Three statisticians each created a linear model to show the

Three statisticians each created a linear model to show the relationship between two quantitative variables. After creating their linear models, each analyzed the residuals by creating residual plots. These residual plots are shown below and labeled a, b, and c.

Discuss what each of the residual plots indicates about the appropriateness of the linear model that was fit to the data. What can you tell about the relationship between the data and the least square regression line in each of the three cases? Be sure to indicate which statistician has the \"best\" model based on this analysis.

Solution

(a)The residual plot pattern is non-random (U-shaped), suggesting a better fit for a non-linear model.

--------------------------------------------------------------------------------------------------------------

(b)The residual plot pattern has a trend.

--------------------------------------------------------------------------------------------------------------

(c)The residual plot shows a random pattern, indicating a good fit for a linear model.