Question

five scatter plots were fit with linear models. the resulting residual plots are shown. which residual plots indicate that the linear model used is a good fit for the data set? select all that apply.

Explanation:

Step1: Recall residual - plot criteria

A good - fitting linear model has residual plots with randomly scattered points around the horizontal axis with no discernible pattern (such as a curve, increasing or decreasing trend).

Step2: Analyze each plot

Check each of the given residual plots for random scatter. If the points are randomly distributed above and below the horizontal axis, the linear model is a good fit. If there is a pattern like a U - shape, an increasing or decreasing trend, the linear model is not a good fit.

Since no specific plots are labeled as correct or incorrect in the text and we don't have the ability to visually analyze the plots in a detailed way here, in general, for a residual plot to indicate a good fit of a linear model:

1. The points should be randomly scattered around the horizontal line \(y = 0\).
2. There should be no obvious pattern such as a curve (e.g., quadratic - like U - shape), a funnel - shape (indicating non - constant variance), or a linear trend in the residuals.

Answer:

We need to visually inspect each residual plot for random scatter of points around the horizontal axis. If a plot has randomly scattered points with no pattern, it indicates a good fit of the linear model to the data set. Without seeing the actual visual inspection results of each individual plot, we cannot specifically select which ones apply. But the general rule is that plots with randomly scattered points around \(y = 0\) are the ones that indicate a good fit.