Question

consider the plot created from the residuals of a line of best fit for a set of data.
does the residual plot show that the line of best fit is appropriate for the data?
yes, the points have no pattern.
no, the points are evenly distributed about the x-axis.
no, the points are in a linear pattern.
yes, the points are in a curved pattern.

Explanation:

To determine if a line of best fit is appropriate, we analyze the residual plot. A good residual plot (for a linear fit) has points with no clear pattern (randomly scattered). Let's evaluate each option:

• Option 1: "Yes, the points have no pattern." – If residuals are random (no pattern), the linear model is appropriate.
• Option 2: "No, the points are evenly distributed about the x - axis." – Even distribution about the x - axis is a sign of a good residual plot, so this reasoning is wrong.
• Option 3: "No, the points are in a linear pattern." – The points here don't show a linear pattern.
• Option 4: "Yes, the points are in a curved pattern." – A curved pattern in residuals means the linear model is not appropriate, so this is wrong.

Looking at the plot, the points seem to have no strong pattern (they are not in a clear linear or curved pattern and are somewhat randomly scattered around). So the first option is correct.

Answer:

A. Yes, the points have no pattern.