Question

the owner of a restaurant gathered data for several weeks about the number of first-time customers at the restaurant and the number of new memberships in the restaurants rewards program. the data and the line of best fit are shown in the scatter plot.

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?

yes, because the points in the plot are all very close to the line, which indicates a strong association.
yes, because the slope of the line is closer to 0 than to 1, which indicates a strong association.
no, because the points in the plot are all very close to the line, which indicates a weak association.

Explanation:

Analyze the scatter plot and line of best fit

The scatter plot shows data points representing the relationship between first-time customers and new memberships. All the plotted data points lie extremely close to the drawn line of best fit.

Evaluate the strength of the association

When data points in a scatter plot lie very close to the line of best fit, it indicates a strong linear association between the two variables. This strong association means the line of best fit can be used to make highly reasonable predictions.

Match with the given options

• Option 1: "Yes, because the points in the plot are all very close to the line, which indicates a strong association." (Correct, as closeness to the line directly corresponds to a strong association and reliable predictions).
• Option 2: "Yes, because the slope of the line is closer to 0 than to 1..." (Incorrect, slope value relative to 0 or 1 does not determine the strength of the association).
• Option 3: "No, because the points in the plot are all very close to the line, which indicates a weak association." (Incorrect, closeness indicates a strong association, not a weak one).

Answer:

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