Example 9.5 A bank is interested in understanding the relationship between the credit score of its...

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Example 9.5 A bank is interested in understanding the relationship between the credit score of its customers (independent variable) and the interest rate they are offered on personal loans (dependent variable). The bank has collected data from a sample of loan applicants. Here is a sample data table: Customer A B C D E F Credit Score (X) 700 730 650 710 680 730 Interest Rate (Y) 6% 4% 7% 4% 6% 3% Using a simple linear regression model, analyze the data and answer the following questions: UPSA Emmanuel Kpeglo (Ph.D.) Scholarship with Professionalism 74 Example 9.5 (continued) (a) What is the regression equation that represents the relationship between credit scores and interest rates? Interpret these coefficients in the context of the problem. (b) If a customer has a credit score of 800, what is the predicted interest rate based on the regression model? (c) Determine the association between Credit Score and Interest Rate and interpret your results. (d) Calculate the coefficient of determination for the regression model. What does this value indicate about the goodness of fit of the model? (e) What variation in Interest Rate is not attributable to Credit Score? (f) Perform, at the 0.05 level of significance, a hypothesis test to determine the significance of the correlation between Credit Score and Interest Rate. UPSA Scholarship with Professionalism Emmanuel Kpeglo (Ph.D.) 75 Example 9.5 A bank is interested in understanding the relationship between the credit score of its customers (independent variable) and the interest rate they are offered on personal loans (dependent variable). The bank has collected data from a sample of loan applicants. Here is a sample data table: Customer A B C D E F Credit Score (X) 700 730 650 710 680 730 Interest Rate (Y) 6% 4% 7% 4% 6% 3% Using a simple linear regression model, analyze the data and answer the following questions: UPSA Emmanuel Kpeglo (Ph.D.) Scholarship with Professionalism 74 Example 9.5 (continued) (a) What is the regression equation that represents the relationship between credit scores and interest rates? Interpret these coefficients in the context of the problem. (b) If a customer has a credit score of 800, what is the predicted interest rate based on the regression model? (c) Determine the association between Credit Score and Interest Rate and interpret your results. (d) Calculate the coefficient of determination for the regression model. What does this value indicate about the goodness of fit of the model? (e) What variation in Interest Rate is not attributable to Credit Score? (f) Perform, at the 0.05 level of significance, a hypothesis test to determine the significance of the correlation between Credit Score and Interest Rate. UPSA Scholarship with Professionalism Emmanuel Kpeglo (Ph.D.) 75