ECMT2150 INTERMEDIATE ECONOMETRICS
Week 2 Tutorial
Linear Regression and OLS
1. Which of the following models are (or can be transformed into) linear regression
models?
a. ௜ ൌ ଴ ൅ ଵ௜ଶ ൅ ௜
b. ௜ ൌ ଴ ൅ ଵ ln ௜ ൅ ௜
c. ln௜ ൌ ଴ ൅ ଵ௜ ൅ ௜
d. ௜ ൌ ଴ expሺଵ௜ ൅ ௜ሻ
e. ௜ ൌ ଴ ൅ ଵଷ௜ ൅ ௜
f. ௜ ൌ ଴ ൅ ଵሺ1 ௜⁄ ሻ ൅ ௜
2. Suppose someone has given you the following regression results:
yˆt = 2.6911 − 0.4795xt
where y is the coffee consumption in Australia (cups per person per day); x is
the retail price of coffee ($ per kilo); and t is the time period.
[Let us assume for simplicity that this is a demand curve. Note that demand
and supply side factors will jointly determine the relationship between price and
quantity, so estimating a demand equation can be complicated.]
a. What is the interpretation of the intercept in this example? Does it make
economic sense?
b. How would you interpret the slope coefficient?
c. Is it possible to tell what the true least squares line is? That is, can you find
β0 and β1?
d. The price elasticity of demand is defined as the percentage change in the
quantity demanded for a percentage change in the price. That is, the
elasticity of y with respect to x is defined as ൌ డ௬డ௫
௫
௬. Note that
డ௬
డ௫ is just the
slope of y with respect to x. From the above regression results, can you
determine the elasticity of demand for coffee? If not, what additional
information do you need?
3. (Computer Exercise) Use the data in WAGE2 to estimate a simple regression
explaining monthly salary (wage) in terms of IQ score (IQ). IQ (intelligence
quotient) tests were developed over 100 years ago and attempt to measure a
person’s innate cognitive ability (IQ tests are sometimes referred to as tests of
‘general intelligence’). There is a substantial body of research which examines
whether IQ is related to a range of outcomes such as occupational status, income
and even criminal activity. In this exercise we consider whether and how IQ affect
the wage people earn in the labour market.
a. Report the average, minimum and maximum values, and the standard
deviation for wage, education and IQ in the sample (IQ scores are
standardized so that the average in the population is 100 with a standard
deviation equal to 15).
b. Estimate a simple regression model where a one-point increase in IQ
changes wage by a constant dollar amount. Use this model to find the
predicted increase in wage for an increase in IQ of 15 points. Does IQ
explain most of the variation in wage?
c. Now, estimate a model where each one-point increase in IQ has the same
percentage effect on wage. If IQ increases by 15 points, what is the
approximate percentage increase in predicted wage?
d. Do you think the simple regression captures a causal effect of IQ on the
wage? Explain.
4. (Wooldridge Question 3.4) The median starting salary for new law school
graduates is determined by:
logሺሻ ൌ ଴ ൅ ଵ ൅ ଶ ൅ ଷ logሺሻ ൅ ସ logሺሻ ൅ ହ ൅ ,
where is the median LSAT score for the graduation class, is the median
college GPA for the class, is the number of volumes in the law school
library, is the annual cost of attending law school, and is a law school
ranking (with ൌ 1 being the best).
i. Explain why we expect ହ ൑ 0.
ii. What signs do you expect for the other slope parameters? Justify your
answers.
iii. Using the data in LAWSCH86 (you do not need to do any regression),
the estimated equation is
logሺሻ෣ ൌ 8.34 ൅ .0047 ൅ .248 ൅ .095 logሺሻ ൅.038 logሺሻ െ .0033
ൌ 136, ଶ ൌ .842
What is the predicted ceteris paribus difference in salary for schools with
a median GPA different by one point? (Report your answer as a
percentage.)
iv. Interpret the coefficient on the variable logሺሻ.
v. Would you say it is better to attend a higher ranked law school? How
much is a difference in ranking of 20 worth in terms of predicted starting
salary?