Question

the graphs give three residual plots for linear, quadratic, and exponential regressions. which of the following is true about the residual plots for these regressions?
a the residual plots for the linear and exponential regressions are without pattern, and the residual plot for the quadratic regression shows a pattern. therefore, the quadratic model is appropriate.
b the residual plot for the quadratic regression is without pattern, and the residual plots for the linear and exponential regressions show patterns. therefore, the linear and exponential models are appropriate.
c the residual plots for the linear and exponential regressions are without pattern, and the residual plot for the quadratic regression shows a pattern. therefore, the linear and exponential models are appropriate.
d the residual plot for the quadratic regression is without pattern, and the residual plots for the linear and exponential regressions show patterns. therefore, the quadratic model is appropriate.

Explanation:

Step1: Recall the property of a good residual plot

A good regression model (appropriate model) has a residual plot without a pattern. If a residual plot shows a pattern, the model is not appropriate.

Step2: Analyze each option

• Option A: Incorrect. If linear and exponential residual plots are without pattern, then linear and exponential models should be appropriate, not quadratic.
• Option B: Incorrect. If quadratic residual plot is without pattern, quadratic model is appropriate, not linear and exponential.
• Option C: Incorrect. If linear and exponential residual plots are without pattern, linear and exponential models are appropriate, not quadratic.
• Option D: Correct. Since quadratic residual plot is without pattern (so quadratic model is appropriate) and linear and exponential residual plots show patterns (so linear and exponential models are not appropriate)

Answer:

D. The residual plot for the quadratic regression is without pattern, and the residual plots for the linear and exponential regressions show patterns. Therefore, the quadratic model is appropriate.