Chap3

Problem 4

(3)

For Log-level model:

$$
\frac{\Delta y}{y} \approx \beta_1 \Delta x
\tag{1}
$$

In this case, salary changes by:

$$
0.248 * 1 = 0.248 = 24.8 \%
\tag{2}
$$

(4)

For Log-log model:

$$
\frac{\Delta y}{y} \approx \beta_1 \frac{\Delta x}{x}
\tag{3}
$$

In this case, the coefficient on the $log(libvol)$ means that, the percentage salary changes by is $0.095$ times the percentage $libvol$ changes by.

(5)

Yes, because the coefficient on $rank$ is negtive, the higher it ranked, the higher your salary will be. (Higher $rank$ means low value in $rank$.)

According to equation(1), with $rank$ changes by 20, the $salary$ will changes by:

$$
(-0.0033) * 20 = 0.066 = 6.6 \%
\tag{4}
$$

(6)

According to equation(1), $0.248$ means the salary will change by a percentage which equals to $0.248$ times the $\Delta GPA$.

C2

(1)

According to the ls result:

$$
\hat{price} = -19.315 + 0.128 sqrft + 15.198 bdrms
\tag{5}
$$

(2)

Price will increases by:

$$
1*15.198=15.198
\tag{6}
$$

(3)

In this case, we have one more bedroom and a 140 square feet space. So the price changes by:

$$
0.128 140 + 15.198 1 = 33.118
\tag{7}
$$

(4)

For both variables, it's a Level-level model,so:

$$
\Delta y \approx \beta_1 \Delta x_1 + \beta_2 \Delta x_2
\tag{8}
$$

In this case:

$$
\frac{\Delta y}{y} \approx \frac{\beta_1 \Delta sqrft}{y} + \frac{\beta_2 \Delta bdrms}{y}
\tag{9}
$$

(5)

According to equation(6):

$$
\hat{price} = -19.315 + 0.128 2438 + 15.198 4 = 353.541
$$