tion as shown below models annual salary in relation to education where Y is the

Question

tion as shown below models annual salary in relation to education where Y is the annual salary in units of £1,000 of individual i X is the number of years individual i has in education Using Ordinary Least Squares estimation based on 100 equation is written as: observations, a regression 0.01 +0.4% (0.8) (0.2) The figures in parentheses below show the estimated coefficient estima standard errors Suppose you predict that spending more years with higher annual salaries. Set up a hypothesis test and compute t-statistic a p-value for your test for this hypothesis. What would you conclude using a significance level of 5%? 2.1) on the education is associated nd [15%] For question (2.1), you now consider gender and race as also likely to affect the annual salary. A different regression equation as shown below models annual salary in relation to education, gender and race: 2.2) where Y is the annual salary in units of £1,000 of individual i Xi is the number of years individual i has in education D = 1 if female, 0 otherwise Da 1 if nonwhite, 0 otherwise From the above equation what is the expectation of average salary of a nonwhite female given her education? [1096] Based on 100 observations the regression results are provided to you as follows (t-statistic in parentheses below): 2.3) Y, = _0.262.36D,,-1 .73D,i-125D,,n, + 5.83X, (9.91) (1.48) (-1.18) (-1.96) R2 0.2032 Discuss whether being female and/or nonwhite individuals earn lower salary using 5% significance level. [15%) Based on data in Question (2.3), compute how much, on average, a female and nonwhite individual income is lower than a male and while individual if both individuals have the same education in years. 2.4) [10%!

Explanation / Answer

Question

2.1 H0 : = 0

Ha : 0

Test statistic

t = ^/ se = 0.4/ 0.2 = 2

here dF = 100 -2 = 98 and alpha = 0.05

p - value = Pr(t > 2; 98; 0.05) = 0.0483 < 0.05

so we shall reject the null hypothesis.

tcritical = t0.05,98 = 1.9845

so here t > tcritical so we shalll reject the null hypothesis and can conclude that the slope coefficient or linear relation is signifant.

Question2

Here expected salary of non white female

that means D2 =1 , D3 =1

Yi = 1 + 2 D2 + 3 D3 + 4 D2 D3 + X

so Y(non white female) = 1 + 2 + 3 + 4 + [X = number of education]

Question 3

Here null hypothesis : H0 : 2 = 3 = 4

Ha :  2 , 3 , 4 0

so for 2

Test statistic t = -2.36/-1.48 = 1.595

p - value = Pr(t > 1.595; 98; 0.05) = 0.1139 > 0.05

for 3

Test statistic t = -1.73/-1.18 = 1.466

p - value = Pr(t > 1.466; 98; 0.05) = 0.14585 > 0.05

for 4

Test statistic t = -1.25/-1.96 = 0.637

p - value = Pr(t > 0.637; 98; 0.05) = 0.5256 > 0.05

here dF = 100 -2 = 98 and alpha = 0.05

tcritical = t0.05,98 = 1.9845

so here, for 2 , 3 , 4

t values < tcrtical so not significant in nature and the following factors doesn't earn lower salary level.

2-4

Here education level is same

y^(white and male, education) = -0.26  -2.36 D2 - 1.73 D3 -1.25 D2 D3 + 5.83X = -0.26 + 5.83 xi

y^ (female and non white) = -0.26 - 2.36 - 1.73 - 1.25 + 5.83 xi = -5.6 + 5.83 xi

so average difference = (-0.26 + 5.83 xi ) - (-5.6 + 5.83 xi ) = 5.34 (in thousands)

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