Question

pretest: special linear relationships
new membership
first-time customers
the equation of the line of best fit is $y = 0.171x + 2.241$.
could this line of best fit be used to make reasonable predictions?
a. yes, because the points in the plot are all very close to the line, which indicates a strong association.
b. yes, because the slope of the line is closer to 0 than to 1, which indicates a strong association.
c. no, because the points in the plot are all very close to the line, which indicates a weak association.
d. no, because the slope of the line is closer to 0 than to 1, which indicates a weak association.

Explanation:

To determine if the line of best fit can make reasonable predictions, we analyze the scatter plot and the concept of association strength. A strong association (where points are close to the line) means the line can predict well.

• Option A: Points are close to the line, indicating a strong linear association, so the line can make reasonable predictions.
• Option B: Slope proximity to 0 or 1 doesn’t determine association strength; it’s about how close points are to the line. Eliminate B.
• Option C: Close points indicate strong, not weak, association. Eliminate C.
• Option D: Slope doesn’t determine association strength here, and close points mean strong association. Eliminate D.

Answer:

A. Yes, because the points in the plot are all very close to the line, which indicates a strong association.