4: Simple Linear Regression
ECON 837
Brian Krauth (adapted from notes by Simon Woodcock), Spring 2010
We will begin our discussion of linear regression by considering the simplest possible
model specication, namely, a single equation in two variables. The
3: Introduction to Estimation and Inference
ECON 837
Brian Krauth (adapted from notes by Simon Woodcock), Spring 2010
Typically, the data we observe consist of repeated measurements on one or more variables
of interest. We usually think of these as being
6: The k-Variable Linear Model 1
ECON 837
Brian Krauth (adapted from notes by Simon Woodcock), Spring 2010
Matrix Formulation
Now we turn our attention to the generalization and matrix formulation of the linear model.
Suppose that:
y1 = 1 x11 + 2 x21 + +
2: Joint Distributions
ECON 837
Brian Krauth (adapted from notes by Simon Woodcock), Spring 2010
The last lecture focused on probability and distribution in the case of a single random
variable. However, in econometrics we are almost always interested in
5: More About Simple Regression
ECON 837
Brian Krauth (adapted from notes by Simon Woodcock), Spring 2010
Recall from last time that and are the least squares estimators of and . We call
i the predicted values.
yi = + x
We turn now to the fraction of var
1: Probability and Distribution Basics
ECON 837
Brian Krauth (adapted from notes by Simon Woodcock), Spring 2010
Random Variables
Econometrics is the application of economic models to economic data. Economic data are
measurements of some aspect of the eco
10: Introduction to Asymptotic Theory - Revised
ECON 837
Brian Krauth (adapted from notes by Simon Woodcock), Spring 2010
To this point, our discussion has focused on the nite sample properties of estimators
(primarily least squares, but also sample means
9: k-Variable Linear Model Miscellany
ECON 837
Brian Krauth (adapted from notes by Simon Woodcock), Spring 2010
Specication Error
Suppose the data generating process is y = X + but the model we t is y = X +
with least squares estimator
1
b = (X X )
X y =
8: The k-Variable Linear Model 3
ECON 837
Brian Krauth (adapted from notes by Simon Woodcock), Spring 2010
The model so far
At this point Id like to review what we have so far, and give everyone a shorthand for
stating our assumptions clearly. The classic
7: The k-Variable Linear Model 2
ECON 837
Brian Krauth (adapted from notes by Simon Woodcock), Spring 2010
Normality
To this point we have made two assumptions: linearity and spherical errors. We now add
a third assumption so that we can derive sampling d