1.  According to the following estimated equation, try to study the tradeoff between time spent sleeping and working.

SLEEP_hat= 3,586.25 — 0.148 TOTWRK — 11.13 EDUC +2.20 AGE

         (112.28)     (0.017)         (5.88)     (1.45)

n= 706, R-squared= 0.113, Adj. R_squared= 0.110,

Here sleep and totwrk are the time spent in sleeping and working per week in minutes, educ and age are measured in years. The standard errors are in the parentheses below the estimated coefficients.

(i) Is either education or age individually significant at 5% level against a two-sided alternative? Show your work.

(ii) Dropping educ and age from the equation gives

SLEEP_hat= 3,586.38 — 0.151 TOTWRK

(38.91) (0.017)

        n = 706, R-squared= 0.103, Adj. R_squared= 0.102.

       Are educ and age jointly significant in the original equation at 5% level? Show your work.

(iii)   Dropping age from the original equation gives

SLEEP_hat = 3756.22 — 0.149*TOTWRK — 13.50*EDUC

             (81.29)     (0.017)        (5.68)

      n = 706, R-squared= 0.103.

       What is the estimated adjusted R-squared? (keeping 3 decimals)

(iii) Which of the above three estimated equations do you prefer? Why?

(iv) What is the estimated tradeoff between time spent sleeping and working? Is that statistically significant at 1% level?

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