CORRELATION AND REGRESSION

Name___________________________

(Printed)

Student Number___________________

(Social Security Number)

E-mail__________________________

We need some experience obtaining and especially interpreting data. I would like you to read and retrieve the data set "State Public Expenditures," which is located in the Data section of the course web page. These data pertain to states' "ability" to pay for various types of public programs.

In particular one wants to know why is there variation among the states in per capita public expenditures. One theory held that expenditures reflected a state's political culture and ideology, with more "liberal" or "Democratic" states spending more (per capita) than others. An alternative explanation is that quite apart from "politics" the main determinant is a state's economic base. The wealthier the state, the more spent on public programs. You can investigate this latter hypothesis by using the ability to pay data.

1. First locate the data. You can find them on the course web site, as indicated above, or retrieve them directly from the Data and Story Library:



2. Read the information, noting in particular the data definitions.



3. Extract the data using the methods described in previous examples and assignments. For instance, open Notepad, go back to the page, highlight just the data, and copy them to a separate file, say, expend.DAT.
1. You should have 7 columns of numbers plus an eighth column of state abbreviations.
1. Make sure that there is no other text or blank lines in the data file.
2. Start either version of MINITAB
3. Go to Import ASCII data or Other files.
4. You want to read the seven columns so type c1-c7. (You will for the moment ignore the abbreviations.)
1. Locate the file on your hard drive and diskette.



4. Attach a labeled plot of per capita expenditures (the dependent variable) and "Economic Ability Index." (The names in the original data file are "EX" and "ECAB" respectively.)



5. What is the correlation between these two variables? r = ____________________
1. What in substantive terms does this number tell you about the second alternative or hypothesis?















6. Now find the regression equation. Write it in the form: Y = a + bX, where you substitute the regression parameters for alpha and beta and short variable names for Y and X.



1. _______________________________________________________



2. Explain the substantive meaning of the regression coefficient.















7. What is R²? ______________________
1. What does it mean to you?





8. Save the worksheet because we may use these data again.



9. Why don't you explore other hypotheses with these data. If you find something interesting let me know. In addition, these data are now rather dated. An interesting project would be to collect more recent information and test the hypothesis with it.

• Any questions? H. T. Reynolds

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Go to H. T. Reynolds page.