Credit score is a strong predictor of interest rate on a 36-month auto loan. Borrowers with higher credit scores tend to qualify for lower interest rates.
(a) In the given scenario, the explanatory variable is likely to be the credit score, which serves as a quantitative measure of a borrower's creditworthiness.
The response variable is likely to be the interest rate on a 36-month auto loan. Credit scores are commonly utilized by lenders to assess the risk associated with a borrower.
Typically, borrowers with lower credit scores are considered higher risk, and lenders often charge them higher interest rates to compensate for the perceived increased likelihood of default.
(c) The linear correlation coefficient between credit score and interest rate on a 36-month auto loan is reported as -0.89.
This coefficient value of -0.89 indicates a strong negative correlation between the two variables.
A negative correlation suggests that as the credit score increases, the interest rate on the auto loan tends to decrease.
In this context, a correlation coefficient close to -1 further emphasizes the strength and direction of the relationship.
(d) The observed linear correlation coefficient of -0.89 affirms the existence of a strong linear relationship between credit score and interest rate.
The scatter diagram accompanying this analysis displays a discernible downward trend, reinforcing the negative correlation.
This relationship aligns with expectations, as higher credit scores are typically associated with lower interest rates due to the reduced perceived risk for lenders.
The combination of a clear trend in the scatter diagram and a highly negative correlation coefficient provides robust evidence supporting the existence of a linear relationship between credit score and interest rate on a 36-month auto loan.