Question

Q1.

Please download the dataset “Social W orkers” from Canvas and use Minitab for all the analysis. The dataset contains salary and years of experience for 50 social workers. The consulting group working on these data is interested in evaluating how salary ($) changes as a person builds up years of experience (x) in the job. Let’s investigate this question using some of the concepts of linear regression discussed in class this far.

a)Fit a linear regression model to these data. Provide the fitted regression equation

b)Are there any unusual observations? If yes, how many unusual observations and what type of unusual observations they are (outlier or high leverage)?

c)Construct a residual plot against fitted values (^y ) Comment on whether the assumption of constant error variance is reasonably satisfied.

d)Construct a normal probability plot. Comment on whether the assumption that E has a normal distribution is reasonably satisfied.

here is data

years salary

7 26075

28 79370

23 65726

18 41983

19 62308

15 41154

24 53610

13 33697

2 22444

8 32562

20 43076

21 56000

18 58667

7 22210

2 20521

18 49727

11 33233

21 43628

4 16105

24 65644

20 63022

20 47780

15 38853

25 66537

25 67477

28 64785

26 61581

27 70678

20 51301

18 39346

1 24833

26 65929

20 41721

26 82641

28 99139

23 52624

17 50594

25 53272

26 65343

19 46216

16 54288

3 20844

12 32586

23 71235

20 36530

19 52745

27 67282

25 80931

12 32303

11 38371

Answer #1

**1.**

Estimate | Std. Error | t value | Pr(>|t|) | |

Intercept | 11368.7 | 3160.3 | 3.597 | 0.000758 |

Years | 2141.4 | 160.8 | 13.314 | < 2e-16 |

Salary = 11368.7 + 2141.4 * Years

**2.** From boxplot of salary we are not able to
see any outliers. When we look at leverage plot there are 4
observations which have high leverage (Observation 9, Observation
31, Observation 35, Observation 45)

**3.** **& 4.**

Looking at the plots the assumption of constant variance and normality both are reasonably satisfied. Though it would be better to drop the outliers with high leverage

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