The correlation coefficient between two quantitative variables is 0.8. What does the value of this correlation coefficient indicate about how well the model fits the data?

Question

A.
The correlation coefficient is not within the correct range.
B.
The model is a good fit.
C.
The model is not a good fit.
D.
No conclusion can be drawn regardin

Answer 1

The correlation coefficient (often denoted as \( r \)) measures the strength and direction of a linear relationship between two quantitative variables. Values of \( r \) range from -1 to 1:

• A value of \( r = 1 \) indicates a perfect positive linear relationship.
• A value of \( r = -1 \) indicates a perfect negative linear relationship.
• A value of \( r = 0 \) indicates no linear relationship.

In this case, a correlation coefficient of \( 0.8 \) indicates a strong positive linear relationship between the two variables. This suggests that as one variable increases, the other variable also tends to increase.

Given these points, the best answer is:

B. The model is a good fit.

However, it's important to note that correlation does not imply causation, and strong correlation does not necessarily mean the model is perfect or appropriate for all types of analysis.