Question

1. mr. passwater used a set of data to create a quadratic regression model. the residual plot for his model is shown above. based on the residual plot above, which of the following conclusions is correct? (a) the residual plot has no apparent pattern, so the quadratic model was appropriate. (b) the residual plot has no apparent pattern, so the quadratic model was not appropriate. (a) the residual plot displays a pattern, so the quadratic model was appropriate. (a) the residual plot displays a pattern, so the quadratic model was not appropriate.

Explanation:

Step1: Understand residual plot concept

A good - fitting quadratic regression model should have a residual plot with no apparent pattern. If there is a pattern in the residual plot, it indicates that the model is not appropriate.

Step2: Analyze each option

• Option (A): Says the residual plot has no pattern so the quadratic model is appropriate. But we need to check the plot.
• Option (B): Says the residual plot has no pattern so the quadratic model is not appropriate. This is wrong because no pattern in residual plot for a regression model (here quadratic) means the model is appropriate.

Since the residual plot (assuming it has no pattern as per the general rule for a well - fitting regression model, and in the context of regression model diagnostics, a lack of pattern in the residual plot of a regression model (quadratic in this case) implies the model is appropriate.

Answer:

A. The residual plot has no apparent pattern, so the quadratic model was appropriate.