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...

  1. 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

  1. (8 points) In the estimation, β0=__________, β1=__________, β2=__________, β3=__________.
  2. (2 points) All other factors being equal, is there evidence that men sleep more than women?
  3. (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

Solutions

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 2 years ago
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