Question

use the given data to find the equation of the regression line. examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.
x 13 6 9 4 3 11 10 8 5 7 12
y 19.24 13.16 17.90 8.24 5.24 19.28 18.76 16.68 10.88 15.10 19.44
identify a characteristic of the data that is ignored by the regression line.
a. there is an influential point that strongly affects the graph of the regression line.
b. the data has a pattern that is not a straight line.
c. there is no trend in the data.
d. there is no characteristic of the data that is ignored by the regression line.

Explanation:

To determine the correct option, we analyze each choice:

• Option A: An influential point would be an outlier or a point that significantly changes the regression line, but the data here shows a curved (non - straight - line) pattern, not an influential point issue.
• Option B: By examining the scatterplot (and the data trend), the data seems to follow a curved pattern (e.g., a quadratic or other non - linear pattern) rather than a straight line. The regression line (which is linear) ignores this non - linear pattern.
• Option C: The data does have a trend (as x increases, y generally increases initially and then maybe changes, but there is a trend), so this is incorrect.
• Option D: Since the data has a non - linear pattern which the linear regression line ignores, this is incorrect.

Answer:

B. The data has a pattern that is not a straight line.