Question

janice is considering buying a new home. she wants to estimate the monthly utilities (heating and air conditioning). she figures that the utilities are dependent on the size (square footage) of the home. she collects data on 10 homes in the neighborhood and finds a linear model to give the relationship between the size of the home and the monthly utilities. the equation of the line is $hat{y}=-8.1 + 1.91x$, where $hat{y}$ is the mean monthly cost in utilities and $x$ is the square footage of the home. the residual plot is shown. 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, there are no homes between 2,300 and 2,900 square feet. yes, half of the residuals are positive and half are negative.

Explanation:

In regression analysis, a residual plot is used to check the appropriateness of a linear model. If the residual plot has no clear pattern (such as a curve, increasing - decreasing trend, etc.), it indicates that the linear model is appropriate. The presence of a pattern (e.g., quadratic - like curve) would suggest a non - linear relationship. Also, the number of positive and negative residuals (as long as there is no pattern) is not the key factor. The absence of data in a certain range (\(2300 - 2900\) square feet in this case) is not relevant to the model's appropriateness.

Answer:

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