1. Statistical Analysis SC504/HS927 Spring Term 2008 Session 6: Week 22: 29 th February OLS (3): multiple regression and dummy coding

2. 2 Example from Suicide data:

3. 3 E.g.: Using the data set alcohol

4. 4 Hierarchical Regression

5. 5 ‘Dummy’ variables  variables given the values 1 or 0  typically to indicate ‘yes’ or ‘no’  e.g. 1=‘female’ 0=‘not female’ (i.e. male)  Dummy coding will change the value of the constant (intercept) but NOT the gradient (b)  NB: create one dummy variable even though there are two possible genders

6. 6 Working out Predicted Y Value  You need to work out 2 regression equations  If Females = 1, then: Y = a + b 1 (age) + b 2 (1)  If Males = 0, then: Y = a + b 1 (age) + b 2 (0)

7. 7 dummy variables with multiple categories  suppose you want to investigate the effect of housing tenure  you have a variable coded:  1=owns outright  2=owns with a mortgage  3=part owns, part rents  4=rents  5=rent free  NB: the coding is arbitrary. You could have 5=owns outright. 3= owns with a mortgage, 1=rents, 2=rent free, 4=part owns, part rents

8. 8 Multiple categories (cont)  If the categorical variable has z categories, create z-1 dummy variables e.g.  d 1 =1 if owns with a mortgage, 0 otherwise  d 2 =1 if part owns, part rents, 0 otherwise  d 3 =1 if rents, 0 otherwise  d 4 =1 if rent free, 0 otherwise  The omitted category is known as the ‘reference’ or ‘baseline’ category  each case will have a maximum of one dummy coded 1, outright owners will have them all coded 0

9. 9 Choice of reference category  Any category can be the reference  Choose for ease of and meaningful interpretation  e.g.  the ‘norm’ or most common category  the majority ethnic group in a study of the consequences of being from a minority ethnic group  unemployed people if you are studying the effects of unemployment