Tutorial 2 - Linear Regression II (Polynomials, Dummy variables, logs...)

Question 1

How would you add a polynomial into the regression?

Answer 1

in addition to linear term, add polinomial term, i.e.:

Question 2

How can you find out the returns to experience in this example (=wage increase for an additional year of experience, holding all other factors fixed)?

Answer 2

Question 3

What do you need to consider when interpreting regression coefficients?

Answer 3

• Direction of the effect (positive/ negative)?
• Magnitude of the effect? What are the units of measurement of x and y? (e.g. years, Dollars, cm,…)
• Significance

Question 4

How can you interpret a one unit change in x in this regression?

Answer 4

Question 5

What is the appriximation of the log effect of a one unit change in variable x? When can you apply this approximation?

Answer 5

Question 6

How can you interpret the coefficients of this model?

Answer 6

Question 7

Why would you use a log or log-log model?

Answer 7

• Some theories in economics predict a certain functional form, e.g. Cobb-Douglas production function in log-log form,
• Using log(y) as dep. var. ensures that predicted values of y are always positive (makes sense for variables like wages, which can only be positive).
• Taking logs of the dependent variable reduces the influence of outliers (alternative to eliminating outliers).
• Taking logs of the dependent variable sometimes reduces heteroskedasticity problems.

Question 8

What does “UNCONDITIONAL estimate” mean? What is a conditional estimate then?

Answer 8

• Unconditional: Only one regressor, do not condition on other variables
• Conditional: With other variables