Discussion:
Dr. Parker is hypothesizing that income is positively related to education. You need to choose some other topic. I recommend that you do not try to estimate a demand function. Write the model in a general form. For example, from Dr. Parker's handout
INSTRUCTIONS FOR REGRESSION PAPER
You will have to write a short paper (5-6 pages not counting the data and excel output tables etc.) with a microeconomic application, utilizing regression techniques.
Read the Regression 1-3 power point handouts, and an Excel file named Regression (they are courtesy of Dr. Chuck Parker - there are some review materials from stat class, so some of you may have seen them before. Thank you Dr. Parker.) Also, read the section on Regression Analysis in Ch. 3 of the text book pp. 95-109.
Please choose a topic, develop the model you want to estimate, and give a logical explanation of your model. For example, in the handout Dr. Parker is hypothesizing that income is positively related to education. You need to choose some other topic. I recommend that you do not try to estimate a demand function.
Write the model in a general form. For example, from Dr. Parker's handout
Y = f(N), where
Y = income
N = Number of years of schooling.
Also note that the variable (Y) on the left-hand side of the equation; it is the dependent variable, and the variable on the right hand side of the equation (N) is the independent variable.
In this equation income depends on the number of years of schooling. Now you need to write the equation in specific form: [Use appropriate notation for the variable you have chosen. In other words, do not just write your model as Y = f(N).]
Y = a + bN (this is essentially a general equation of a straight line; you have already seen some of these in ch. 2.)
In the above linear function "a" and "b" are called coefficients. Specify what kind of value you are expecting for the coefficients. In this example, I am expecting a > 0 because even if a person has no education may still earn some money doing manual, unskilled jobs or be self-employed. A person may learn on-the-job and get promoted to a higher paying positions. Number of years of experience on the job itself contributes to higher wages/salaries. Think of it another way; if you put N = 0 in the above equation you will have Y = a. Notice "a" is the vertical intercept of the two dimensional graph.
Now for the coefficient "b", according to algebra, this is the slope of a linear (straight-line) function. I am also expecting b > 0 because higher the number of years of education, higher will be the income; someone with 12 years of education (high school diploma) will command lower level of salary compared to someone with 16 years of education (college degree.) In other words, level of education and income is positively related. Therefore coefficient "b" should have a positive sign.
In the algebraic form the above equation reads: If N increases by 1, (meaning one more year of education) Y will increase by the multiple of b.
You will be collecting data for the dependent and independent variables. Next, using the OLS method you will be estimating the value of aand b, and testing the statistical significance of the estimated coefficients.
You need at least 25 data points. There are two types of data: time series or cross-section. In time series data you are gathering data for last 25 years, 25 months or 25 weeks. In cross-section data you are collecting data on 25 firms, 25 households, 25 individuals, 25 states etc. All of these will depend on what is your model specification and what kind of data you can gather. Some researchers collect data by survey instruments. Those are called primary data. You will be using secondary data, which are already available publicly or from personal sources. For example, a student used data from the family business and estimated the relationship between different types of advertising and total revenue of her family business.
You may choose more than one explanatory or independent variable. However, for this exercise one variable will be sufficient.
The paper must have the following sections:
Introduction
Introduce your topic to the reader/s. Make it interesting with some statistics, quote, or reference to a news article etc. Add a thesis statement at the end of the paragraph, clearly stating the objective of the paper.
Model Specification:
Write out the model in general form and specific form.
Explain the variables
Explain the expected values of the coefficient and
Explain the logic of the relationship you are expecting.
Data source and data:
Explain the type and the source of your data. (Please include your data set in the paper with proper label, unit of measurement, date, source etc.)
Regression Results:
Write out estimated equation.
Include a copy of the Regression Output. Please incorporate it in the paper (doc file) and do not submit separate Excel file.
Interpretation of the results
1. Estimated values of the coefficients and what do they mean?
2. Using t-statistics determine statistical significance of your estimated coefficients.
(You do not have to interpret p-values or explain confidence intervals in the paper. You should have an understanding of these. Interpretation of t-stat will include those.)
3. Goodness of fit test using R2 and its interpretation.
Conclusion: Summarize the paper, there should be no new thoughts or ideas included at this point.
References
Please use at least 5 references plus the data sources. Use proper citation within the paper (See APA style in the folder).
Sample paper: In this folder I have included two graded sample papers from previous classes. This is just to give you some more ideas of what the paper should include. Please do not just choose one of those topics. You can think, you can come up with ideas from the materials covered in this course, subjects studied in other undergraduate and graduate courses or simply from your experiences in your profession. There is also a pdf file on CEO pay to give you some ideas as to how regression analysis is used.
Outline should include title, introduction, the model in general and specific form, and the data sources. Also explain what relationship you expect between your independent and dependent variables, and why you expect such relationship.
Please wait until I return the outline with my comments before you work on the regression analysis, interpretation and completion of the paper. At this stage I may ask a student to change the topic. You may call me during my office hours, or send a message through Sakai, to discuss your thoughts and get some guidance in finalizing the topic.