Regression Assigment

Individual Assignment – Regression Case

 

The risk manager for Big Mac is undertaking a comprehensive analysis of the workers’ compensation injury claims for the firm’s U.S. operations. She has collected monthly data over the last three years with regard to workers’ compensation claims and several other items that she feels may be helpful in predicting future claims.

 

You are a consultant with a risk management consulting firm specializing in detailed quantitative analysis of problems facing corporate risk managers. Your firm has been retained by Big Mac to perform a comprehensive regression analysis of its workers’ compensation claims.

The data provided to you by Big Mac consists of the following information stored in the file data.XLS.

 

Variable Name Description of Variable

 

CLAIMS The number of workers’ compensation injury claims.

 

MALE The proportion of the work force that is male.

 

SAFETY The dollar amount of expenditures on safety programs in thousands.

 

SALES The dollar amount of gross sales in millions.

 

PARTTM The proportion of the work force that is part-time.

 

EMPLOYS The number of employees in thousands.

 

Before you start, please make sure you understand the underlying analytical techniques that you are using (regression analysis). In your written report, please address all of the following points and/or recommendations to the risk manager at Big Mac:

 

1. Before looking at the data, please use intuition to describe each variable’s probable predictive power and direction of relationship with CLAIMS.

 

2. Calculate and analyze the correlation matrix. Explain some of the more significant correlations between the independent variables and CLAIMS, as well as between the independent variables themselves. Please make sure to include in your report the correlation

table you obtain from Excel.

 

3. Perform a comprehensive regression analysis for CLAIMS. This includes calculation and analysis of coefficients, p-values (or t-values), coefficients of determination (R
2), etc. Please make sure to include in your report the regression output from Excel including the following: Regression Statistics including R Square, Adjusted R Square, Standard Errors; as well as coefficient, standard error, p-value and t stat for all explanatory/independent variables.

 

4. Identify and describe the model (i.e., which independent variables should be included – a hint here, not all variables are necessarily needed, pending on statistical significance) that you feel best predicts CLAIMS. Justify the selection of this model from both conceptual and statistical viewpoints. This includes a statement of the identified model that a “non-statistician” could understand.

 

5. Is there an alternative model that is almost as good as your first choice as identified in your answer to number 4? If so, describe it.

  

6. State several managerial recommendations that you would make based on the model identified in number 4.

2

>REGRESS

0

.5

0

80

4

2 0.200

80

0

0

80

4 0.220

80

5

0

1

80

6

0

80

7

8

0

90

9

0

90 0.000 240

10

0

.839

90

11 0.280

90

6

12

0

90

13

0

220

14

105

15

0

105

16

105

4

17

0

105

18

105

19

20

120

21

120

22 0.410

120

23

120

24

120

25

26

135

27

135

28

135

29 0.470

135

30 0.480

135

31 0.480

13.741

32

145

33 0.490

329

34

333

35 0.500

360

36 0.500

160

PERIOD	PARTTM	MALE	SALES	EMPLOYS	SAFETY	CLAIMS
1		0.	20	0.	5	25		4							8	4.	6	10		18
0.50	9	10.448	8.604		16
3		0.		22	0.601	5.598		0.000	20	7
0.547	6.0	19	7.978	166
0.	23	0.645	2.	11	1.9	33	201
0.		24	0.692	3.8	15	3.6	30	191
0.250	0.474	10.723						90	6.746	204
0.	26	0.519	8.039	5.074	2	14
0.	27	0.522	3.957
	0.	28	0.603		13	11.462	188
0.595	10.5	12	14.3	35		17
0.	29	0.505	4.576	18.583		145
0.	32	0.484	7.252						105	11.029
0.330	0.569	5.269	9.354	232
0.	34	0.542	15.503	7.177	243
0.350	0.541	9.525	14.780		21
0.		36	0.458	6.921	10.016	237
0.370	0.471	14.801	8.940	249
0.380	0.425	11.381						120		13.741	251
0.390	0.414	11.129	4.940	298
0.400		0.410	10.364	23.187	215
0.555	12.814	9.275	281
0.420			0.480	12.371	5.582	300
0.430	0.429	15.707	11.202	274
0.440	0.427	15.132						135	11.894	304
0.450	0.462	14.636	14.407	299
0.460	0.	329	16.993	14.258	295
	0.470	0.454	16.179	7.374	3	31
0.436	19.858	16.141	285
0.247	21.200	7.475		333
0.419	17.854	140	312
	0.490	0.459	23.358	13.664	321
0.319	18.892	150	12.683
		0.500	0.422	22.224	155	14.503
0.383	23.571		160	12.877
0.318	19.690	24.507	302