MAT 510 - Homework Assignment Homework Assignment 7 Due in Week 8 and worth 30 points The experiment data in below table was to evaluate the effects of three variables on invoice errors for a company. Invoice errors had been a major contributor to lengthening the time that customers took to pay their invoices and increasing the accounts receivables for a major chemical company. It was conjectured that the errors might be due to the size of the customer (larger customers have more complex orders), the customer location (foreign orders are more complicated), and the type of product. A subset of the data is summarized in the following Table. Table: Invoice Experiment Error Customer Size Customer Location Product Type + + + + + + + + + + + + Customer Size: Small (-), Large (+) Customer Location: Foreign (-), Domestic (+) Product Type: Commodity (-), Specialty (=) Number of Errors 15 18 6 2 19 23 16 21 Reference: Moen, Nolan, and Provost (R. D. Moen, T. W. Nolan and L. P. Provost. Improving Quality through Planned Experimentation. New York: McGraw-Hill, 1991) Use the date in table above and answer the following questions in the space provided below: 1. What is the nature of the effects of the factors studied in this experiment? 2. What strategy would you use to reduce invoice errors, given the results of this experiment? Type your answers below and submit this file in Week 8 of the online course shell: MAT 510 - Homework Assignment Answer: 1) We assign a value of 0 for small customer size and 1 for large customer size. Similarly we assign 0 for foreign customer and 1 for Domestic customer and 0 for commodity and 1 for specialty. Customer Size Customer Location Product Type 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 1 Number of Errors 15 18 6 2 19 23 16 21 This assignment will make regression analysis easy in excel. Now we enter the table in excel and run multiple regression analysis which is inside the excel file. From the regression analysis we see that: Coefficient s 0 Intercept 0 8.5 Standard Error #N/A 4.198213906 0 -1 4.198213906 0 16 4.198213906 t Stat #N/A 2.02467053 6 0.23819653 4 3.81114453 9 P-value #N/A 0.11289556 1 0.82343329 2 0.01892153 2 Lower 95% #N/A -3.15611045 12.6561104 5 4.34388955 Upper 95% #N/A 20.1561104 5 10.6561104 5 27.6561104 5 Highest correlation coefficient is 16 and is for specialty product type. This means that the specialty products contribute the maximum to the number of errors in the invoice. The second factor is the customer size. It has a coefficient of 8.5 which means that the number of error increase as the customer size goes large. MAT 510 - Homework Assignment The Customer location is seen to have least impact on the invoice errors and the coefficient is -1 which means that foreign customer has higher invoice errors than domestic customers. 2) The highest contributor to the invoice error is the specialty product and hence we will try to reduce the errors in specialty product to a minimum and try to find out the reasons behind the invoice errors in specialty product. We may also want to focus on commodity products and supply less of specialty product as there are so many errors in specialty products. SUMMARY OUTPUT Regression Statistics Multiple R 0.9505993685 R Square 0.9036391594 Adjusted R Square 0.6054587391 Standard Error 6.8556546004 Observations 7 ANOVA df SS 3 4 7 MS F Significance F 1763 587.66666667 12.503546099 0.0334414765 188 47 1951 0 8.5 -1 16 Standard Error t Stat P-value Lower 95% #N/A #N/A #N/A #N/A 4.1982139059 2.0246705362 0.1128955606 -3.1561104497 4.1982139059 -0.2381965337 0.8234332915 -12.6561104497 4.1982139059 3.8111445387 0.0189215325 4.3438895503 Regression Residual Total Coefficients Intercept 0 0 0 Upper 95% #N/A 20.15611045 10.65611045 27.65611045 Lower 95.0% Upper 95.0% #N/A #N/A -3.1561104497 20.15611045 -12.65611045 10.65611045 4.3438895503 27.65611045 Customer Size Customer Location 0 1 0 1 0 1 0 1 Number of Errors Product Type 0 0 1 1 0 0 1 1 0 0 0 0 1 1 1 1 15 18 6 2 19 23 16 21 Run 1 2 3 4 5 6 7 8 Size (x1) Small(-) Large(+) Small(-) Large(+) Small(-) Large(+) Small(-) Large(+) Display (x2) Shelf(-) Shelf(-) Isle(+) Isle(+) Shelf(-) Shelf(-) Isle(+) Isle(+) Package (x3) Paper(-) Paper(-) Paper(-) Paper(-) Plastic(+) Plastic(+) Plastic(+) Plastic(+) x1 x2 + + + + x1x3 + + + + x2x3 + + + + x1x2x3 + + + + sum+ sumave + aveeffect t-ratio 272 229 68 57.25 10.75 4.19 298 203 74.5 50.75 23.75 9.25 271 230 67.75 57.5 10.25 3.99 280 221 70 55.25 14.75 5.74 257 244 64.25 61 3.25 1.27 260 241 65 60.25 4.75 1.85 Average 51.5 44.5 56 78 54 53 67.5 96.5 251 250 62.75 62.5 0.25 0.10 180 160 140 f(x) = 4.7261904762x + 103.9821428571 120 Regression Coefficients b0 = 125.25 b1= 5.375 b2= 11.875 b3= 5.125 b4= 7.375 b5 = 1.625 b6= 2.375 b7= 0.125 1 1 1 1 1 1 1 1 Run =8 (Look at raw number 10) 125.25 Sign of bo (+) 5.375 Sign of x1 (+) 11.875 Sign of x2 (+) 5.125 Sign of x3 (+) 7.375 Sign of x1x2 (+) 1.625 Sign of x1x3 (+) 2.375 Sign of x2x3 (+) 0.125 Sign of x1x2x3 (+) 159.125 Summary for Runs Run Regression data 1 114.125 51.5 2 107.125 44.5 3 118.625 56 4 140.625 78 5 116.625 54 6 115.625 53 7 130.125 67.5 8 159.125 96.5 Regression Model y = 125.25 + 5.375 x1 + 11.875 X2 +5.125 x3 + 7.375 x1 x2 +1.625 x1 x3+2.375x2 x3 +0.125 x1 x2 x3 facotrs x1 x2 x3 x1 x2 x1 x3 x2 x3 x1 x2 x3 Regression 114.125 107.125 118.625 140.625 116.625 115.625 130.125 159.125 Data 51.5 44.5 56 78 54 53 67.5 96.5 Predicted 57.0625 53.5625 59.3125 70.3125 58.3125 57.8125 65.0625 79.5625 Error -5.5625 -9.0625 -3.3125 7.6875 -4.3125 -4.8125 2.4375 16.9375 E Squared 30.94141 82.12891 10.97266 59.09766 18.59766 23.16016 5.941406 191.2526 S(effect) 7.263715 2.568111 Run =1 (Look at raw number 3) 1 125.25 Sign of bo (+) -1 -5.375 Sign of x1 (-) -1 -11.875 Sign of x2 (-) -1 -5.125 Sign of x3 (-) 1 7.375 Sign of x1x2 (+) 1 1.625 Sign of x1x3 (+) 1 2.375 Sign of x2x3 (+) -1 -0.125 Sign of x1x2x3 (-) 114.125 100 80 60 40 20 0 0 1 2 3 Note: Run =1 and 8 are examples. In same way calculate for run =2,3,4,5,6,7 4 5 6 7 8 9