Question

1. make a residual plot for the linear model and the data set it represents. how well does the model fit its data set?

y = 0.14x + 12.8

1. describe the type of correlation indicated by each correlation coefficient.

a. r = -0.89
b. r = 0.94

Explanation:

Step1: Recall the correlation coefficient interpretation

The correlation coefficient \( r \) measures the strength and direction of a linear relationship. If \( r = - 0.89 \), the negative sign indicates a negative linear relationship. The magnitude \( |r|=0.89 \) which is close to \( 1 \), so it is a strong negative linear relationship.

Step2: Analyze \( r = 0.94 \)

For \( r = 0.94 \), the positive sign shows a positive linear relationship. The magnitude \( |r| = 0.94\) (close to \(1\)) implies a strong positive linear relationship.

Answer:

a. A strong negative linear relationship.
b. A strong positive linear relationship.