ECMT1020: Introduction to Econometrics
Tutorial questions, Week 1
Introduction + Math Tools
2020 Semester 2
Welcome to ECMT1020 first week tutorial! At the begining of your class your tutor will show you
how to access STATA and use Ed discussion board.
Below questions are aimed to fresh your memory with the mathematical tools & concepts. If you
find that the algebra during the tutorial is moving too fast for you. Don’t be ashamed or afraid, we are
here to help!
Question 1. Assume that n = 5. Compute
(a) zi = 1.
(b) zi = i − 3.
(c) zi = i2 / 20.
(d) zi = 1/i.
n
X
zi in each of the following cases.
i=1
Question 2. Suppose the relationship between annual savings and annual income, measured in dollars , is savings = −300 + 0.09income .
(a) Draw a graph that depicts this relationship.
(b) What is the predicted level of savings for the individual who earns $10,000 ?
(c) What is the predicted level of savings for the individual who earns $0 ?
(d) What is the effect of $1 extra dollar earnings on savings? Does this effect depend on level of savings
? (i.e is the effect same if an individual earns $20,000 vs $10,000 ? )
(e) Is this a realistic model ?
Question 3. Bankrate.com provided the probability distribution in the following table, which reflects the
number of credit cards that its readers carry:
Number of Credit Cards
0
1
2
3
4
Percentage
2.5%
9.8%
?%
16.5%
54.6%
What is the probability that the reader carries less than three cards ?
Question 4.
(a) What is the total percentage change in the following situation? Decrease of 40% followed by an
increase of 60%.
(b)In 1980, 40 percent of the population smoked, and in 1990 only 30 percent smoked. We can thus say
that from 1980 to 1990, the incidence of smoking decreased by ( ) percentage points and ( )percent.
Question 5.
(a) Suppose y = exp(a + bx) What is lny ?
(b) Suppose ln(y) = c + dx What is ey ?
(c) Suppose x increases from 40 to 40.4 ? What is the proportionate change in x? What is the absolute
change in ln(x)?