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