Question

a. match each scatterplot below with its corresponding residual plot.
scatterplot i scatterplot ii scatterplot iii
residual plot a residual plot b residual plot c

Explanation:

Step1: Analyze Residual Plot A

Residual Plot A has a random scatter of points around the horizontal axis. This indicates that the linear model is a good fit for the data in the scatter - plot. Looking at the scatter - plots, Scatterplot I has a relatively linear relationship with points somewhat evenly distributed around the line of best fit.

Step2: Analyze Residual Plot B

Residual Plot B has a pattern. There is a "fan - like" appearance (the spread of the residuals increases). This suggests that the variance of the response variable is not constant (heteroscedasticity). Scatterplot II has a similar pattern where the spread of the data points around the line of best fit seems to increase as the \(x\) - values increase.

Step3: Analyze Residual Plot C

Residual Plot C also has a pattern. The residuals seem to follow a non - linear trend. Looking at the scatter - plots, Scatterplot III has a non - linear trend in the original data (the points do not follow a perfect straight - line pattern as closely as Scatterplot I and has a different non - constant variance pattern compared to Scatterplot II).

Answer:

Scatterplot I - Residual Plot A, Scatterplot II - Residual Plot B, Scatterplot III - Residual Plot C