2. Introduction to Statistics for the Social Sciences SBS200, COMM200, GEOG200, PA200, POL200, or SOC200 Lecture Section 001, Spring 2015 Room 150 Harvill Building 8:00 - 8:50 Mondays, Wednesdays & Fridays.

4. Labs continue this week with Project 2 presentations

5. Schedule of readings Before next exam (Monday May 4 th ) Please read chapters 10 – 14 Please read Chapters 17, and 18 in Plous Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions

6. No homework due – Friday (April 17 th ) Homework due – Monday (April 20 th ) On class website: Please print and complete homework worksheet #19 Completing Simple Regression using Excel On class website: Please print and complete homework worksheet #19 Completing Simple Regression using Excel

7. Next couple of lectures 4/15/15 Use this as your study guide Logic of hypothesis testing with Correlations Interpreting the Correlations and scatterplots Simple and Multiple Regression

8. +0.9199 3 0.878

10. +0.9199 3 0.878 Yes The relationship between the hours worked and weekly pay is a strong positive correlation. This correlation is significant, r(3) = 0.92; p < 0.05

11. -0.73 3 0.878 No The relationship between wait time and number of operators working is negative and strong, but not reliable enough to reach significance. This correlation is not significant, r(3) = -0.73; n.s. 3

12. We are measuring 9 students

14. 4.0 3.0 2.0 1.0 0 1 2 3 4 High School GPA GPA r(7) = 0.50 r(7) = + 0.911444123 0 200 300 400 500 600 SAT (Verbal) GPA r(7) = + 0.80 r(7) = + 0.616334867 SAT (Mathematical) GPA r(7) = + 0.80 r(7) = + 0.487295007 4.0 3.0 2.0 1.0 4.0 3.0 2.0 1.0 0 200 300 400 500 600 Critical r = 0.666 Reject Null r is significant Do not reject null r is not significant Do not reject null r is not significant

15. 4.0 3.0 2.0 1.0 0 1 2 3 4 High School GPA GPA r(7) = 0.50 r(7) = + 0.911444123 0 200 300 400 500 600 SAT (Verbal) GPA r(7) = + 0.80 r(7) = + 0.616334867 SAT (Mathematical) GPA r(7) = + 0.80 r(7) = + 0.487295007 4.0 3.0 2.0 1.0 4.0 3.0 2.0 1.0 0 200 300 400 500 600

16. 4.0 3.0 2.0 1.0 0 1 2 3 4 High School GPA GPA r(7) = 0.50 r(7) = + 0.911444123 0 200 300 400 500 600 SAT (Verbal) GPA r(7) = + 0.80 r(7) = + 0.616334867 SAT (Mathematical) GPA r(7) = + 0.80 r(7) = + 0.487295007 4.0 3.0 2.0 1.0 4.0 3.0 2.0 1.0 0 200 300 400 500 600

17. 4.0 3.0 2.0 1.0 0 1 2 3 4 High School GPA GPA r(7) = 0.50 r(7) = + 0.911444123 0 200 300 400 500 600 SAT (Verbal) GPA r(7) = + 0.80 r(7) = + 0.616334867 SAT (Mathematical) GPA r(7) = + 0.80 r(7) = + 0.487295007 4.0 3.0 2.0 1.0 4.0 3.0 2.0 1.0 0 200 300 400 500 600

18. Correlation: Independent and dependent variables When used for prediction we refer to the predicted variable as the dependent variable and the predictor variable as the independent variable Dependent Variable Dependent Variable Independent Variable Independent Variable What are we predicting?

19. Correlation - What do we need to define a line Expenses per year Yearly Income Y-intercept = “a” ( also “b 0 ”) Where the line crosses the Y axis Slope = “b” ( also “b 1 ”) How steep the line is If you spend this much If you probably make this much The predicted variable goes on the “Y” axis and is called the dependent variable The predictor variable goes on the “X” axis and is called the independent variable

20. Angelina Jolie Buys Brad Pitt a $24 million Heart-Shaped Island for his 50th Birthday Expenses per year Yearly Income Angelina spent this much Angelina probably makes this much Dustin spends $12 for his Birthday Dustin spent this much Dustin probably makes this much Revisit this slide

21. Assumptions Underlying Linear Regression These Y values are normally distributed. The means of these normal distributions of Y values all lie on the straight line of regression. For each value of X, there is a group of Y values The standard deviations of these normal distributions are equal.

22. Correlation - the prediction line Prediction line makes the relationship easier to see (even if specific observations - dots - are removed) identifies the center of the cluster of (paired) observations identifies the central tendency of the relationship (kind of like a mean) can be used for prediction should be drawn to provide a “best fit” for the data should be drawn to provide maximum predictive power for the data should be drawn to provide minimum predictive error - what is it good for?