Question

a real estate agent would like to develop a model for predicting sale price of homes in a suburban area. one variable that can be useful for predicting home value is home interior size, which is measured in square feet. using 13 homes sold recently in the area, the real estate agent uses software to find a least - square line to summarize the relationship. the resulting equation is \\( \widehat{\text { sale price }}=0.152(\text { size })-32.84 \\). based on the scatterplot and residual plot shown, is a linear model appropriate for summarizing the relationship? a linear model is appropriate because the residual plot shows no pattern. a linear model is appropriate because the mean of the residuals appears close to zero. a linear model is not appropriate because there are potential outliers in the residual plot. a linear model is not appropriate because of the random scatter of points in the residual plot.

Explanation:

To determine if a linear model is appropriate, we check the residual plot. A random scatter of points in the residual plot indicates that the linear model is a good fit. If there is a pattern (like a curve, funnel - shape etc.) in the residual plot, the linear model is not appropriate. Also, the mean of the residuals being close to zero is a property of the least - squares regression line (by construction, \(\sum_{i = 1}^{n}e_{i}=\sum_{i = 1}^{n}(y_{i}-\hat{y}_{i}) = 0\) for the least - squares line, so this is not a good criterion for model appropriateness). Outliers in the residual plot do not necessarily mean the linear model is inappropriate (they may just be extreme data points). A random scatter of points in the residual plot is a sign of a good linear model.

Answer:

A linear model is appropriate because the residual plot shows no pattern.