Reference no: EM132232632
Assignment - LINEAR REGRESSION AND THE CORRELATION COEFFICIENT
Part A -
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
|
29
|
|
2
|
27
|
|
14
|
25.8
|
|
3
|
33.8
|
|
15
|
34
|
|
4
|
30
|
|
16
|
26
|
|
5
|
32.5
|
|
17
|
29
|
|
6
|
34
|
|
18
|
25.6
|
|
7
|
36
|
|
19
|
29
|
|
8
|
31
|
|
20
|
22.4
|
|
9
|
29
|
|
21
|
28.5
|
|
10
|
29
|
|
22
|
23
|
|
11
|
38.6
|
|
23
|
24
|
|
12
|
39.3
|
|
24
|
23
|
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.)
Part B - QUESTIONS
Q1. What is the linear regression equation for the old process? Round the intercept to one decimal place and the slope to three decimal places.
29.3 x + .514
.293 - .514x
y = 29.3 + .514x
y = 29.3% + 51.4%x
Q2. What is the linear regression equation for the new process? Round the intercept to one decimal and the slope to three decimal places.
30.3% - 0.57%X
Y = 30.3 - 0.57X
-.57 + 30.3X
Y= -30.3 + 0.57X
Q3. Interpret what the slope given the linear equation predicted y = 29.3 + 0.514x in this equation means?
For every increase of one in the independent variable x there is an increase of 0.514 in predicted y.
For every increase of one in the independent variable x there is an decrease of 0.514 in predicted x.
For every increase of one in the dependent variable x there is an increase of 0.514 in predicted y.
For every increase of one in the independent variable x there is an decrease of 0.514 in predicted y.
Q4. Interpret the slope for the equation y = 30.3 - 0.57x
For every increase of one in the independent variable x there is an increase of 0.57 in predicted x.
For every increase of one in the independent variable x there is an decrease of 0.57 in predicted x.
For every increase of one in the independent variable x there is an increase of 0.57 in predicted y.
For every increase of one in the independent variable x there is an decrease of 0.57 in predicted y.
Q5. What is the interpretation of the y-intercept in the liner regression equation?
Given: y = 29.3 + 0.514x
The interpretation of the y-intercept is the value for predicted y given the absence of explanatory variable x.
The interpretation of the y-intercept is the value for y given the absence of response variable y.
The interpretation of the y-intercept is the value for x given the absence of explanatory variable y.
The interpretation of the y-intercept is the value for predicted y given the absence of response variable x.
Q6. What is the interpretation of predicted y given the absence of explanatory variable x given the equation 30.3 - 0.57x?
The interpretation of the y-intercept is the value for predicted y given the absence of explanatory variable x. In this case, predicted y is 30.3 given the absence of x.
The interpretation of the y-intercept is the value for predicted y given the absence of response variable x. In this case, predicted y is 30.3 given the absence of x.
The interpretation of the y-intercept is the value for predicted x given the absence of explanatory variable x. In this case, predicted y is 30.3 given the absence of x.
The interpretation of the y-intercept is the value for predicted y given the absence of explanatory variable x. In this case, predicted y is 30.3 given the absence of y.
Q7. Comparing the old process to the new process was there an increase or decrease relative to the time spent?
No change
Increase
Decrease
Unable to determine
Q8. What is the correlation coefficient for the old process? Round your answer to three decimals.
r = 0.481
r(squared) = 0.481
r = -0.481
r = 48.1%
Q9. What is the correlation coefficient for the new process? Round your answer to three decimals.
r ( squared) = 0.603
r = -0.603
r = 0.603
r^2 = 0.603
Q10. What is the value of the coefficient of variation for the old process?
R2 = 0.231
R = 0.231
23.1
23.1%
Q11. What is the value of the coefficient of variation for the NEW process?
R2 = 0.363
R = 0.363
36
36%
Q12. Interpret the coefficient of determination for the old process. Round your answer to one decimal.
23.1% of the variability present in predicted y can be explained by variability present in the model.
23.1% of the variability present in predicted y can be explained by variability present y.
We do not have enough data to interpret this model.
23.1% of the variability present in the model can be explained by variability present in y.
Q13. Interpret the coefficient of variation in the new process. Round your answer to one decimal.
36.3% of the variability present in predicted y can be explained by variability present in the model.
36.3% of the variability present in predicted x can be explained by variability present in the response variable.
36.3 is the variability present in x and can be explained by variability present in the model.
No conclusion can be drawn as we do not have enough information.
Q14. What was the average effect of the process change? Did the process average increase or decrease and by how much?
The new process reduces the claim time by 6 days. It reduces the elapsed time from 32.6 days to 26.6 days. As a result, the new process reduces claim process time and eliminates work load accumulations.
The new process has a negative effect on improving policy holder satisfaction. The new process improves the average elapsed time from 32.6 days to 26.6 days.
The new process has a positive effect on improving policy holder satisfaction. The new process remains the same the average elapsed time from 32.6 days to 26.6 days.
The new process has a neutral effect on improving policy holder satisfaction. The new process improves the average elapsed time from 32.6 days to 26.6 days.
Q15. 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.)
The new process reduces the claim time by 6 days. It reduces the elapsed time from 32.6 days to 26.6 days. As a result, the new process reduces claim process time and eliminates work load accumulations.
The new process increases the claim time by 6 days. It reduces the elapsed time from 26.6 days to 32.6 days. As a result, the new process reduces claim process time and eliminates work load accumulations.
The new process negatively affects the claim time by 6 days. It reduces the elapsed time from 26.6 days to 32.6 days. As a result, the new process reduces claim process time and eliminates work load accumulations.
The new process reduces the claim time by 6 days. It reduces the elapsed time from 32.6 days to 26.6 days. As a result, the new process increases claim process time and eliminates work load accumulations.