An aircraft company wanted to predict the number of worker-hours necessary to finish the design of a new plane. Relevant explanatory variables were thought to be the plane's top speed, its weight, and the number of parts it had in common with other models built by the company. A sample of 27 of the company's planes was taken, and the following model was estimated:
$$
y=\beta_0+\beta_1 x_1+\beta_2 x_2+\beta_3 x_3+\varepsilon
$$
where
$y=$ design effort, in millions of worker-hours
$x_1=$ plane's top speed, in miles per hour
$x_2=$ plane's weight, in tons
$x_3=$ percentage of parts in common with other models
The estimated regression coefficients were as follows:
$$
b_1=0.661 \quad b_2=0.065 \quad b_3=-0.018
$$
The total sum of squares and regression sum of squares were found to be as follows:
$$
S S T=3.881 \text { and } S S R=3.549
$$
a. Compute and interpret the coefficient of determination.
b. Compute the error sum of squares.
c. Compute the adjusted coefficient of determination.
d. Compute and interpret the coefficient of multiple correlation.