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. She fits a least-squares regression line to the data and determines the equation of the line is ŷ =26 – 0.18x, where ŷ is the score earned on the exam and x is the number of hours of sleep the night before the exam. The residual plot is given. 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).

Answer 1

The correct choice is: No, there is no clear pattern in the residual plot.

In a regression analysis, a residual is the difference between the observed value and the predicted value. The residual plot is a graphical representation of these differences. It's a crucial tool to assess whether a linear model is appropriate for the data. Here are some key points to consider:

In a good linear model, residuals should exhibit a random pattern. A random pattern suggests that the model is capturing the underlying trend in the data, and there are no systematic errors in the predictions. The statement "No, there is no clear pattern in the residual plot" reflects the idea that the residuals are randomly distributed, supporting the appropriateness of the linear model.