The data below represent commute times (in minutes) and scores on a well-being survey. Complete parts (a) through (d) below. Commute Time (minutes), $x$ Well-Being Index Score, $y$ \[ \begin{array}{cccccccc} 5 & 15 & 30 & 40 & 60 & 84 & 105 \\ 69.0 & 67.8 & 66.3 & 65.6 & 64.1 & 62.9 & 60.6 \end{array} \] (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 asked 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 data provided is as follows: $x = [5, 15, 30, 40, 60, 84, 105]$ and $y = [69.0, 67.8, 66.3, 65.6, 64.1, 62.9, 60.6]$

Step 3 ：The number of observations, $n$, is 7.

Step 4 ：The sum of $x$, denoted as $\sum x$, is 339.

Step 5 ：The sum of $y$, denoted as $\sum y$, is 456.3.

Step 6 ：The sum of the product of $x$ and $y$, denoted as $\sum xy$, is 21467.6.

Step 7 ：The sum of the square of $x$, denoted as $\sum x^2$, is 24431.

Step 8 ：The mean of $x$, denoted as $\bar{x}$, is approximately 48.43.

Step 9 ：The mean of $y$, denoted as $\bar{y}$, is approximately 65.19.

Step 10 ：We can calculate the slope of the least-squares regression line, $b1$, using the formula $b1 = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$. Substituting the known values, we find that $b1$ is approximately -0.079.

Step 11 ：We can calculate the y-intercept of the least-squares regression line, $b0$, using the formula $b0 = \bar{y} - b1\bar{x}$. Substituting the known values, we find that $b0$ is approximately 68.995.

Step 12 ：\(\boxed{\text{Final Answer: The least-squares regression line is } \hat{y}=-0.079x+68.995}\)