Question: A real estate agent would like to develop a model for predicting sale price of homes in a suburban…

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 sale price = 0.152(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.

Home Price vs. Home Size (Square Feet)

(Thousands of Dollars) 1,000 900 800 700 600 500

Solution

A real estate agent is trying to model the sale price of homes in a suburban area based on the home’s interior size. The resulting least-square line equation given is: \[ \text{sale price} = 0.152 \times \text{size} - 32.84 \] The image asks whether a linear model is appropriate based on the scatterplot and residual plot. To determine this, consider these options: 1. A linear model is appropriate if the residual plot shows no pattern. This implies that the errors are randomly distributed, suggesting a good fit for linear regression. 2. A linear model is appropriate if the mean of the residuals is close to zero, indicating that the predictions are unbiased. 3. A linear model is not appropriate if there are potential outliers in the residual plot, as these could disrupt the model’s accuracy. 4. A linear model is not appropriate if the residual plot shows random scatter, which usually means the current model does not capture any particular trend. You need to examine the scatterplot and residual plot (not visible here) to determine which option applies. If the residuals show no clear pattern and the average is close to zero, option 1 or 2 is likely suitable. If there are clear patterns or outliers, then options 3 or 4 might be appropriate.