Reference no: EM131133798
1. Tins exercise uses the data in "SLEEP75.dta" from Biddle and Hamermesh (1990) to study whether there is a tradeoff between the tune spent sleeping per week and the time spent in paid work and whether there are any differences in men's and women's sleeping time.
i) Report in a table the mean values and standard deviations of sleep, torwrk educ, age, yngkid, and south for men and women separately. Comment on main differences between the two groups.
ii) Using a 5% level of significance test the following hypotheses: 1) women spend more time sleeping, than men; 2) men spend more time in paid work than women; 3) people with young children sleep less than people without; 4) working people spend less time sleeping than non-working people; 5) working women sleep less than working men.
iii) Estimate the following equation:
sleep = α1 + α2,totwrk + α3educ + α4age+ α5agesq +α6male + α7yngkid + α8south + u (1)
a. Report the regression results in the usual way.
b. All other factors being equal, is there evidence that men sleep more than women? How strong is the evidence? Explain the result.
c. Test the null hypothesis that, holding other factors fixed, age has no effect on sleeping at the 5% level of significance.
d. Using interactive dummy variables, test separately the following hypotheses: 1) having young children makes no difference in men's and women's sleeping time; 2) there is no gender difference regarding the sleep work tradeoff; 3) there is no difference in the sleep-work tradeoff between those having young children and those not having young children; 4) more educated men sleep more than more educated women. Use a 5% level of significance. Comment on the results.
iv) Estimated the following equation separately for men and women and report the result in usual form. Are there notable differences in the two estimated equations?
sleep = α1 + α2totwrk + α3educ + α4age + α5agesq + α6yngkid + α7south + u (2)
v) Compute the Chow test for equality of the parameters in equation (2) for men and women. Should you reject the null at the 5% level?
vi) Test for equality of the parameters in equation (2) using the form of the test that adds male and the interactive terms male*totwrk, ..., male*south and uses the fall set of observations. Use the 5% level of significance. Is the tent result different from that of the Chow test?
vii) Now allow for a different intercept for males and females and determine whether the interactive terms involving male are jointly significant.
viii) Given the results from v) and vi), what Ivould be your final model?
2. A 1974 study related lung capacity to smoking habits and occupation. The study included 1,072 individuals from four occupations (chemical, workers, firemen, farm workers and physicians). The estimated regression with standard errors in parenthesis is:
AIRi = 3605 - 39AGEi + 98HTi - 9.0PRSMOKi - 0.0039 PASMOKi - 2.6CPSMOKi - 350CHEMi - 180FIREi - 380FARMi
(933) (1.8) (7.5) (2.2) (0.070) (1.1) (46) (54) (53) R2 = 0.519
AIR= air capacity (in cubic centimeter) that a subject can expire in 1 second
AGE = age in years
HT = height in inches
PRSMOK = number of cigarettes presently smoked per day
PASMOK = number of cigarettes smoked in the past (= number of years smoking x number of cigarettes per day)
CPSMOK = number of cites and pipes presently smoked per week
CHEM = 1 if chemical worker; = 0 otherwise
FIRE = 1 if fireman = 0 otherwise
FARM= 1 if farm worker = 0 otherwise
a. Why isn't a dummy variable included for physicians?
b. Indicate whether each coefficient is significantly different front zero at the 5% level or not.
c. What is the effect on air capacity if a person becomes one year older (all other variable unchanged)?
d. Test the hypothesis that an extra inch of 'height will increase lung capacity by 110 cubic centimeters against the alternative that lung capacity will increase by less than the amount. Use a 5% level of significance.
e. Which of the occupations is most hazardous to health, in terms of reducing lung capacity? What is the decrease in air capacity associated with this occupation?
f. In terms of effects on air capacity, smoking one pack (20 cigarettes) per day is equivalent to aging how many years.
g. Test the hypothesis that all the coefficients in the regression model (except the intercept) are simultaneously equal to zero at the 1% level of significance.
h. When the regression is re-estimated without the three dummy variables, the R2 is 0.485. Test the null hypothesis that the occupation variables as a group are unrelated to air capacity. Use a 5% significance level.