(2)}& \widehat{GPA}=0.568+0.102\ast ACT\end{array}$$

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 $5\ast 0.102=0.51$

(2)

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

$$\begin{array}{}\text{(3)}& 0.08571+0.37912-0.22527+0.17253+0.06813-0.12308-0.42308+0.06593=-1\ast {10}^{-5}\approx 0\end{array}$$

(3)

$$\begin{array}{}\text{(4)}& GPA=0.568+0.102\ast 20=2.608\end{array}$$

(4)

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

(5)

$SER=0.269$, so

$$\begin{array}{}\text{(5)}& {\sigma }^2=SE{R}^2=0.072\end{array}$$

$$\begin{array}{}\text{(6)}& \widehat{{\beta }_0^2}={0.928}^2=0.861\end{array}$$

$$\begin{array}{}\text{(7)}& \widehat{{\beta }_1^2}={0.036}^2=0.001\end{array}$$

Problem C2

(3)

The result is showed above.

$$\begin{array}{}\text{(8)}& \log salary=6.505+0.0097\ast ceoten\end{array}$$

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