can someone help me with part d and part e please 9) A subsample from the Curren
ID: 3063696 • Letter: C
Question
can someone help me with part d and part e please 9) A subsample from the Current Population Survey is taken on weekly earnings of individuals, their age, and their gender. You have read in the news that women make 70 cents for every $1 that men earn. To examine this hypothesis, you first regress weekly earnings on a constant and a binary variable Femalc, which takes on a value of 1 for females and 0 otherwise. The results are: Earn = 570.70-170.72 . Female, R2-0084, RMSE = 282.12 (a) There are 850 females in your sample and 894 males. What are the mean earnings of males and females in 2b) A classmate argues that you should control for education. He breaks education into 3 mutually exclusive and exhaustive categories: high school dropout, high school graduate, and at least one year of college. He says uayiabc vou should add three dummy variables into the model, one for each category, Is this good advice? Explain. You decide to control for age (in years) in your regression results because you hypot at older people earn more on average than younger people, but at a decreasing rate as they age. This regression output is as follows: 135 Ear 323,.70-169.78 Female 15.15 Age 021 Age2, R2 0135, RMSE 2744s wt to preeict Aius (c) Interpret the two measures of fit.3b (d) How much more, on werage, does wWhut youcbserve Thevove female make per year in your sample compared to a 25 year old femaleem (e) Assuming homoskedasticity, test whether Age and Age2 are jointly significant at the 5% level. R.5 se: 2099Explanation / Answer
(d)
The regression equation is,
Earn = 323.70 - 169.78 * Female + 15.15 Age - 0.021 Age^2
For 30 year old female, Female = 1, Age = 30
Earn = 323.70 - 169.78 * 1 + 15.15 * 30 - 0.021 * 30^2 = 589.52
For 25 year old female, Female = 1, Age = 25
Earn = 323.70 - 169.78 * 1 + 15.15 * 25 - 0.021 * 25^2 = 519.545
So, on average, earning of 30 year old female is greater than that of 25 year old female is by,
= 589.52 - 519.545 = 69.975
(e)
Let the unrestricted model be
Earn = 323.70 - 169.78 * Female + 15.15 Age - 0.021 Age^2 with R2 = 0.135
The restricted model be
Earn = 570.70 - 170.72 * Female with R2 = 0.084
Null hypothesis H0: The coefficients of Age and Age^2 are zero. That is, they are not jointly significant.
Alternative hypothesis Ha: Atleast one of coefficients of Age and Age^2 are not zero. That is, they are jointly significant.
Test Statistic, F = [(R2UR - R2R) / q] / [(1 - R2UR ) / (n-k)]
where R2R is the R2of the restricted model, and R2UR is the R2of the unrestricted model and q is the number of restrictions.
k is number of coefficients in the unrestricted model including intercept.
n is number of observations.
R2UR = 0.135, R2R = 0.084
q = 2, n = 850 + 894 = 1744, k = 4
F = [(0.135- 0.084) / 2] / [(1 - 0.135) / (1744 - 4)] = 51.2948
Degree of freedom of the test statistic is q, n-k = 2, 1740
Critical value of F at significance level of 0.05 and df = 2, 1740 is 3.00 (From, F distribution calculator)
As, observed F (51.2948) is greater than the critical value of F (3.00), we reject the null hypothesis and conclude that there is significant evidence that Age and Age^2 are jointly significant at 5% significance level.
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