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 Multiple Regression

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. Homework due – Monday (April 27 th ) On class website: Homework worksheet #20 Creating multiple choice questions On class website: Homework worksheet #20 Creating multiple choice questions Extra Credit Opportunity Please note: - No class on Friday – - A morning of rest - Please note: - No class on Friday – - A morning of rest -

7. Next couple of lectures 4/22/15 Use this as your study guide Logic of hypothesis testing with Correlations Interpreting the Correlations and scatterplots Simple and Multiple Regression

8. Homework Review

9. the hours worked and weekly pay is a strong positive correlation. This correlation is significant, r(3) = 0.92; p < 0.05 The relationship between +0.92 positive strong up down 6.0857 55.286 y' = 6.0857x + 55.286 207.43 85.71.846231 or 84% 84% of the total variance of “weekly pay” is accounted for by “hours worked” For each additional hour worked, weekly pay will increase by $6.09

10. 400 380 360 340 320 300 4 8 5 6 7 Number of Operators Wait Time 280

11. -.73 The relationship between wait time and number of operators working is negative and moderate. This correlation is not significant, r(3) = 0.73; n.s. negative strong number of operators increase, wait time decreases 458 -18.5 y' = -18.5x + 458 365 seconds 328 seconds.53695 or 54% The proportion of total variance of wait time accounted for by number of operators is 54%. For each additional operator added, wait time will decrease by 18.5 seconds Critical r = 0.878 No we do not reject the null

12. 39 36 33 30 27 24 21 Median Income Percent of BAs 45 48 51 54 57 60 63 66

13. 0.8875 The relationship between median income and percent of residents with BA degree is strong and positive. This correlation is significant, r(8) = 0.89; p < 0.05. positive strong median income goes up so does percent of residents who have a BA degree 3.1819 25% of residents 35% of residents.78766 or 78% The proportion of total variance of % of BAs accounted for by median income is 78%. For each additional $1 in income, percent of BAs increases by.0005 Percent of residents with a BA degree 10 8 0.0005 y' = 0.0005x + 3.1819 Critical r = 0.632 Yes we reject the null

14. 30 27 24 21 18 15 12 Median Income Crime Rate 45 48 51 54 57 60 63 66

15. -0.6293 The relationship between crime rate and median income is negative and moderate. This correlation is not significant, r(8) = -0.63; p < n.s. [0.6293 is not bigger than critical of 0.632]. negative moderate median income goes up, crime rate tends to go down 4662.5 2,417 thefts 1,418.5 thefts.396 or 40% The proportion of total variance of thefts accounted for by median income is 40%. For each additional $1 in income, thefts go down by.0499 Crime Rate 10 8 -0.0499 y' = -0.0499x + 4662.5 Critical r = 0.632 No we do not reject the null

16. Multiple regression equations Can use variables to predict behavior of stock market probability of accident amount of pollution in a particular well quality of a wine for a particular year which candidates will make best workers Review

17. Y’ = b 1 X 1 + b 2 X 2 + b 3 X 3 + a Measured current workers – the best workers tend to have highest “success scores”. (Success scores range from 1 – 1,000) Try to predict which applicants will have the highest success score. We have found that these variables predict success: Age (X 1 ) Niceness (X 2 ) Harshness (X 3 ) According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula: Both 10 point scales Niceness (10 = really nice) Harshness (10 = really harsh) Success score = (1)( Age ) + (20)( Nice ) + (-75)( Harsh ) + 700 Y’ = b 1 X 1 + b 2 X 2 + b 3 X 3 + a Can use variables to predict which candidates will make best workers Review

18. Y’ = b 1 X 1 + b 2 X 2 + b 3 X 3 + a According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula: Success score = (1)( Age ) + (20)( Nice ) + (-75)( Harsh ) + 700 Review

