Econ 488 – Applied Managerial Econometrics

Cameron Kaplan, Fall 2010

10/1/2010

Lab 5 – Hypothesis Testing

Use the salary.gdt file to answer questions 1 & 2

1. Suppose you want to estimate the following regression model:

salnowi = β0 + β1salbegi + β2timei + β3edleveli + εi

where salnowi is the respondent’s current salary, salbegi is their beginning salary, timei is the number of months at their current job, and edleveli is the number of years of schooling the respondent had.

a)  State your null and alternative hypotheses for the coefficient on salbegi (β1).

b)  Run the regression in gretl. Interpret the estimated regression coefficient on salbegi. (i.e. write a sentence describing the meaning of this coefficient in words).

c)  Can you reject your null hypothesis? Explain.

d)  Can you determine the probability that your null hypothesis is true? If so, what is it?

e)  Can you determine the probability that your null hypothesis is false? If so, what is it?

f)  Have you proved that β1 is not zero?

g)  What does the p-value for β1 tell you?

h)  Use the F-test to test whether time and edlevel are jointly significant. Report your findings and explain.

i)  Suppose that it is company policy that, on average, salaries are supposed to be increased by approximately $50 on average for each additional month an employee works at the company. You are hired to test whether the company adheres to the policy. What are your null and alternative hypotheses?

j)  Based on the 95% confidence interval for the coefficient on timei can you reject your null hypothesis? Explain.

2. In this study, each employee was randomly assigned an id number (variable id) ranging from 1 to 474 in order to keep track of the survey results.

a)  Do you expect the relationship between current salary and employee id number to be statistically significant? Why or why not?

b)  Add the variable idi to your model from question 1 and rerun the regression. What is the coefficient on idi? Is it statistically significant from 0? Explain your criteria (e.g. the significance level).

c)  Do you think that employee id should be included in this model? Why or why not?

d)  Based on the descriptions in the data set, which other variables in the data set do you think should be included in this model? Explain.