1. 1 G89.2229 Lect 1w Structure of course Overview of Regression Topics Some Advanced Topics (beyond this course) Example 1 Expectations Example 2 G89.2229 Multiple Regression in Psychology

2. 2 G89.2229 Lect 1w Overview of Regression Topics Overview of regression topics »Bivariate & multiple regression Y=B 0 + B 1 X 1 + B 2 X 2 + e »Path analysis »Logistic regression X2X2 X1X1 Y e

3. 3 G89.2229 Lect 1w Introduction, continued Areas of application included in course »Comparative or survey studies »Experimental studies with fixed effects Advanced topics not included in this course »Generalized linear models »Factor analysis »Structural equation methods »Random regression

4. 4 G89.2229 Lect 1w Uses of regression methods Prediction: Accuracy rather than theory »E.g. Success in graduate school Time horse takes to run a race Forecasting stock prices »Prediction may be “good enough” Adjustment (statistical control) »“Holding constant” confounding variables »What is effect of X above and beyond a confounding variable that is related to X »Eg: Age, SES, IQ Modeling processes »Studying structural variation of phenomena »Aim to describe nature in mathematical metaphor »Eg: Salary increase data, productivity effects of training,

5. 5 G89.2229 Lect 1w Example 1: Anxiety and Time to Bar Exam Bolger asked 68 persons to report daily anxiety for 30 days before NY State Bar Exam, 2 days of the exam, and three days following.

6. 6 G89.2229 Lect 1w E(Anx|day) Daily Means of Anxiety The expected anxiety for each day is estimated by the mean. What kinds of math functions could we fit to this pattern?

7. 7 G89.2229 Lect 1w Expected Values: Useful for Modelling The expected value of Anxiety is simply the mean (over all days and all people) »E(Y) The Conditional Expected Value of Anxiety GIVEN day is simply a series of daily means. »E(Y|X) We will find that the conditional expected value of Y given X can often be described by a mathematical model such as E(Y|X) = b 0 + b 1 X

8. 8 G89.2229 Lect 1w Comparing Fits Can be Instructive Deviations from the linear model show »Warm up effect »Weekend effects »Exam effect »Post exam effect

9. 9 G89.2229 Lect 1w Example 2: Okazaki (1997) Sampled 348 White and Asian Americans Collected self-report information on »Psychological Distress Depression Fear of Negative Evaluation Social Avoidance and Distress »Culture-related self-construal Independent self Interdependent self Analyzed each distress partialling other kinds of distress »All unadjusted distress show ethnic effects »Ethnic difference remains only for SAD when other distress measures are partialled Analyzed SAD adjusting for self-construal »Ethnic effect is not much reduced by adjusting for self-construal. »Self-construal was related to FNE and SAD within ethnic groups

10. 10 G89.2229 Lect 1w Example 3: Temperature Temperatures for Jan/Feb 2003 Unlike bar exam data, we have limited data for each time point. Instead of averaging over observations within time points, we could average over adjacent time points »Called a Moving Average