The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the tradeoff between time spent sleeping and working and to look at other factors affecting sleep:

sleep = Î²0 + Î²1totwrk + Î²2educ + Î²3age + u,

where sleep and totwrk (total work) are measured in minutes per week and educ and age are measured in years. (See also Computer Exercise.)

(i) If adults trade off sleep for work, what is the sign of Î²1?

(ii) What signs do you think Î²2 and Î²3 will have?

(iii) Using the data in SLEEP75.RAW, the estimated equation is

= 3,638.25 - .148 totwrk - 11.13 educ + 2.20 age n = 706, R2 = .113.

If someone works five more hours per week, by how many minutes is sleep predicted to fall? Is this a large tradeoff?

(iv) Discuss the sign and magnitude of the estimated coefficient on educ.

(v) Would you say totwrk, educ, and age explain much of the variation in sleep? What other factors might affect the time spent sleeping? Are these likely to be correlated with totwrk?

Use the data in SLEEP75.RAW from Biddle and Hamermesh (1990) to study whether there is a tradeoff between the time spent sleeping per week and the time spent in paid work. We could use either variable as the dependent variable. For concreteness, estimate the model

sleep =Î²0+ Î²1totwrk+u, where sleep is minutes spent sleeping at night per week and totwrk is total minutes worked during the week.

(i) Report your results in equation form along with the number of observations and R2. What does the intercept in this equation mean?

(ii) If totwrk increases by 2 hours, by how much is sleep estimated to fall? Do you find this to be a large effect?

2. The sign of i²2 is likely to be negative. This is because due to the demands placed on them, more educated people are likely to sleep less. Also, general as age increases some people sleep less. While some others sleep more as it increases. So i²3 is a bit complicated to judge.

3. Using the data

^sleep = 3638.24-0.148toteork-11.13educ + 2.20age

N = 706 r² = 0.113

We will convert 5 hours to minutes = 60x5 = 300

Coefficient of totwork = 0.148

O.148x300 = 44.4 minutes

In a week approximately 45 minutes of less sleep is not too much a change.

4. We are to discuss the sign and magnitude of estimated education

More education indicates less sleeping time. This is obvious given the sign of the variable educ. It is negative, but it's effect is quite small. Magnitude is -11.13.

So as education increases by 1 year, expected sleeping time decreases by 11.13 minutes weekly.

5. R² is 0.113. the 3 predictor variables gives us 11.3% of total variations in sleep and rest. 88.7% is unexplained.

Some factors that might also affect it are general health, number and age of children are factors that could correlate with totwork