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)

1. Study the Course Contract avialable on WebCT. The course contract is also available on line at Make sure you understand the contract Send me your questions via WebCT’s Discussion available at –Post your question under the topic Questions on Course Contract –For the subject put your name

2. Are you eligible for ODE membership? Find out more about ODE and see if you qualify. Information is available at 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 –His campus extension is 4630

3. Learn more about ERT Information is available at 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.

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

5. Study the textbook’s Preface Believe me it is not a waste of time to read the Preface of a book Ask me Questions via WebCt’s Discussion –Post your question under the topic Questions on Preface –For the subject put your name

6. If your book is new, it comes with a little card entitled Go to to register your serial numberhttp://econapps.swlearning.com We will mainly use this source for data. Don’t panic if you don’t have a new book. –We will find another way to get the data if we need it.

7. Another assignment Go to WebCt’s 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

Chapter 1 of the textbook PP 1-11 Factors affecting a student’s GPA –A person’s 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

More on the model Y = β 0 + β 1 X 1 + β 2 X 2 + e –Where Y is GPA (our dependent variable) β 0 is read beta null (or beta zero) is a constant that needs to be estimated. β 1 (reads beta 1) measures the effect of X 1 (X 1 is hours of study) on Y. ß 1 is also called a coefficient. β 2 (reads beta 2) measures the effect of X 2 (X 2 is the degree of intelligence) on Y. ß 2 is also called a coefficient. e is the stochastic error term.

Why the Stochastic Error (e)? Causes of error (PP 4 & 5) 1.Measurement errors 2.Captures the effects of other factors on GPA 3.Captures the effects of random factors

A Figure Equivalent to Figure 1-1 on Page 3 X1X1 Y 0 This is a theoretical regression line that shows the relationship between the hours of study (X 1 ) and GPA, holding X 2 (degree of intelligence) constant and assuming that the error is zero. (Note: The theoretical line is not observable.) ß 0=1.0 Slope = ß 1 = 0.2

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

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 student’s IQ score)

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 = β 0 + β 1 H + e –W is the weight and H is the height

Note: the theoretical line describing the relationship between height and weight is not observable. That means that we don’t know the actual values of β 0 & β 1 But we try to estimate them.  ^ 0 “beta zero hat” is the estimated constant term (β 0, the true constant) in a regression equation.  ^ 1 “beta one hat” is the estimated β 1, 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 β 0 and β 1 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.

Say we collect some observations on 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

Look at Figure 1-3 now 1.Remember Y is weight and X is height 2.Y – Ŷ is the same as W –W^ =e^ (which is the residual.

The OLS Method Chooses the intercept (β^ 0 ) and β^ 1 (slope coefficient) of the line (regression equation) in such a way that the sum of squared residuals is minimized –The formulas for calculating β^ 0 and β^ 1 are given on Page 8 (Equations 1-5 & 1-6)