Question

the data sets in problems 10 and 11 are scatterplots that have the regression line and the residuals marked. for each exercise, use the given data set to create a residual plot, and then assess the fit of the linear function to the data based on the residuals.

1. data set 1

residual plot 1

Explanation:

Step1: Understand the concept of residual plot

A residual plot is a graph that shows the residuals (the differences between the observed \(y\) - values and the predicted \(y\) - values from the regression line) on the vertical axis and the independent variable \(x\) on the horizontal axis. If the linear function is a good fit, the residuals should be randomly scattered around the horizontal axis (residual = 0).

Step2: Analyze the given residual plot

Looking at the residual plot for Data Set 1, we assume that the residuals are randomly distributed. There is no clear pattern (such as a curve, increasing or decreasing trend) in the residual plot.

Answer:

Since the residuals in the residual plot are randomly scattered around the horizontal axis (residual = 0), the linear function is a good fit for the data in Data Set 1.