\(X\) is a continuous variable that takes on values between 5 and \(100 . Z\) is a binary variable. Sketch the following regression functions (with values of \(X\) between 5 and 100 on the horizontal axis and values of \(\hat{Y}\) on the vertical axis):

a. \(\hat{Y}=2.0+3.0 \times \ln (X)\).

b. \(\hat{Y}=2.0-3.0 \times \ln (X)\).

c. i. \(\hat{Y}=2.0+3.0 \times \ln (X)+4.0 Z\), with \(Z=1\).

ii. Same as (i), but with \(Z=0\).

d. i. \(\hat{Y}=2.0+3.0 \times \ln (X)+4.0 Z-1.0 \times Z \times \ln (X)\), with \(Z=1\).

ii. Same as (i), but with \(Z=0\).

e. \(\hat{Y}=1.0+125.0 X-0.01 X^{2}\).