Question

The residual plot for a data set is shown.

Based on the residual plot, which statement best explains whether the regression line is a good model for the data set and why?




The regression line is a good model because the points in the residual plot are close to the x-axis and randomly spread around the x-axis.

The regression line is not a good model because only one point in the residual plot is on the x-axis.

The regression line is a good model because the residuals approach 0 as x increases.

The regression line is not a good model because there is no pattern in the residuals.

Answer 1

It is a good model, they are spaced out and distributed randomly.

Explanation:

Answer 2

The first thing we will do is define the linear regression:
In statistics, linear regression or linear adjustment is a mathematical model used to approximate the dependency relationship between a dependent variable Y, the independent variables Xi and a random term ε.
For this case, the linear regression line is:
y = 0 (x axis).
It is a good model because the points of the scatter diagram are all very close to the x axis.
Answer:
The regression line is a good model because the points in the residual plot are close to the x-axis and randomly spread around the x-axis.