A study provides data on variables that may be related to the number of weeks a manufacturing worker has been jobless. The dependent variable in the study (Weeks) was defined as the number of weeks a worker has been jobless due to a layoff. The following independent variables were used in the study. Age The age of the worker Educ The number of years of education Married A dummy variable; 1 if married, 0 otherwise Head A dummy variable; 1 if head of household, 0 otherwise Tenure The number of years on the previous job Manager A dummy variable; 1 if management occupation, 0 otherwise Sales A dummy variable; 1 if sales occupation, 0 otherwise The data are available in the file named Layoffs.MTW. Develop an estimated regression equation that can be used to predict the number of weeks a worker has been jobless due to a layoff given age, education and marital status of the worker. Develop an estimated regression equation that can be used to predict the number of weeks a worker has been jobless due to a layoff given age, education, marital status and the number of years on the previous job of the worker. Does the addition of the variable in part (b) add significant benefit to the model? Why or why not? Weeks Age Educ Married Head Tenure Manager Sales 37 30 14 1 1 1 0 0 62 27 14 1 0 6 0 0 49 32 10 0 1 11 0 0 73 44 11 1 0 2 0 0 8 21 14 1 1 2 0 0 15 26 13 1 0 7 1 0 52 26 15 1 0 6 0 0 72 33 13 0 1 6 0 0 11 27 12 1 1 8 0 0 13 33 12 0 1 2 0 0 39 20 11 1 0 1 0 0 59 35 7 1 1 6 0 0 39 36 17 0 1 9 1 0 44 26 12 1 1 8 0 0 56 36 15 0 1 8 0 0 31 38 16 1 1 11 0 1 62 34 13 0 1 13 0 0 25 27 19 1 0 8 0 0 72 44 13 1 0 22 0 0 65 45 15 1 1 6 0 0 44 28 17 0 1 3 0 1 49 25 10 1 1 1 0 0 80 31 15 1 0 12 0 0 7 23 15 1 0 2 0 0 14 24 13 1 1 7 0 0 94 62 13 0 1 8 0 0 48 31 16 1 0 11 0 0 82 48 18 0 1 30 0 0 50 35 18 1 1 5 0 0 37 33 14 0 1 6 0 1 62 46 15 0 1 6 0 0 37 35 8 0 1 6 0 0 40 32 9 1 1 13 0 0 16 40 17 1 0 8 1 0 34 23 12 1 1 1 0 0 4 36 16 0 1 8 0 1 55 33 12 1 0 10 0 1 39 32 16 0 1 11 0 0 80 62 15 1 0 16 0 1 19 29 14 1 1 12 0 0 98 45 12 1 0 17 0 0 30 38 15 0 1 6 0 1 22 40 8 1 1 16 0 1 57 42 13 1 0 2 1 0 64 45 16 1 1 22 0 0 22 39 11 1 1 4 0 0 27 27 15 1 0 10 0 1 20 42 14 1 1 6 1 0 30 31 10 1 1 8 0 0 23 33 13 1 1 8 0 0

A study provides data on variables that may be related to the number of weeks a manufacturing worker has been jobless. The dependent variable in the study (Weeks) was defined as the number of weeks a worker has been jobless due to a layoff. The following independent variables were used in the study. Age The age of the worker Educ The number of years of education Married A dummy variable; 1 if married, 0 otherwise Head A dummy variable; 1 if head of household, 0 otherwise Tenure The number of years on the previous job Manager A dummy variable; 1 if management occupation, 0 otherwise Sales A dummy variable; 1 if sales occupation, 0 otherwise The data are available in the file named Layoffs.MTW. Develop an estimated regression equation that can be used to predict the number of weeks a worker has been jobless due to a layoff given age, education and marital status of the worker. Develop an estimated regression equation that can be used to predict the number of weeks a worker has been jobless due to a layoff given age, education, marital status and the number of years on the previous job of the worker. Does the addition of the variable in part (b) add significant benefit to the model? Why or why not? Weeks Age Educ Married Head Tenure Manager Sales 37 30 14 1 1 1 0 0 62 27 14 1 0 6 0 0 49 32 10 0 1 11 0 0 73 44 11 1 0 2 0 0 8 21 14 1 1 2 0 0 15 26 13 1 0 7 1 0 52 26 15 1 0 6 0 0 72 33 13 0 1 6 0 0 11 27 12 1 1 8 0 0 13 33 12 0 1 2 0 0 39 20 11 1 0 1 0 0 59 35 7 1 1 6 0 0 39 36 17 0 1 9 1 0 44 26 12 1 1 8 0 0 56 36 15 0 1 8 0 0 31 38 16 1 1 11 0 1 62 34 13 0 1 13 0 0 25 27 19 1 0 8 0 0 72 44 13 1 0 22 0 0 65 45 15 1 1 6 0 0 44 28 17 0 1 3 0 1 49 25 10 1 1 1 0 0 80 31 15 1 0 12 0 0 7 23 15 1 0 2 0 0 14 24 13 1 1 7 0 0 94 62 13 0 1 8 0 0 48 31 16 1 0 11 0 0 82 48 18 0 1 30 0 0 50 35 18 1 1 5 0 0 37 33 14 0 1 6 0 1 62 46 15 0 1 6 0 0 37 35 8 0 1 6 0 0 40 32 9 1 1 13 0 0 16 40 17 1 0 8 1 0 34 23 12 1 1 1 0 0 4 36 16 0 1 8 0 1 55 33 12 1 0 10 0 1 39 32 16 0 1 11 0 0 80 62 15 1 0 16 0 1 19 29 14 1 1 12 0 0 98 45 12 1 0 17 0 0 30 38 15 0 1 6 0 1 22 40 8 1 1 16 0 1 57 42 13 1 0 2 1 0 64 45 16 1 1 22 0 0 22 39 11 1 1 4 0 0 27 27 15 1 0 10 0 1 20 42 14 1 1 6 1 0 30 31 10 1 1 8 0 0 23 33 13 1 1 8 0 0

