Question

Table: Insurance Claim Approval Times (days)

Old Process			New Process
Week	Elapsed Time		Week	Elapsed Time
1	31.7		13	24
2	27		14	25.8
3	33.8		15	31
4	30		16	23.5
5	32.5		17	28.5
6	33.5		18	25.6
7	38.2		19	28.7
8	37.5		20	27.4
9	29		21	28.5
10	31.3		22	25.2
11	38.6		23	24.5
12	39.3		24	23.5

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

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

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

9.     What is the coefficient of variation for the old process?

10.  Interpret the coefficient of variation for the old process.

11.  What is the coefficient of variation for the new process?

12.  Interpret the coefficient of variation for the new process.

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

14.  How much did the process performance change on the average? (Hint: Compare the values of b1 and the average of new process performance minus the average of the performance of the old process.)

Answer 1

1. Old process:

Here, we consider the Time Taken as the dependent variable and week as independent variable.

So, the Linear regression Equation for the Old process is given by,

(the following Simulation of generating the Linear Regression Equation is done in Excel)

Intercept	29.32424242
X Variable 1	0.647552448

R Square	0.330109865
Adjusted R Square	0.263120852

Elapsed Time = 29.32 + 0.648 Week

2. Interpretation:

Here, the slope of the Linear regression equation is = 0.647552448 which means for each unit increase in the number of weeks the Elapsed time to settle the insurance claim will increase by 0.648 times.

3. New process:

Here, we consider the Time Taken as the dependent variable and week as independent variable.

So, the Linear regression Equation for the New process is given by,

(the following Simulation of generating the Linear Regression Equation is done in Excel)

Intercept	28.48461538
X Variable 1	-0.115384615

R Square	0.029348638
Adjusted R Square	-0.067716498

Elapsed Time_1 = 28.48 - 0.115 Week_1

4. Interpretation(slope):

Here, the slope of the Linear regression equation is = -0.115384615 which means for each unit increase in the number of weeks the Elapsed time to settle the insurance claim will decrease by 0.115 times.

5. Interpretation(intercept):

Here, the intercept of the Linear regression equation is = 28.48 which means time elapsed to settle the insurance claims with number of weeks =0 is 28.48.

6. Comparison of the 2 process:

The Time elapsed for settling an insurance claim in New process has decreased as compared to the old model.

7. Correlation coefficient (old process):

Excel formula for calculating this = correl(Range)

r=0.574551882

8. Correlation coefficient (old process):

r= -0.171314442

9. Coefficient of variation (old process):

The Coefficient of variation is calculated for the variable Elapsed Time.

Excel formula for calculating this =stdev(range)/average(range))

C.V = 11.60236082 %

11) Coefficient of variation (old process):

C.V = 8.82369944 %

(10) & (12) Interpretation:

Generally, C.V is a relative measure of dispersion used for comparing the dispersion of 2 data sets or variables under study.

C.V = 11.60 %

C.V = 8.82 %

So, we can conclude that the Dispersion of First data set or the old process is more than the new process.