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 sale price hat = 0.152 (size) minus 32.84. A graph titled home price versus home size (square feet) has home size (Square feet) on the x-axis, and home price (thousands of dollars) on the y-axis. Points increase in a line with positive slope. A graph titled residuals versus home size (square feet) has home size (square feet) on the x-axis, and residual on the y-axis. Points are scattered throughout the graph. 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.

Answer 1

Based on the information provided, a linear model is not appropriate for summarizing the relationship between home size and sale price because of the random scatter of points in the residual plot. In a linear model, the residuals should be randomly distributed around a mean of zero, without any discernible pattern. However, the residual plot shown in the question indicates that the residuals are randomly scattered throughout the graph, which suggests that a linear model may not be the best way to summarize the relationship between the variables. Therefore, a linear model is not appropriate for this data.

Answer 2

Not Appropriate

Explanation:

Based on the information provided in the problem, it appears that a linear model is not appropriate for summarizing the relationship between home size and sale price. This is because the residual plot shows a random scatter of points, which suggests that there is not a strong linear relationship between these variables. Furthermore, the scatterplot of home price versus home size shows a line with a positive slope, which indicates that there is some relationship between these variables, but it is not necessarily a linear relationship. In this situation, it would be more appropriate to use a non-linear model to summarize the relationship between home size and sale price.