Question

a real estate agent is interested in the relationship between the size of a home (measured in square feet) and the selling price of the home. she collects a simple random sample of nine homes in her area and records the size and price of each house. she finds a linear model to give the relationship between the size of the home (measured in thousands of square feet) and the selling price of the home (measured in thousands of dollars). the equation of the line is \\( \hat { y } = 5102 + 112 x \\), where \\( \hat { y } \\) is the selling price of the home and \\( x \\) is the square footage. 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, most of the residuals are positive. yes, the residuals are relatively large.

Explanation:

A residual plot is used to assess the appropriateness of a linear model. If there is no clear pattern (such as a curve, funnel - shape, etc.) in the residual plot, it indicates that the linear model is appropriate. The sign (positive or negative) of residuals (unless there is a systematic pattern) does not determine model inappropriateness. Also, relatively large residuals (if they are randomly distributed) do not make the model inappropriate.

Answer:

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