Question

the graph shows a bivariate data set and its least squares regression line. which graph shows the residual plot for the same data set? choose 1 answer.

Explanation:

Step1: Recall residual definition

Residual = Observed - Predicted. For a good - fitting linear regression, the residuals should be randomly scattered around the horizontal axis at \(y = 0\).

Step2: Analyze the scatter of points

In a residual plot for a linear regression, there should be no discernible pattern. The points should be randomly distributed above and below the \(x\) - axis.

Step3: Evaluate options

Option A shows points randomly scattered around \(y = 0\) with no pattern. Option B has a somewhat U - shaped pattern which indicates non - linearity in the data that the linear regression did not capture. Option C has a left - to - right decreasing pattern which also indicates that the linear model is not appropriate.

Answer:

A.