Model 1 a) Interpret the regression coefficients (both slope and the intercept) in model 1. b) Write
Question:
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?
Basic Business Statistics Concepts and Applications
ISBN: 978-0132168380
12th edition
Authors: Mark L. Berenson, David M. Levine, Timothy C. Krehbiel