1. Bivariate & Multivariate Regression Analysis
Ordinal least-squares regression analysis (OLS) is commonly used and some familiarity with the technique is essential for any social science major. This will only be an brief introduction with some SPSS examples, since none of your research projects will use this technique (because of the measurement level of variable, especially the dependent variable, which assumes a interval—ratio measurement with a normal distribution. There are many extensions of regression to cover variables measured at lower levels but are only taught in advanced quantitative methods courses.

2. Learning Objectives Understand the basic ideas behind regression
Learn how to do bivariate regression using SPSS
Learn to interpret slopes, intercepts, & the R2
Learn how to extend regression techniques to multivariate situations

3. Advantages of Regression Analysis
Powerful technique for testing relationships between one DV and one or more IVs
Allows researchers to control for extraneous factors
Assesses the cumulative effect of multiple factors (a more comprehensive description of complex social behavior)
Talk about what “control” means and give examples. Extraneous variables are any variable that affects the dependent variable, but is not of interest to the researcher. In is usually an effect that you want to take out, so you can see the net effect of your main IV.

4. The Basic Idea of Regression
The relationship between two variables is linear
The assumption of linearity means that a straight line will be the best fit for the data
Note that there are extensions to linear regression analysis that allow testing of nonlinearity (show examples: inverted-U for Y_inequality vs X_devt). Graph shows a strong linear relationship, connect the dots and you have a nearly straight line.

5. Calculating the Regression Line
The calculations produce a formula which approximates the linear relationship between two variables (e.g., the regression line)
Formula: Y = a + bX + e
where Y = value of DV; a = intercept (or constant); b = slope coefficient; e = error
Error term = 0 if “exact” or perfect relationship.

6. Slope & Intercept
Graph two variables on the board (e.g., income and education), draw a line and show the slope, intercept and errror. This equation has an error term (i.e., Y = a + bX + e), due to the unexplained variation around the regression line. Error can be random or due to other factors, e.g., work experience. If we wanted to isolate the effects of education on income, we might want to control for work experience.

7. Interpreting Regression Output
B or unstandardized b-coefficient (i.e., the slope of the regression equation)
Beta or standardized b (used to compare the impact of independent variables)
T-statistic & probability level (tells you if the effect of an IV is statistically significant)
R2 or r-square (tells you how much variance in DV is explained by IVs)
R-square in bivariate regression is simply Pearson’s r squared.

8. Step 1: Are your variables appropriate?
Check level of measurement of variables (need interval-ratio)
Run frequencies to check for missing values, range, and outliers
Run measures of central tendencies (mean, median) & dispersion (standard deviation, skewness)
Variables must be interval-ratio and normally distributed (hence skewness test).

9. Step 2: Is there a relationship between your variables?
Run scatterplot to check for linearity
Calculate correlations (check for an association)
Check for time ordering (strengthens causal claims)
Run regression
Scatterplots help to spot nonlinear relationships and outliers or extreme values that can affect results.

10. SPSS Example of Regression: Bivariate Regression
Research topic: Traditional gender ideology in Turkey.
Research question: Do older people have more traditional gender ideology?
Do run and write out the regression line equation (i.e., Y=A + b(age) + e with correct intercept and slope).

11. SPSS Example of Regression: Multivariate Regression
Research topic: Impact of family socioeconomic status on children’s education.
Research question: Does parent’s education affect a child’s educational attainment net of income?
Other examples: mother’s ed on child’s educ (cf father’s educ). Income variable is income at age 16 (remind them about time ordering—both mother’s education and income occur prior to completing schooling). The results show us effects of parent’s education and income. Each coefficient is the net effect controlling or holding constant the effect of the other variable on child’s educational level.

12. The Structure of a Research Report
Title
Abstract (briefly describe research & findings)
Introduction (introduce project & its significance)
Literature review (discuss previous research, and theory and concepts used)
Methods (describe data, sample, measures, methods of analysis)
Findings (report results of analysis)
Discussion/Conclusions (discuss implications of findings for theory, any limitations)
References