* ---------------------------------------------------------
* Example of polynomial regression using SAS PROC REG
* and the Detroit data set.
* This program illustrates
* (1) the impact of scale on polynomial regression
* (2) the use of orthogonal polynomials
* ---------------------------------------------------------
*;
*
* SAS source code to input the Detroit Homicide data
* see the file detroit for more information
*;
TITLE Psychology 7291: Example of polynomial regression;
TITLE2 using the Detroit Homicide Data;
DATA TEMP;
SET p7291.Detroit;
*
* --- create three sets of variables for the polynomial
* (1) YEAR, YEARSQ: Raw Years
* (2) DYEAR, DYEARSQ: Years measured as 1, 2, 3, ..., 13
* (3) OYEAR, OYEARSQ: Orthogonal coding
*;
yearsq = year**2;
dyear = year - 1960;
dyearsq = dyear*dyear;
oyear = year - 1967;
oyearsq = oyear*oyear;
RUN;
*;
PROC REG CORR;
VAR hom year yearsq dyear dyearsq oyear oyearsq;
RAW: MODEL hom = year yearsq;
RECODE: MODEL hom = dyear dyearsq;
ORTHO: MODEL hom = oyear oyearsq;
RUN;
*
* Learning questions and observations:
* (1) compare the Rsquares for the three methods
* (2) why do the Rsquares have this pattern?
* (3) what substantive conclusions would you draw
* about the existence of linear and quadratic
* effects using the three methods?
* (4) examine the correlation matrix for the variables.
* Collinearity diagnostics were not requested in this
* example, but if they were, which method would give
* the most problems and which the least problems?
* (5) Is there a "correct" method?
*;