Transcript The World’s Fastest Crash Course in Statistics
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 …
0 1 2 Tea 3 4 5 0 1 2 Tea 3 4 5
… Compared to This
5 10 15 P260 20 25 30 5 10 15 P260 20 25 30
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.