Question

students in a science class are constructing a model for a data set. the residual plot for their quadratic regression model is given. which of the following is the best conclusion?
a the quadratic model is appropriate because the residuals show a pattern.
b the quadratic model is appropriate because the residuals show no pattern.
c the quadratic model is not appropriate because the residuals show a pattern.
d the quadratic model is not appropriate because the residuals show no pattern.

Explanation:

Step1: Recall the property of a good regression model

A good regression model (in this case quadratic) should have residuals that show no pattern. If there is a pattern in the residual plot, it indicates that the model is not capturing some underlying relationship in the data.

Step2: Analyze the given options

• Option A: Incorrect. If residuals show a pattern, the model is not appropriate.
• Option B: Incorrect. The residuals in the given plot show a pattern (not random scatter).
• Option C: Correct. Since the residuals show a pattern, the quadratic model is not appropriate.
• Option D: Incorrect. The residuals do show a pattern.

Answer:

C. The quadratic model is not appropriate because the residuals show a pattern.