19. Y’ is the dependent variable “Success score” is your dependent variable. X 1 X 2 and X 3 are the independent variables “Age”, “Niceness” and “Harshness” are the independent variables. Each “b” is called a regression coefficient. Each “b” shows the change in Y for each unit change in its own X (holding the other independent variables constant). a is the Y-intercept Y’ = b 1 X 1 + b 2 X 2 + b 3 X 3 + a According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula: Success score = (1)( Age ) + (20)( Nice ) + (-75)( Harsh ) + 700 Y’ = b 1 X 1 + b 2 X 2 + b 3 X 3 + a Review

20. 14-19 The Multiple Regression Equation – Interpreting the Regression Coefficients b 1 = The regression coefficient for age (X 1 ) is “1” The coefficient is positive and suggests a positive correlation between age and success. As the age increases the success score increases. The numeric value of the regression coefficient provides more information. If age increases by 1 year and hold the other two independent variables constant, we can predict a 1 point increase in the success score. Y’ = b 1 X 1 + b 2 X 2 + b 3 X 3 + a Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

21. 14-20 The Multiple Regression Equation – Interpreting the Regression Coefficients b 2 = The regression coefficient for age (X 2 ) is “20” The coefficient is positive and suggests a positive correlation between niceness and success. As the niceness increases the success score increases. The numeric value of the regression coefficient provides more information. If the “niceness score” increases by one, and hold the other two independent variables constant, we can predict a 20 point increase in the success score. Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 Y’ = b 1 X 1 + b 2 X 2 + b 3 X 3 + a

22. 14-21 The Multiple Regression Equation – Interpreting the Regression Coefficients b 3 = The regression coefficient for age (X 3 ) is “-75” The coefficient is negative and suggests a negative correlation between harshness and success. As the harshness increases the success score decreases. The numeric value of the regression coefficient provides more information. If the “harshness score” increases by one, and hold the other two independent variables constant, we can predict a 75 point decrease in the success score. Success score = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 Y’ = b 1 X 1 + b 2 X 2 + b 3 X 3 + a

23. Y’ is the dependent variable “Success score” is your dependent variable. X 1 X 2 and X 3 are the independent variables “Age”, “Niceness” and “Harshness” are the independent variables. Each “b” is called a regression coefficient. Each “b” shows the change in Y for each unit change in its own X (holding the other independent variables constant). a is the Y-intercept Y’ = b 1 X 1 + b 2 X 2 + b 3 X 3 + a According to your research, age has only a small effect on success, while workers’ attitude has a big effect. Turns out, the best workers have high “niceness” scores and low “harshness” scores. Your results are summarized by this regression formula: Success score = (1)( Age ) + (20)( Nice ) + (-75)( Harsh ) + 700

24. Here comes Victoria, her scores are as follows: Age = 30 Niceness = 8 Harshness = 2 What would we predict her “success index” to be? Y’ = = 3.812 Prediction line: Y’ = b 1 X 1 + b 2 X 2 + b 3 X 3 + a Y’ = 1X 1 + 20X 2 - 75X 3 + 700 Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 We predict Victoria will have a Success Index of 740 Y’ = 740 (1)(30) + (20)(8) - 75(2) + 700 Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

25. Here comes Victor, his scores are as follows: Here comes Victoria, her scores are as follows: Age = 30 Niceness = 8 Harshness = 2 What would we predict her “success index” to be? Y’ = = 3.812 We predict Victor will have a Success Index of 175 Prediction line: Y’ = b 1 X 1 + b 2 X 2 + b 3 X 3 + a Y’ = 1X 1 + 20X 2 - 75X 3 + 700 Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 Y’ = 740 (1)(30) + (20)(8) - 75(2) + 700 Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700 Age = 35 Niceness = 2 Harshness = 8 We predict Victoria will have a Success Index of 740 What would we predict his “success index” to be? Y’ = Y’ = 175 (1)(35) + (20)(2) - 75(8) + 700 Y' = (1)(Age) + (20)(Nice) + (-75)(Harsh) + 700

26. We predict Victor will have a Success Index of 175 We predict Victoria will have a Success Index of 740 Can use variables to predict which candidates will make best workers Who will we hire?