Question

a student is preparing to take a standardized exam. she was told that she needs to get plenty of sleep the night before the exam. she is interested in the relationship between the number of hours of sleep a student gets before the exam and the score earned on the exam. she collects information from 10 other students who have already taken the exam as shown in the table.
based on the residual plot, is the linear model appropriate?
no, there is no clear pattern in the residual plot.
yes, there is no clear pattern in the residual plot.
no, the student who got the most sleep had a negative residual.
yes, there are more negative residuals (6) than positive residuals (4).

Explanation:

A linear model is appropriate if the residual plot has no clear pattern. Residuals are the differences between the observed and predicted values. If there is no clear pattern (such as a curve, increasing or decreasing trend), it means the linear model fits the data well. The number of positive or negative residuals or a single data - point (like the student with most sleep having a negative residual) does not determine the appropriateness of the linear model. The key is the overall pattern (or lack of it) in the residual plot.

Answer:

Yes, there is no clear pattern in the residual plot.