Assignment #6: Logarithms

Objective:  Students will continue to become familiar with the basic use of logarithms.

Good news!  This assignment re-uses the 28 nations/infant mortality data from the first assignment, so you should have most or all of the data saved already.  Click here if you need the data from assignment #1.
 

Part I.  Logging Variables in SPSS
1.  To log a variable, from the menus choose:
        Transform
            Compute...
A new window will open.
2.  Type the name of your new variable in the Target Variable box (upper left).  For example, you might name the log of Infant Mortality variable "logim."
3.  To label your new variable, click the Type and Label button, type your label and click "Continue."
4.  Select "LG10" from the Functions menu (on the right side of the window) and move it into the Numeric Expression box either by double clicking on it or by using the up-arrow button. "LG10( )" will appear in the Numeric Expression box.
5.  Select the variable you want to log from the box on the left and place it between the parentheses either by using the right-arrow button or by typing the name of the old variable there exactly as it appears.  Then click "OK."
7.  Check "Data View" to make sure the new "logged" variable is correct.
6.  Repeat this process for each variable you want to log.

Remember to change the name in the "Target Variable" box every time so that you don't paste over your newly computed values.
 

Part II.  Using Logs: Correlations and Linear Regression
Answer the following questions about the variables from assignment #1.  Please type your responses.

1.  Would it make sense to log these variables?  (Answer for each variable, and explain why/why not.)  Think about the issue of "is the real meaning of some particular difference in the value the same at low values of the variable as at high values of the variable?"

2.  Suppose you log all of them.  Compare the correlations among the original versions of the variables with the correlations among the logged versions.  Does the collinearity issue seem similar? 

3.  Use logged infant mortality as the dependent variable.  Run 2 regressions like those used for the example given in class (click here for example output) where you make decisions to address/solve collinearity problems. What happens? Does the collinearity issue seem similar to the one in the in-class example?  Are the results similar (in terms of sign and significance)?

4.  Look at some statistically significant b in your results from a regression in #3.  Interpret the value of b in terms of the original variables. 

5 .  Run a third regression with a log X (a logged independent variable).  Look at some statistically significant b in your results.  Interpret the value of b in terms of the original variables (putting together what we said about interpreting with logged Y and interpreting with logged X).

Hints on Logarithmic Interpretation
Regarding interpretation of b, if you have log Y (with the log being base 10) and regular X, then for a 1 unit increase in X, the predicted Y is multiplied by 10^b (where the ^ indicates an exponent).

If you have log X and regular Y, then a 1 unit increase in log X means multiplying X by 10, so multiplying X by 10 changes predicted Y by b.

If you do both, and have log X and log Y, then multiplying X by 10 multiplies predicted Y by 10^b.

Maybe multiplying X by 10 is too extreme a change to be interesting.  If X doubles, that is like adding .301 to log X.  Then predicted Y would be multiplied by 10^(.301b).