Step 1 :The given data represents commute times (in minutes) and scores on a well-being survey. The commute times are represented by the variable 'x' and the well-being index scores are represented by the variable 'y'. The data is as follows: \[x = [5, 15, 30, 40, 60, 84, 105]\] \[y = [69.0, 67.8, 66.3, 65.6, 64.1, 62.9, 60.6]\]
Step 2 :We are asked to interpret the y-intercept of the linear regression model of this data. The y-intercept is the value of y when x is zero. In this context, it represents the predicted well-being index score for a person with a commute time of zero minutes.
Step 3 :To find the y-intercept, we need to calculate the linear regression model of the given data. The linear regression model is given by the equation \(y = mx + b\), where 'm' is the slope and 'b' is the y-intercept.
Step 4 :The y-intercept is the predicted well-being index score for a person with a commute time of zero minutes. This is represented by the variable 'b' in the linear regression model.
Step 5 :Final Answer: The correct choice is B. For a commute time of zero minutes, the index score is predicted to be approximately \(\boxed{68.995}\). This is the y-intercept of the linear regression model.