Question

In: Statistics and Probability

Use the date set in SLEEP75 to estimate the multiple regression model sleep= β0+β1totwrk+β2educ+β3male+u. and answer...

Use the date set in SLEEP75 to estimate the multiple regression model

sleep= β0+β1totwrk+β2educ+β3male+u.

and answer the following questions. Here the variable sleep is total minutes per week spent at night, totwrk is total weekly minutes spent working, educ and age are measured in years, and male is a gender dummy.

please give some good details

(8 points) In the estimation, β0=__________, β1=__________, β2=__________, β3=__________.
(2 points) All other factors being equal, is there evidence that men sleep more than women?
(3 points) Based on the corresponding estimate, explain in words the estimated tradeoff between working and sleeping.

educ	male	sleep	totwrk
12	1	3113	3438
14	1	2920	5020
17	1	2670	2815
12	0	3083	3786
14	1	3448	2580
12	1	4063	1205
12	1	3180	2113
13	1	2928	3608
17	1	3368	2353
15	1	3018	2851
8	1	1575	6415
16	0	3295	370
16	1	3798	2438
5	1	3008	2693
12	1	3248	2526
12	1	3683	2950
17	1	3201	3003
14	1	2580	4011
12	1	3420	2300
17	1	3090	1543

Expert Solution

	sleep
	3113
	2920
	2670
	3083
	3448
	4063
	3180
	2928
	3368
Y=	3018
	1575
	3295
	3798
	3008
	3248
	3683
	3201
	2580
	3420
	3090

		totwrk	educ	male
	1	3438	12	1
	1	5020	14	1
	1	2815	17	1
	1	3786	12	0
	1	2580	14	1
	1	1205	12	1
	1	2113	12	1
	1	3608	13	1
	1	2353	17	1
X=	1	2851	15	1
	1	6415	8	1
	1	370	16	0
	1	2438	16	1
	1	2693	5	1
	1	2526	12	1
	1	2950	12	1
	1	3003	17	1
	1	4011	14	1
	1	2300	12	1
	1	1543	17	1

	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
	3438	5020	2815	3786	2580	1205	2113	3608	2353	2851	6415	370	2438	2693	2526	2950	3003	4011	2300	1543
X'=	12	14	17	12	14	12	12	13	17	15	8	16	16	5	12	12	17	14	12	17
	1	1	1	0	1	1	1	1	1	1	1	0	1	1	1	1	1	1	1	1

	20	58018	267	18
X'X=	58018	200879306	746890	53862
	267	746890	3747	239
	18	53862	239	18

	2.2023116	-0.00015131	-0.099135	-0.43324787
	-0.000151	3.67451E-08	5.35E-06	-2.9731E-05
(X'X)-1=	-0.099135	5.35396E-06	0.006286	-0.00035514
	-0.433248	-2.9731E-05	-0.000355	0.582482709


	62689
X'Y=	172500717
	844807
	56311

	3813.0166
B^=(X'X)-1X'Y=	-0.2981
	-0.3231
	211.7362

The regression equation is

sleep= 3813.0166 - 0.2981*totwrk- 0.3231*educ+211.7362*male

1. In the estimation, β0=3813.0166 , β1=- 0.2981, β2=- 0.3231, β3=211.7362.

2. All other factors being equal, is there evidence that men sleep more than women?

Ans: The value of slope corresponding to the Male factor is 211.7362 with a positive sign. Whereas the p-value for the test is 0.465 and greater than 0.05 level of significance. Hence, under all other factors being equal, there is no evidence that men sleep more than women at the 0.05 level of significance.

3. (3 points) Based on the corresponding estimate, explain in words the estimated trade-off between working and sleeping.

Ans: The value of the slope corresponding to total weekly minutes spent working is - 0.2981 with p-value 0.001 So, when a minute increased on the spent working decreases the mean sleep by 0.2981 minutes per week spent at night.

orchestra answered 1 year ago

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