A researcher is interested to check the relationship between the salaries of workers involved in the production process of a company. To accomplish this, she/he has decided to develop a multiple regression model to predict their weekly salaries. For this purpose, he/she has selected a random sample of 50 workers involved in the production process. The information on their current monthly salaries in hundreds (Y), lengths of employment in months (X1), and job classifications (X2; 0 for technical job and 1 for clerical job) are summarised in the following table:
| Employee | Y | X1 | X2 |
| 1 | 495 | 74 | 1 |
| 2 | 406 | 51 | 0 |
| 3 | 567 | 130 | 1 |
| 4 | 523 | 25 | 1 |
| 5 | 575 | 178 | 1 |
| 6 | 437 | 42 | 0 |
| 7 | 664 | 242 | 1 |
| 8 | 491 | 57 | 1 |
| 9 | 472 | 72 | 0 |
| 10 | 407 | 129 | 1 |
| 11 | 378 | 17 | 1 |
| 12 | 725 | 318 | 1 |
| 13 | 600 | 296 | 0 |
| 14 | 440 | 39 | 0 |
| 15 | 662 | 280 | 1 |
| 16 | 523 | 116 | 1 |
| 17 | 428 | 19 | 1 |
| 18 | 535 | 94 | 1 |
| 19 | 533 | 193 | 0 |
| 20 | 528 | 49 | 1 |
| 21 | 446 | 26 | 0 |
| 22 | 528 | 40 | 1 |
| 23 | 498 | 51 | 1 |
| 24 | 478 | 48 | 1 |
| 25 | 507 | 32 | 0 |
| 26 | 478 | 24 | 1 |
| 27 | 645 | 234 | 1 |
| 28 | 577 | 281 | 0 |
| 29 | 554 | 335 | 1 |
| 30 | 654 | 336 | 1 |
| 31 | 566 | 77 | 1 |
| 32 | 433 | 90 | 0 |
| 33 | 466 | 89 | 1 |
| 34 | 365 | 30 | 0 |
| 35 | 677 | 225 | 0 |
| 36 | 473 | 36 | 1 |
| 37 | 644 | 305 | 1 |
| 38 | 685 | 316 | 1 |
| 39 | 356 | 11 | 0 |
| 40 | 444 | 23 | 1 |
| 41 | 478 | 94 | 0 |
| 42 | 408 | 81 | 0 |
| 43 | 456 | 58 | 0 |
| 44 | 409 | 22 | 0 |
| 45 | 691 | 359 | 0 |
| 46 | 463 | 69 | 0 |
| 47 | 436 | 93 | 0 |
| 48 | 413 | 16 | 1 |
| 49 | 734 | 412 | 0 |
| 50 | 463 | 69 | 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.
i) Scatter Plot:
Before diving into the statistical analysis, it's helpful to visualize the relationship among the variables using a scatter plot. In the plot below, the x-axis represents the lengths of employment (X1), the y-axis represents the current monthly salaries (Y), and the colors differentiate between technical (0) and clerical (1) job classifications.
```python
import matplotlib.pyplot as plt
import seaborn as sns
# Data
employee = list(range(1, 51))
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