The World’s Fastest Crash Course in Statistics Or, What You Need to Know to Answer Your Research Question 13 November 2006

Regression Answers the question, “What is the effect of (different) (levels of) ___________ on __________?” –First blank is our IV of interest – sometimes called the X variable –Second blank is the DV (aka Y) –All Xs and Ys must vary across observations Many other statistical techniques exist that answer research questions. –This one is simple, powerful, and generates predictions easily. It’s also the most frequently used model for survey data.

A Regression Model DV = B 0 + B 1 X 1 + B 2 X 2 + B 3 X 3 Formally, a regression asks, “What is the effect on the dependent variable of a one- unit change in the independent variable?” We enter the dependent variable, the independent variable of interest (the one in the hypothesis), and also any other control variables that we suspect influence the outcome.

Answering the Question Answers to the regression question come as coefficients. –The Bs of the model. –Tell us the slope of the line that best fits the pattern of data we gave it. –Effect of each variable, holding all other variables constant Look for the 3 S’s on each coefficient. ign ureness ize

1. Sign Does the coefficient go in the direction our theory predicted? + Positive (or direct) relationship - Negative (or inverse) relationship

2. Sureness The world is not perfect: observations always have a ‘random’ component. How sure are we that the sign we got is actually the right one? –The points don’t line up perfectly. –Our degree of sureness is related to how closely the points cluster around the prediction line. –If we had had a slightly different sample, would the line look different?

An Example: This …

… Compared to This

3. Size Size matters, but it’s not the only thing. Regression coefficients tell us the effect on the DV of a one-unit increase in the independent variable, holding all other variables constant. –In other words, the units matter! A variable like ‘age’ might have a very small coefficient if the units of ‘age’ are one year. If the variable’s coefficient is correctly signed, and it meets conventional levels of sureness, then you can compare the substantive effects of different IVs.

Getting the Answers in Stata Download the dataset to your computer’s desktop. Double-click on the file to open it. In the command box, type “reg” then use the Variables box to select your DV first, then any IVs or controls. Add an ‘if’ string if necessary. Hit ‘enter’ to run. Results display in the Results window.

Interpreting the Results Sureness shortcut: we are pretty sure the sign is right if this number is smaller than 0.05

Your Mission With a couple other people from your group, formulate a specific hypothesis in which one or more independent variables affects a dependent variable. Write out the model. Indicate which direction you hypothesize for the coefficients. Run the model. Did your answer agree with your predictions? –If not, are some variables perhaps missing from your model? Prepare a slide or two, or a Word document, to share your conclusions with the group.

Getting the Answers in Excel Sort the data table by values of your intended DV. Go to Tools, Data Analysis… Scroll down and select ‘Regression,’ then click OK. Identify your dependent variable. –Click on the ‘range selection’ icon at the corner of the text box to highlight on the data sheet. Start where the values of interest begin (i.e., omit -9, -8,.). –Remember, observations are ROWS now. You should be highlighting part of a column. Make a note of what rows you choose.

Getting Answers, Part 2 Select your independent variables. –Click the range selection icon to return to the data sheet. –You must select the same range of observations as the DV. –To select non-contiguous IVs, highlight one, press and hold control (on PCs) then highlight the next. Click OK. The results will be presented in another tab.