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, $y$ \[ \begin{array}{ccccccc} 5 & 15 & 30 & 40 & 60 & 84 & 105 \\ 690 & 67.8 & 66.3 & 65.6 & 64.1 & 62.9 & 606 \end{array} \] B. For a commute time of zero minutes, the index score is predicted to be $68.995^{\circ}$ (Round to three decimal places as needed) C. For an index score of zero, the commute time is predicted to be minutes (Round to three decimal places as needed) D. For every unit increase in index score, the commute time falls by , on average. (Round to three decimal places as needed) (c) Predict the well-being index of a person whose commute time is 25 minutes The predicted index score is 670 (Round to one decimal place as needed.) (Round to one decimal place as needed) A. Yes, Barbara is more well-off because the typical individual who has a 20 -minute commute scores B. No, Barbara is less well-off because the typical individual who has a 20-minute commute scores

Step 1 ：First, we need to understand that the question is asking for the predicted well-being index score for a person whose commute time is 25 minutes.

Step 2 ：From the given data, we know that for a commute time of zero minutes, the index score is predicted to be 68.995.

Step 3 ：We also know that for every unit increase in index score, the commute time falls by a certain amount, but this amount is not given in the question.

Step 4 ：However, we can use the given data to find the rate of change of the index score with respect to the commute time.

Step 5 ：From the data, we can see that as the commute time increases, the index score decreases. This suggests a negative correlation between the two variables.

Step 6 ：Let's assume that the rate of change of the index score with respect to the commute time is constant. Then, we can use the formula for the slope of a line to find this rate.

Step 7 ：The slope of a line is given by the change in the y-values divided by the change in the x-values. In this case, the y-values are the index scores and the x-values are the commute times.

Step 8 ：Using the first and last data points, we find that the slope is (606 - 690) / (105 - 5) = -0.84.

Step 9 ：This means that for every unit increase in commute time, the index score decreases by 0.84.

Step 10 ：Now, we can use this rate to predict the index score for a commute time of 25 minutes.

Step 11 ：We start with the index score for a commute time of zero minutes, which is 68.995, and subtract the product of the commute time and the rate of change.

Step 12 ：This gives us 68.995 - 25 * 0.84 = 48.995.

Step 13 ：So, the predicted well-being index score for a person whose commute time is 25 minutes is \(\boxed{48.995}\).