Question

What is the best indication that a least-squares regression line is an appropriate model for an association?

Option (a) A large value of r^2.
Option (b) A small value of r.
Option (c) A slope that is close to 0.
Option (d) A residual plot that shows an obvious pattern.
Option (e) A residual plot that does not show an obvious pattern.

Answer 1

The best indication that a least-squares regression line is an appropriate model for an association is a residual plot that does not show an obvious pattern. Correct option is e)

Step-by-step explanation:

The best indication that a least-squares regression line is an appropriate model for an association is option (e) A residual plot that does not show an obvious pattern.

When a residual plot does not show an obvious pattern, it suggests that the residuals are randomly scattered around the horizontal line at zero. This indicates that the model is able to capture the underlying relationship between the variables without any systematic bias.

On the other hand, if there is an obvious pattern in the residual plot (option (d)), it suggests that the least-squares regression line is not an appropriate model for the association between the variables.