A consulting group offers courses in financial management for executives. At the end of these courses, participants are asked to provide overall ratings of the value of the course. To assess the impact of various factors on ratings, the model
$$
Y=\beta_0+\beta_1 X_1+\beta_2 X_2+\beta_3 X_3+\varepsilon
$$
was fitted for 25 such courses, where
$Y=$ average rating by participants of the course
$X_1=$ percentage of course time spent in group discussion sessions
$X_2=$ amount of money (in dollars) per course member spent on the preparation of subject matter material
$X_3=$ amount of money per course member spent on the provision of non-course-related material (food, drinks, and so for th)
Part of the SAS computer output for the fitted regression is shown next.
$$
\begin{array}{|c|c|c|c|}
\hline \text { Parameter } & \text { Estimate } & \begin{array}{c}
\text { Student's } t \\
\text { for } H_0 \text { : } \\
\text { Parameter }=0
\end{array} & \begin{array}{c}
\text { Std. Error of } \\
\text { Estimate }
\end{array} \\
\hline \text { Intercept } & 42.9712 & & \\
\hline \mathrm{X}_1 & 0.3817 & 1.89 & 0.2018 \\
\hline \mathrm{X}_2 & 0.5172 & 2.64 & 0.1957 \\
\hline \mathrm{X} 3 & 0.0753 & 1.09 & 0.0693 \\
\hline
\end{array}
$$
a. Interpret the estimated regression coefficients.
b. Interpret the coefficient of determination.
c. Test, at the $5 \%$ level, the null hypothesis that, taken together, the three independent variables do not linearly influence the course rating.
d. Find and interpret a $90 \%$ confidence interval for $\beta_1$.
e. Test the null hypothesis
$$
H_0: \beta_2=0
$$
against the alternative
$$
H_1: \beta_2>0
$$
and interpret your result.
f. Test at the $10 \%$ level the null hypothesis
$$
H_0: \beta_3=0
$$
against the alternative
$$
H_1: \beta_3 \neq 0
$$
and interpret your result.