Question

1. tony is examining the residual plot of the data to which he fit a linear model. the residual plot is shown. his friends made the following statements about the residual plot. alizeh says the residual plot shows that the linear model is a good fit for the data as the points are scattered about the line ( y = 0 ). bruce says the residual plot shows that the linear model is not a good fit for the data as the points are scattered about the line ( y = 0 ). caine says the residual plot shows that the linear model is a good fit for the data as the points show a distinct pattern about the line ( y = 0 ). daniella says the residual plot shows that the linear model is not a good fit for the data as there are an equal number of points above and below the line ( y = 0 ). which friend is correct? alizeh is correct because the linear model is a good fit when the residual plot has scattered points close to the ( x )-axis. bruce is correct because the linear model is not a good fit when the residual plot has scattered points close to the ( x )-axis.

Explanation:

To determine the correct friend, we analyze the concept of residual plots for linear models:

1. A good - fitting linear model has residual points that are randomly scattered (no distinct pattern) and close to the \(y = 0\) (x - axis) line.
2. Alizeh says the linear model is a good fit as points are scattered about \(y = 0\). This aligns with the concept of a good - fitting linear model (random scatter, close to the axis).
3. Bruce is incorrect because scattered points close to the axis indicate a good fit, not a bad fit.
4. Caine is incorrect because a distinct pattern in residuals indicates a bad fit, not a good fit.
5. Daniella is incorrect because an equal number of points above and below the axis is not the criterion for a bad fit; the random scatter (or lack of pattern) and closeness to the axis matter.

Answer:

Alizeh is correct because the linear model is a good fit when the residual plot has scattered points close to the \(x\) - axis.