Question
A researcher is interested in studying the impact of the weekly working hours and type of machine used (0 for Machine A and 1 for Machine B) on the number of produced items of a particular type. The data were collected for 40 weeks and shown in the following table:
| Week | Produced Item | Working Hours | Machine Type |
| 1 | 9 | 48 | 1 |
| 2 | 15 | 67 | 1 |
| 3 | 12 | 61 | 1 |
| 4 | 17 | 86 | 0 |
| 5 | 19 | 93 | 1 |
| 6 | 17 | 80 | 1 |
| 7 | 12 | 55 | 0 |
| 8 | 9 | 51 | 1 |
| 9 | 7 | 44 | 0 |
| 10 | 18 | 89 | 0 |
| 11 | 13 | 55 | 1 |
| 12 | 10 | 56 | 0 |
| 13 | 15 | 67 | 1 |
| 14 | 13 | 63 | 1 |
| 15 | 15 | 73 | 0 |
| 16 | 15 | 73 | 0 |
| 17 | 14 | 70 | 0 |
| 18 | 15 | 67 | 1 |
| 19 | 12 | 57 | 1 |
| 20 | 14 | 68 | 0 |
| 21 | 13 | 57 | 1 |
| 22 | 11 | 57 | 0 |
| 23 | 11 | 64 | 0 |
| 24 | 13 | 67 | 0 |
| 25 | 10 | 56 | 0 |
| 26 | 7 | 47 | 0 |
| 27 | 8 | 47 | 0 |
| 28 | 12 | 64 | 0 |
| 29 | 7 | 42 | 0 |
| 30 | 11 | 60 | 0 |
| 31 | 15 | 67 | 1 |
| 32 | 13 | 60 | 1 |
| 33 | 16 | 69 | 1 |
| 34 | 10 | 44 | 1 |
| 35 | 18 | 83 | 1 |
| 36 | 20 | 94 | 1 |
| 37 | 17 | 82 | 0 |
| 38 | 19 | 93 | 1 |
| 39 | 10 | 57 | 0 |
| 40 | 7 | 35 | 0 |
i) Prepare a scatter plot to get an idea about the relationship among the variables.
ii) Fit a linear regression model and its related analysis at 1% level of significance.
iii) Does the fitted regression model satisfy the linearity and normality assumptions?
iv) Also, draw both fitted regression lines on the scatter plot.
Answer :
Word Count : 155
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To solve this numerically, we can model the relationship between the number of produced items (dependent variable) and the working hours and machine type (independent _________ __________ _______ _____ ________.
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