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, $y$
\[
\begin{array}{ccccccc}
5 & 15 & 30 & 40 & 60 & 84 & 105 \\
69.0 & 67.8 & 66.3 & 65.6 & 64.1 & 62.9 & 60.6
\end{array}
\]
(c) Predict the well-being index of a person whose commute time is 25 minutes.
The predicted index score is
(Round to one decimal place as needed.)

Step 1 ：Given the commute times (in minutes) and scores on a well-being survey, we are asked to predict the well-being index of a person whose commute time is 25 minutes.

Step 2 ：We can use linear regression to predict the well-being index. Linear regression is a statistical method that allows us to study the relationship between two continuous quantitative variables. In this case, the two variables are commute time and well-being index score.

Step 3 ：The formula for the line of best fit in linear regression is \(y = mx + b\), where \(m\) is the slope of the line and \(b\) is the y-intercept. The slope of the line is the change in \(y\) divided by the change in \(x\), and the y-intercept is the value of \(y\) when \(x\) is zero.

Step 4 ：To calculate the slope and y-intercept, we first need to calculate the mean of \(x\) and \(y\), the sum of the products of \(x\) and \(y\), and the sum of the squares of \(x\).

Step 5 ：Given the commute times \(x = [5, 15, 30, 40, 60, 84, 105]\) and well-being index scores \(y = [69.0, 67.8, 66.3, 65.6, 64.1, 62.9, 60.6]\), we find that the mean of \(x\) is approximately 48.43 and the mean of \(y\) is approximately 65.19.

Step 6 ：Using these means, we calculate the slope \(m\) to be approximately -0.079 and the y-intercept \(b\) to be approximately 68.99.

Step 7 ：Substituting the values of \(m\), \(b\), and \(x = 25\) into the equation \(y = mx + b\), we find that the predicted well-being index score \(y\) is approximately 67.03.

Step 8 ：Rounding to one decimal place as needed, the final answer is \(\boxed{67.0}\).