Q1. Suppose you estimate a model obtaining, wage = 0.620 + 0.506 × educ + 2.27 × female were wage is measured in dollars/hour and female is a binary variable that is equal to one if the person is a female and zero if the person is a male. The standard errors are 0.67, 0.050 and 0.279, respectively.
(a) Is the ‘gender gap' significantly different from zero?
(b) What is the predicted wage for a female worker with 10 years of education with 16 years?
(c) How many years of education a male needs to obtain the hourly wage that a female with 16 years earns?
Q2. Consider you estimate the following regression model, y = α + βx + u
where y is the dependent variable, x is the independent variable and u is the error term.
(a) Explain the difference between correlation and regression and explain the assumptions of the regression model.
(b) What are the interpretation of α and β?
(c) How would you estimate the unknown population parameters?
(d) What are the statistical properties of the method you proposed?
Q3. Suppose that the null hypothesis is H0 : µ = 1000 and the alternative hypothesis H1 : µ 6= 1000. Assuming σ = 200, n = 100, X¯ = 980, and α = 0.01, calculate the value of the test statistic, set up the rejection region, and determine the p-value. Would you reject the null hypothesis?