The data below represent commute times (in minutes) and scores on a well-being survey. Complete parts (a) through (d) below.
\begin{tabular}{lccccccccc}
Commute Time (minutes), $\mathbf{x}$ & 5 & 15 & 30 & 40 & 50 & 72 & 105 \\
Well-Being Index Score, $\mathbf{y}$ & 68.9 & 67.6 & 65.8 & 64.9 & 63.9 & 62.6 & 58.7
\end{tabular}
(a) Find the least-squares regression line treating the commute time, $x$, as the explanatory variable and the index score, $y$, as the response variable.
\[
\hat{y}=\square x+(\square)
\]
(Round to three decimal places as needed.)

Step 1 ：Given the commute times (in minutes) and scores on a well-being survey, we are to find the least-squares regression line treating the commute time, \(x\), as the explanatory variable and the index score, \(y\), as the response variable.

Step 2 ：The least-squares regression line is given by the equation \(\hat{y} = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept.

Step 3 ：The slope \(m\) is calculated as the covariance of \(x\) and \(y\) divided by the variance of \(x\).

Step 4 ：The y-intercept \(c\) is calculated as the mean of \(y\) minus the slope times the mean of \(x\).

Step 5 ：Given the values of \(x\) and \(y\), we calculate the mean of \(x\) as 45.286 and the mean of \(y\) as 64.629.

Step 6 ：Calculating the covariance of \(x\) and \(y\) gives -693.057 and the variance of \(x\) gives 7103.429.

Step 7 ：Dividing the covariance of \(x\) and \(y\) by the variance of \(x\) gives the slope \(m\) as -0.098.

Step 8 ：Subtracting the product of the slope and the mean of \(x\) from the mean of \(y\) gives the y-intercept \(c\) as 69.047.

Step 9 ：Substituting the values of \(m\) and \(c\) into the equation gives the least-squares regression line as \(\hat{y} = -0.098x + 69.047\).

Step 10 ：\(\boxed{\text{Final Answer: The least-squares regression line is } \hat{y} = -0.098x + 69.047}\)