Question

•         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.)

Answer 1

1.

Old Process Old Process Elapsed Time 31.7 27 33.8 30 32.5 34. 36 31 29 29 38.6 39.3 Week SUMMARY OUTPUT Regression Statistics MultipleR R Square Adjusted R Square 0.154239183 Standard Error Observations 0.480756207 0.23112653 3.542634271 12 ANOVA MS Significance F 12 0.113617398 Regression Residual Total 1 37.72659091 37.72659 3.006041 10 125.5025758 12.55026 11 163.2291667 Coefficients Standard Errort Stat P-value 29.31969697 2.180340672 13.4473 9.94E-08 0.513636364 0.29624996 1.733794 0.113617 Lower 95% er 95% Intercept X Variable 1 24.4615952134.17779873 0.146449683 1.17372241

$x=Week,~y=Elapsed~time\\ Regression~equation~of~Old~process:\\ \hat{y}=29.3197+0.5136x\\ 2.~If~we~increase~one~week~then~expected~elapsed~time~is~increased~by~0.5136~unit.$

3.

$x=Week,~y=Elapsed~time\\ Regression~equation~of~New~process:\\ \hat{y}=37.1585-0.5703x\\ 4.~If~we~increase~one~week~then~expected~elapsed~time~is~decreased~by~0.5703~unit.$

New Process New Process Elapsed Time 29 25.8 34 26 29 25.6 29 22.4 28.5 23 24 23 Week 13 14 SUMMARY OUTPUT Regression Statistics 16 Multiple R R Square Adjusted R Square Standard Error Observations 0.602841686 0.363418098 0.299759908 2.854169853 12 17 20 21 ANOVA 23 24 MS F Significance F Regression Residual Total 46.50631119 46.506315.708898 0.03800207 81.46285548 8.146286 127.9691667 10 coefficients : Standard Error 37.15850816 0.57027972 tstat P-value Lower 95% Uper 95% Intercept X Variable 1 4.491750635 8.272612 8.77E-06 27.15026406 47.16675226 0.238677673-2.38933 0.038002-1.102086718-0.038472723

5.

At x=o expected y=intercept where x=independent variable and y=dependent variable.

6. Old process is increasing since slope >0 whereas New process is decreasing since slope<0.

7.    The correlation coefficient for the old process=0.4807

8.    The correlation coefficient for the new process=-0.6028

9. Note: I think this should be coefficient of determination

Coefficient of determination for old process=R square=0.2311

10. 23.11% of total variation in Elapsed Time of Old process is explained by Week through this regression equation.

11. Coefficient of determination for New process=R square=0.3634

12. 36.34% of total variation in Elapsed Time of New process is explained by Week through this regression equation.