A researcher estimates the following regression using 1000 observations: W=-3.13+1.47*EDU &n

A researcher estimates the following regression using 1000 observations:

W=-3.13+1.47*EDU

(0.93) (0.07)

Where W is wage, EDU is years of education and the numbers in parentheses are standard errors of the coefficients.

Calculate a 95% confidence interval for the coefficient on EDU.

A high school graduate is contemplating whether to obtain a 4-year college degree. How much is his/her wage expected to rise?

A high school counselor tells a student that college graduates earn a wage $12 per hour higher than high school graduates. Is this statement consistent with the evidence?

Solutions

Expert Solution

a) alpha = 1 - CI/100 = 1- (95/100) = 0.05

df = n - 2 ( 1 variable and one intercept)

= 1000 - 2 = 998

Critical t value from t table at 95% CI is for 2 tailed test is 1.96

Margin of error = critical value*SE = 1.96*0.07 = 0.1372

Thus 95 %CI is 1.47 + -0.1372

1.6072 AND 1.3328

b) From the result it can be said that for increase in 1 year of education, wage increases by 1.47 units.

So, for a 4 year degree course, wage should increase by 4*1.47 units = 5.88 units [ wage units not mentioned in question ]

c) From (b), we observe that for a college degree that is 4 year long, expected increase in wage in 5.88 units.

Assuming the units to be in $/hour, it is much less than $12/hour increment in comparison to high school graduates as mentioned by counselor.

Although the statement is true in terms of increment of wage but magnitude of increment mentioned is inflated by counselor. So, statement is partially consistent.

Rahul Sunny answered 1 year ago

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