Welcome to Econ 420
Applied Regression Analysis
Study Guide
Week Three (continued)
Ending Sunday, September 16
(Assignment 3 which is included in this study guide is
due before Sunday at 10:00 PM)
The Graded Assignment 2 will be
send to you in a couple of days
• Note
• This is an applied class. That means that
you will get a lot of assignments.
• Be ready & don’t complain.
Recap
• Suppose the population of students at Marietta College =
1200
• The model is
– Y = β0 + β1 X1 + β2 X2 + e
• Y = GPA
• X1 = hours of study
• X2 = IQ score
• We don’t see the true βs
• We choose a sample of 50 students and estimate β^s
• Are our β^s the same as true βs?
– No
• What if we chose another sample of 50 observations?
– We will get different β^s
• Most likely
The sampling distribution of the
estimated coefficients
• Displays the values of all possible β^s that
we can get if we draw an infinite number
of samples from the population to estimate
our equation using a given procedure.
• If the error term is normally distributed 
the estimated coefficients are normally
distributed too
So the distribution of β^s will be just
like the Z distribution below.
Biased/ Unbiased Estimator
• Is a method of estimation which results in
β^s that belong to a distributions whose
means are equal to the true βs
Best (most efficient) Estimator
• Is a method of estimation whose β^s belong to
distributions with the lowest possible variances.
Consistent Estimator
Is a method of estimation that results in β^s that get closer and closer
to the true βs as the sample size is increased.
The Gauss- Markov Theorem
• Given assumptions 1 through 6, the OLS
estimator is BLUE (Best Linear Unbiased
Estimator)
Important note on the meaning of
the estimated slope coefficients
• Suppose the estimated model is
• Y^ = β^0 + β^1 X1 + β^2 X2
– β^1 measures the effect of 1 more unit of X1
on Y^, holding X2 constant and ignoring the
effects of other relevant but omitted
independent variables.
• Key: you can only hold an independent variable
constant if it is included in your model. If X3 is
another relevant variable and it is excluded from
your model, you can’t hold it constant.
Assignment 3
• Has 40 points
• It is due before Sunday, September 16, at 10:00
PM.
• Send your answers to me as one (not multiple
documents, please) email attachment.
• Don’t forget to include your name on the
assignment and on the subject of the email.
• Answer Questions 5, 6, 8 and 13 on Pages 37
and 40.