Welcome to Econ 420 Applied Regression Analysis

1
Welcome to Econ 420 Applied Regression Analysis

• Study Guide
• Week One
• Ending Sunday, September 2
• (Note You must go over these slides and complete
  every task outlined here before September 2)

2
1. Study the Course Contract avialable on WebCT.
The course contract is also available on line at
www.marietta.edu/khorassj

• Make sure you understand the contract
• Send me your questions via WebCTs Discussion
  available at http//webct.marietta.edu
• Post your question under the topic Questions on
  Course Contract
• For the subject put your name

3
2. Are you eligible for ODE membership?

• Find out more about ODE and see if you qualify.
  Information is available at http//www.marietta.ed
  u/ema/econ/ode.html
• Ask me questions about ODE via WebCT discussion
• Post your question under the topic Questions on
  ODE
• For the subject put your name
• Contact Dr. Delemeester if you interested in
  becoming a member
• He is in Thomas 118
• He could be reached at delemeeg_at_marietta.edu
• His campus extension is 4630

4
3. Learn more about ERT

• Information is available at www.economicroundtable
  .org
• You can purchase Student Membership only for 5.
• Ask me questions via WebCt Discussion
• Post your question under the topic Questions on
  ERT
• For the subject put your name
• If Interested complete the membership form and
  either directly mail it or give it to Dr.
  Delelmeester with a check for 5.

5
4. Read the EViews Booklet

• EViews is a statistical software that you will be
  using in this course
• Install it on your computer, if you wish.
• Ask me questions via WebCt Discussion
• Post your question under the topic Questions on
  EViews
• For the subject put your name

6
5. Study the textbooks Preface

• Believe me it is not a waste of time to read the
  Preface of a book
• Ask me Questions via WebCts Discussion
• Post your question under the topic Questions on
  Preface
• For the subject put your name

7
6. If your book is new, it comes with a little
card entitled e-con_at_ppc

• Go to http//econapps.swlearning.com to register
  your serial number
• We will mainly use this source for data.
• Dont panic if you dont have a new book.
• We will find another way to get the data if we
  need it.

8
7. Another assignment

• Go to WebCts Discussion and report your weight
  (in ponds) and height (in inches)
• Under the topic Weight-Height, post your height
  in inches and your weight in ponds
• For the subject put your name

9
Chapter 1 of the textbookPP 1-11

• Factors affecting a students GPA
• A persons GPA depends on hours of study, degree
  of intelligence, what else?
• Econometric Model
• GPA f ( hours of study, degree of
  intelligence,etc.)
• GPA is the Dependent Variable
• Hours of study, degree of intelligence are
  Independent or Explanatory Variables

10
More on the model

• Y ß0 ß1 X1 ß2 X2 e
• Where
• Y is GPA (our dependent variable)
• ß0 is read beta null (or beta zero) is a constant
  that needs to be estimated.
• ß1 (reads beta 1) measures the effect of X1 (X1
  is hours of study) on Y. ß1 is also called a
  coefficient.
• ß2 (reads beta 2) measures the effect of X2 (X2
  is the degree of intelligence) on Y. ß2 is also
  called a coefficient.
• e is the stochastic error term.

11
Why the Stochastic Error (e)?

• Causes of error (PP 4 5)
• Measurement errors
• Captures the effects of other factors on GPA
• Captures the effects of random factors

12
A Figure Equivalent to Figure 1-1 on Page 3
This is a theoretical regression line that shows
the relationship between the hours of study (X1)
and GPA, holding X2 (degree of intelligence)
constant and assuming that the error is
zero. (Note The theoretical line is not
observable.)
Y
Slope ß1 0.2
ß01.0
X1
0
13
Regression Analysis

• Uses a data set to estimate the position of the
  theoretical line
• A data set may be CrossSection
• Observation of many individuals (countries,
  items) at a given point in time.
• A data set may be Time Series
• Observation of one individual (country, item)
  over time
• What kind of data set do we need to estimate our
  model?

14
In our case it is more feasible to use a cross
section data set

• the data set may consists of 100 students as of
  this point in time.
• We collect information on each individual's
• GPA
• Hours of study per week
• Degree of intelligence (say measured by each
  students IQ score)

15
Simple Regression Model

• Has only one independent variable
• Example
• What is the relationship between height and
  weight?
• Weight f (Height)
• The theoretical model is
• W ß0 ß1 H e
• W is the weight and H is the height

16
Note the theoretical line describing the
relationship between height and weight is not
observable.

• That means that we dont know the actual values
  of ß0 ß1
• But we try to estimate them.
• ?0 beta zero hat is the estimated constant
  term (ß0, the true constant) in a regression
  equation.
• ?1 beta one hat is the estimated ß1, the true
  coefficient of H (height in our model) in our
  regression equation
• So the equation of our estimated line is
• W ?0 ?1 H
• Note Once you put the value of say my height in
  the equation and also put the estimated values ß0
  and ß1 in the equation, and solve for W, you may
  find a value for W that is not exactly the same
  as my weight. That is why we have W instead of
  W here. W is the estimated (predicted) value of
  W.

17
Say we collect some observationson the height
and weight of 200 individuals (is this a time
series or cross sectional data set?)

• And plot them on a two dimensional graph Like the
  one in Figure 1-2, Page 5
• Where X will be height and Y will be weight.
• No matter how hard we try, there is no way that
  we can fit a linear line through all these
  observation
• We will try to fit a linear line that best
  describes these observations
• Not all observations will be on the line
• There is going to be some errors
• We call these errors residuals
• Residuals are the difference between the actual
  weight and the estimated weight

18
Look at Figure 1-3 now

• Remember Y is weight and X is height
• Y Y is the same as W W e (which is the
  residual.

19
The OLS Method

• Chooses the intercept (ß0) and ß1 (slope
  coefficient) of the line (regression equation) in
  such a way that the sum of squared residuals is
  minimized
• The formulas for calculating ß0 and ß1 are
  given on Page 8 (Equations 1-5 1-6)