- 20 Marks
QMDM – APR 2023 – L2 – Q3 – Regression Analysis for Mistakes and Checks
Analyze mistakes vs. checks data with scatter plot, regression, determination coefficient, and prediction.
Question
Yaa Tabua Travel arrange a large number of holidays, and in some of these they make administrative mistakes. They are about to change their quality control procedures, and have done some experiments to see how the number of mistakes varies with the number of checks. The following table shows their findings:
| Checks | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Mistakes | 92 | 86 | 81 | 72 | 67 | 59 | 53 | 43 | 32 | 24 | 12 |
| (a) Draw a scatter plot of the data; identify the independent variable, x, and the dependent variable, y. [5 Marks] | |||||||||||
| (b) Determine the least square estimates of the regression constant, a, and the regression coefficient, b. i.e y=a+bx. [4 Marks] | |||||||||||
| (c) Comment on your estimates in (b) above. [2 Marks] | |||||||||||
| (d) Calculate the coefficient of determination. [6 Marks] | |||||||||||
| (e) Using your line in (b), predict how many mistakes Yaa Tabua would expect with 20 checks and comment on its reliability. [4 Marks] | |||||||||||
| (f) Use your estimate in (d), to comment on the suitability of your estimate in (e) above. [4 Marks] |
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QMDM – APR 2023 – L2 – Q3 – Regression Analysis for Mistakes and Checks
Analyze mistakes vs. checks data with scatter plot, regression, determination coefficient, and prediction.
Yaa Tabua Travel arrange a large number of holidays, and in some of these they make administrative mistakes. They are about to change their quality control procedures, and have done some experiments to see how the number of mistakes varies with the number of checks. The following table shows their findings:
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