To interpret the y-intercept correctly, we need to first determine what kind of model we're working with. This problem suggests a linear relationship between commute time (x) and the Well-Being Index score (y). Typically, the y-intercept represents the predicted value of $y$ when $x = 0$, which would mean a commute time of zero.

Let's begin by finding the linear equation for the data points provided:

Commute Time (min), $x$	Well-Being Index score, $y$
5	69.1
20	67.6
25	66.9
35	66.2
50	65.1
72	64.3
105	61.3

Step 1: Determine the Linear Equation

We will use linear regression to approximate the relationship:

$y = mx + b$

where $m$ is the slope and $b$ is the y-intercept. To calculate the slope and intercept accurately, let me process the data.The linear regression gives the equation of the line as:

$y = -0.073x + 69.042$

Interpretation of the y-intercept:

The y-intercept is approximately $69.042$. This represents the predicted Well-Being Index score when the commute time $x = 0$.

Thus, option A would be the correct choice:

A. For a commute time of zero minutes, the index score is predicted to be approximately 69.042.

Would you like more details or have any questions?

Here are 5 follow-up questions to expand on this:

1. How is the slope of the line interpreted in this context?
2. What is the significance of the negative slope in the data?
3. How does the line fit the observed data points, and is it a good model?
4. What does the $R^2$ value tell us about this model?
5. Can we predict values for commute times outside the given data set?

Tip: When interpreting the slope, it tells us the rate of change between two variables.