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 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 From the regression analysis we see that: Coefficient s 0 Intercept Standard Error #N/A 0 8.5 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. 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. MAT 510 - Homework Assignment 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