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Question

A study provides data on variables that may be related to the number of weeks a manufacturing worker has been jobless. The dependent variable in the study (Weeks) was defined as the number of weeks a worker has been jobless due to a layoff. The following independent variables were used in the study.

Age The age of the worker

Educ The number of years of education

Married A dummy variable; 1 if married, 0 otherwise

Head A dummy variable; 1 if head of household, 0 otherwise

Tenure The number of years on the previous job

Manager A dummy variable; 1 if management occupation, 0 otherwise

Sales A dummy variable; 1 if sales occupation, 0 otherwise

The data are available in the file named Layoffs.MTW.

Develop an estimated regression equation that can be used to predict the number of weeks a worker has been jobless due to a layoff given age, education and marital status of the worker.
Develop an estimated regression equation that can be used to predict the number of weeks a worker has been jobless due to a layoff given age, education, marital status and the number of years on the previous job of the worker.
Does the addition of the variable in part (b) add significant benefit to the model? Why or why not?

Weeks	Age	Educ	Married	Head	Tenure	Manager	Sales
37	30	14	1	1	1	0	0
62	27	14	1	0	6	0	0
49	32	10	0	1	11	0	0
73	44	11	1	0	2	0	0
8	21	14	1	1	2	0	0
15	26	13	1	0	7	1	0
52	26	15	1	0	6	0	0
72	33	13	0	1	6	0	0
11	27	12	1	1	8	0	0
13	33	12	0	1	2	0	0
39	20	11	1	0	1	0	0
59	35	7	1	1	6	0	0
39	36	17	0	1	9	1	0
44	26	12	1	1	8	0	0
56	36	15	0	1	8	0	0
31	38	16	1	1	11	0	1
62	34	13	0	1	13	0	0
25	27	19	1	0	8	0	0
72	44	13	1	0	22	0	0
65	45	15	1	1	6	0	0
44	28	17	0	1	3	0	1
49	25	10	1	1	1	0	0
80	31	15	1	0	12	0	0
7	23	15	1	0	2	0	0
14	24	13	1	1	7	0	0
94	62	13	0	1	8	0	0
48	31	16	1	0	11	0	0
82	48	18	0	1	30	0	0
50	35	18	1	1	5	0	0
37	33	14	0	1	6	0	1
62	46	15	0	1	6	0	0
37	35	8	0	1	6	0	0
40	32	9	1	1	13	0	0
16	40	17	1	0	8	1	0
34	23	12	1	1	1	0	0
4	36	16	0	1	8	0	1
55	33	12	1	0	10	0	1
39	32	16	0	1	11	0	0
80	62	15	1	0	16	0	1
19	29	14	1	1	12	0	0
98	45	12	1	0	17	0	0
30	38	15	0	1	6	0	1
22	40	8	1	1	16	0	1
57	42	13	1	0	2	1	0
64	45	16	1	1	22	0	0
22	39	11	1	1	4	0	0
27	27	15	1	0	10	0	1
20	42	14	1	1	6	1	0
30	31	10	1	1	8	0	0
23	33	13	1	1	8	0	0