# Linear Regression

To complete the quiz, answer each question. Use the Excel template to calculate the linear regression, the correlation coefficient, the coefficient of determination, and the average of each process.

The data in the table below is from a study conducted by an insurance company to determine the effect of changing the process by which insurance claims are approved. The goal was to improve policyholder satisfaction by speeding up the process and eliminating some non-value-added approval steps in the process. The response measured was the average time required to approve and mail all claims initiated in a week. The new procedure was tested for 12 weeks, and the results were compared to the process performance for the 12 weeks prior to instituting the change.

Please complete the calculations in Excel or use a program of your choice and answer the following 14 questions in the assignment tab for this week. As always please watch the review videos provided in the media gallery.

Table: Insurance Claim Approval Times (days)

 Old Process New Process Week Elapsed Time Week Elapsed Time 1 31.7 13 28 2 27 14 25.8 3 33.8 15 34 4 30 16 25 5 32.5 17 27 6 34 18 25.6 7 36 19 29 8 31 20 22.4 9 29 21 28.5 10 29 22 21 11 38.6 23 23 12 39.3 24 22

Use the date in table above and answer the following questions in the space provided below:

1.     What is the linear regression equation for the old process?

2.     Interpret what the slope in this equation means?

3.     What is the linear regression equation for the new process?

4.     Interpret what the slope in this equation means?

5.     What is the interpretation of the y-intercept in the liner regression equation?

6.     What is the interpretation of predicted y given the absence of explanatory variable x given the equation?

7.     Comparing the old process to the new process was there an increase or decrease?

8.     What is the correlation coefficient for the old process?

9.     What is the correlation coefficient for the new process?

10.     What is the coefficient of determination for the old process?

11.  Interpret the coefficient of determination for the old process.

12.  What is the coefficient of determination for the new process?

13.  Interpret the coefficient of determination for the new process.

14.  What was the average effect of the process change? Did the process average increase or decrease and by how much?