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Question 7 • CMS 2026-2027 NC Math 1 CREDIT RECOVERY

Which residual plot shows that the line of best fit is a good model?

Answer

Image with description A scatter plot. The horizontal x axis and vertical y axis intersect at the origin, 0 comma 0. There are 12 diamond-shaped data points plotted on the plane. One point is located exactly at the origin 0 comma 0. Two points are located to the right of the y axis and just below the x axis in the fourth quadrant. The remaining 9 points are located to the right of the y axis and above the x axis in the first quadrant, forming a hill-like curve that rises and then falls back toward the x axis as they move further.

Image with description A scatter plot across the axes. The horizontal x axis and vertical y axis intersect at the origin, 0 comma 0. There are 11 diamond-shaped data points plotted on the plane. One point is located exactly at the origin 0 comma 0. Another point is located to the right of the y axis and just above the x axis in the first quadrant. The remaining 9 points are scattered to the right of the y axis and below the x axis in the fourth quadrant, showing a general downward pattern.

Image with description A scatter plot. The horizontal x axis and vertical y axis intersect at an unlabeled origin. There are 11 diamond-shaped data points plotted on the plane. One point is located exactly at the origin. Five points are located to the right of the y axis and above the x axis in the first quadrant. The remaining 5 points are located to the right of the y axis and below the x axis in the fourth quadrant. The points are scattered widely above and below the horizontal axis, showing no distinct pattern.

Image with description A scatter plot. The horizontal x axis and vertical y axis intersect at the origin, 0 comma 0. There are 12 diamond-shaped data points plotted on the plane. One point is located exactly at the origin 0 comma 0. Three points are located to the right of the y axis and just above the x axis in the first quadrant, with two near the origin and one near the far right. The remaining 8 points are located to the right of the y axis and below the x axis in the fourth quadrant, forming a valley-like curve that dips downward and then rises back toward the x axis.

Explanation

A line of best fit is a good model when its residuals are scattered randomly above and below zero, with no clear pattern. Choice B shows points on both sides of the horizontal axis without a distinct trend. The curved patterns in A and D, and the downward trend in C, suggest the line misses a pattern in the data.

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