Question

an engineer is interested in the relationship between the weight of a car (measured in pounds) and the fuel economy (measured in miles per gallon of gas). to investigate the relationship, she collects a simple random sample of 10 cars and records their weight and fuel efficiency. she finds the equation of the least - squares regression line to be $hat{y}=69 - 0.0114x$, where $hat{y}$ is the fuel efficiency (mpg) and $x$ is the weight (in pounds). the residual plot is shown. based on the residual plot, is the linear model appropriate? no, the residuals are relatively large. no, there is a clear pattern in the residual plot. yes, there is no clear pattern in the residual plot. yes, about half of the residuals are positive and half are negative.

Explanation:

A linear model is appropriate if the residual plot has no clear pattern (such as a curve, funnel - shape etc.). The size of residuals (whether they are large or small) is related to the goodness - of - fit (how well the model fits the data) but not directly to the appropriateness of the linear model. Also, the fact that half of the residuals are positive and half are negative is a property of the least - squares regression line (the sum of residuals is approximately zero) and does not by itself indicate model appropriateness.

Answer:

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