Model 1

a) Interpret the regression coefficients (both slope and the intercept) in model 1.

b) Write down the predicted model. How much would you expect someone to make if they have 10 years of education?

c) If someone in your sample has 10 years of education and has a wage = 5, what does their residual equal? Give me one possible reason why a person might have such a residual.

d) Is the slope coefficient in model 1 statistically significant at the 5 percent level? Explain using the p-value. (For this problem, you do NOT have to spell out the distribution of the test statistic, etc.) Also be explicit about what we are actually testing- in both the language of hypothesis testing and in everyday English.

e) What is the formula for βˆ1? Based on the available information, what is the variance of education? What is the covariance between education and wages?

f) Given the answer in e, find the correlation between education and wages. Then, square it. What does it equal (find the value that it equals to in the STATA output)? (give both the value it is equal to and the name of what it equals)

g) Give two formulas for the coefficient of determination. Explain the intuitive meaning of each and then show with values from STATA output that the do indeed give you the correct R-squared value.

h) What is (σˆβ1 )? equal to? What is our estimate of this in our sample? 

 

. desc wage educ exper storage variable name type wage educ exper sum wage educ exper Variable | wage I educ exper 1 float byte byte REGRESSION MODEL 1: reg wage educ Source J Model 1. Residual wage | educ I cons | display format $9.0g $8.0g $8.0g Obs 1260 1260 1260 SS Total 1. 27347.4392 Coef .3770664 1.56942 value label Mean 6.30669 12.56349 18.20635 df 1 1232.96548 1232.96548 26114.4737 1258 20.7587231 Std. Err. .0489263 .6279439 Std. Dev. MS 1259 21.7215561 variable label 4.660639 2.624489 11.96349 hourly wage years of schooling. years of workforce experience P>|t| 0.000 7.71 2.50 0.013 Min 1.02 5 0 Max 77.72 17 48 Number of obs F( 1, 1258) = Prob> F = R-squared = Adj R-squared = Root MSE = .2810802 .3374873 1260 59.40 0.0000 0.0451 0.0443 4.5562 [95% Conf. Interval] .4730526 2.801353