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, $y$
\[
\begin{array}{ccccccc}
5 & 15 & 30 & 40 & 60 & 84 & 105 \\
690 & 67.8 & 66.3 & 65.6 & 64.1 & 62.9 & 60.6
\end{array}
\]
C. For every unit increase in index score, the commute time falls by ,on average. (Round to three decimal places as needed.)
D. For a commute time of zero minutes, the index score is predicted to be (Round to three decimal places as needed)
E. It is not appropriate to interpret the slope.
Interpret the $y$-intercept Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. For every unit increase in commute time, the index score falls by $\square$, on average. (Round to three decimal places as needed)
B. For a commute time of zero minutes, the index score is predicted to be (Round to three decimal places as needed)
C. For an index score of zero, the commute time is predicted to be $\square$ minutes (Round to three decimal places as needed)
D. For every unit increase in index score, the commute time falls by $\square$, on average (Round to three decimal places as needed)
E. It is not appropriate to interpret the $y$-intercept because a commute time of zero minutes does not make sense and the value of zero minutes is much smaller than those observed in the data set.

Step 1 ：Given the data for commute times (in minutes) and scores on a well-being survey, we are asked to interpret the slope and y-intercept of the linear regression model for the data.

Step 2 ：The slope represents the change in the Well-Being Index Score for every unit increase in Commute Time, and the y-intercept represents the predicted Well-Being Index Score when the Commute Time is zero.

Step 3 ：First, we calculate the slope and y-intercept of the linear regression model using the formula for the slope and y-intercept of a linear regression model.

Step 4 ：The slope (m) is calculated as \((n(\Sigma xy) - (\Sigma x)(\Sigma y)) / (n(\Sigma x^2) - (\Sigma x)^2)\) and the y-intercept (b) is calculated as \((\Sigma y - m(\Sigma x)) / n\), where n is the number of data points, \(\Sigma xy\) is the sum of the product of x and y for all data points, \(\Sigma x\) and \(\Sigma y\) are the sum of x and y values respectively, and \(\Sigma x^2\) is the sum of the squares of x values.

Step 5 ：Using the given data, we find that the slope of the linear regression model is approximately -3.444, and the y-intercept is approximately 320.690.

Step 6 ：This means that for every unit increase in commute time, the index score falls by 3.444 on average. And for a commute time of zero minutes, the index score is predicted to be 320.690.

Step 7 ：However, these interpretations are based on the assumption that the relationship between commute time and index score is linear, which may not be the case in reality. Also, a commute time of zero minutes does not make sense in the real world context, and the value of zero minutes is much smaller than those observed in the data set. Therefore, it may not be appropriate to interpret the y-intercept.

Step 8 ：Final Answer: The correct choices are: \(\boxed{A}\). For every unit increase in commute time, the index score falls by \(\boxed{-3.444}\), on average. \(\boxed{B}\). For a commute time of zero minutes, the index score is predicted to be \(\boxed{320.690}\). \(\boxed{E}\). It is not appropriate to interpret the y-intercept because a commute time of zero minutes does not make sense and the value of zero minutes is much smaller than those observed in the data set.