2. Stage Screen Row B 13 121110 20191817 14 13 121110 19181716 1514 Gallagher Theater 16 65879 Row R 6 58 7 9 Lecturer’s desk Row A Row B Row C 4 3 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 43 2 43 2 1 1 3 21 3 2 43 21 Row A 17 16 15 Row A Row C 131211 10 1514 6 58 7 9 Row D 13121110 1514 16 6 58 7 9 20191817 Row D Row E 131211 10 1514 6 58 7 9 19181716 Row E Row F 13121110 1514 16 6 58 7 9 20191817 Row F Row G 13121110 1514 6 58 7 9 19181716 Row G Row H 13121110 1514 16 6 58 7 9 20191817 Row H Row I 13121110 1514 6 58 7 9 19181716 Row I Row J 13121110 1514 16 6 58 7 9 20191817 Row J Row K 13121110 1514 6 58 7 9 19181716 Row K Row L 13121110 1514 16 6 58 7 9 20 191817 Row L Row M 13121110 1514 6 58 7 9 19181716 Row M Row N 13121110 1514 16 6 5879 20191817 Row N Row O 13121110 1514 6 58 7 9 19181716 Row O Row P 13121110 1514 16 6 5879 20191817 Row P Row Q 13121110 6 5879 161514 Row Q 4 4 Row R 10 879 Row S Row B Row C Row D Row E Row F Row G Row H Row I Row J Row K Row L Row M Row N Row O Row P Row Q 26Left-Handed Desks A14, B16, B20, C19, D16, D20, E15, E19, F16, F20, G19, H16, H20, I15, J16, J20, K19, L16, L20, M15, M19, N16, P20, Q13, Q16, S4 5 Broken Desks B9, E12, G9, H3, M17 Need Labels B5, E1, I16, J17, K8, M4, O1, P16 Left handed

3. Stage Screen 2213 121110 Row A Row B Row C Row D Row E Row F Row G Row H Row J Row K Row L Row M 17 Row C Row D Row E Projection Booth 65 4 table Row C Row D Row E 30 27 26252423 282726 2524 23 3127262524 23 R/L handed broken desk 16 1514 13 12 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 Social Sciences 100 Row N Row O Row P Row Q Row R 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 2213 121110 2019181716151421 8 7 9 65 4 8 7 9 3 2 6 5 48793 2 1 6 5 48793 2 1 Row F Row G Row H Row J Row K Row L Row M Row N Row O Row P Row Q Row R 6 5 48793 2 1 6 5 48793 2 1 Row I 2213 121110 2019181716151421 Row I 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 6 5 48793 2 1 Lecturer’s desk 6 5 48793 2 1 262524 23 302928 Row F Row G Row H Row J Row K Row L Row M Row N Row O Row P Row Q Row R Row I 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 3127262524 23 302928 Row B 2928 27

4. MGMT 276: Statistical Inference in Management Fall, 2014 Green sheets http://www.youtube.com/watch?v=XWe4GpTaO8I

5. Hand in homework on correlation and regression

6. Hand in homework on correlation and regression

7. Reminder Talking or whispering to your neighbor can be a problem for us – please consider writing short notes. A note on doodling

9. Before our next exam (December 4 th ) Lind (10 – 12) Chapter 13: Linear Regression and Correlation Chapter 14: Multiple Regression Chapter 15: Chi-Square Plous (2, 3, & 4) Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions Schedule of readings

10. Exam 4 – Optional Times for Final Two options for completing Exam 4 Thursday (12/4/14) – The regularly scheduled time Tuesday (12/9/14) – The optional later time Must sign up to take Exam 4 on Tuesday (12/2) Only need to take one exam – these are two optional times

11. Homework due – Tuesday (December 2 nd ) On class website: Please print and complete homework worksheet #19 Completing and interpreting multiple regression

12. Extra Credit: ANOVA Project

17. Next couple of lectures 11/25/14 Use this as your study guide Simple and Multiple Regression Using correlation for predictions r versus r 2 Regression uses the predictor variable (independent) to make predictions about the predicted variable (dependent) Coefficient of correlation is name for “r” Coefficient of determination is name for “r 2 ” (remember it is always positive – no direction info) Standard error of the estimate is our measure of the variability of the dots around the regression line (average deviation of each data point from the regression line – like standard deviation) Coefficient of regression will “b” for each variable (like slope)

18. Regression Example Rory is an owner of a small software company and employs 10 sales staff. Rory send his staff all over the world consulting, selling and setting up his system. He wants to evaluate his staff in terms of who are the most (and least) productive sales people and also whether more sales calls actually result in more systems being sold. So, he simply measures the number of sales calls made by each sales person and how many systems they successfully sold.

19. Regression Example Do more sales calls result in more sales made? Dependent Variable Independent Variable Ethan Isabella Ava Emma Emily Jacob Joshua 60 70 0 1 2 3 4 Number of sales calls made Number of systems sold 10 20 30 40 50 0 Step 1: Draw scatterplot Step 2: Estimate r

20. Regression Example Do more sales calls result in more sales made? Step 3: Calculate r Step 4: Is it a significant correlation?

21. Do more sales calls result in more sales made? Step 4: Is it a significant correlation? n = 10, df = 8 alpha =.05 Observed r is larger than critical r (0.71 > 0.632) therefore we reject the null hypothesis. Yes it is a significant correlation r (8) = 0.71; p < 0.05 Step 3: Calculate r Step 4: Is it a significant correlation?

22. Summary Interpret r = 0.71 Positive relationship between the number of sales calls and the number of copiers sold. Strong relationship Remember, we have not demonstrated cause and effect here, only that the two variables—sales calls and copiers sold—are related.

23. Coefficient of Determination – Excel Example Interpret r 2 = 0.504 (.71 2 =.504) we can say that 50.4 percent of the variation in the number of copiers sold is explained, or accounted for, by the variation in the number of sales calls. Remember, we lose the directionality of the relationship with the r 2

24. Regression: Predicting sales Step 1: Draw prediction line What are we predicting? r = 0.71 b = 11.579 (slope) a = 20.526 (intercept) Draw a regression line and regression equation

25. Regression: Predicting sales Step 1: Draw prediction line r = 0.71 b = 11.579 (slope) a = 20.526 (intercept) Draw a regression line and regression equation

26. Regression: Predicting sales Step 1: Draw prediction line r = 0.71 b = 11.579 (slope) a = 20.526 (intercept) Draw a regression line and regression equation

27. Step 2: State the regression equation Y’ = a + bx Y’ = 20.526 + 11.579x Step 3: Solve for some value of Y’ Y’ = 20.526 + 11.579(1) Y’ = 32.105 If make one sales call You should sell 32.105 systems Regression: Predicting sales Step 1: Predict sales for a certain number of sales calls What should you expect from a salesperson who makes 1 calls? Madison Joshua They should sell 32.105 systems If they sell more  over performing If they sell fewer  underperforming

28. Step 2: State the regression equation Y’ = a + bx Y’ = 20.526 + 11.579x Step 3: Solve for some value of Y’ Y’ = 20.526 + 11.579(2) Y’ = 43.684 Regression: Predicting sales Step 1: Predict sales for a certain number of sales calls What should you expect from a salesperson who makes 2 calls? If make two sales call You should sell 43.684 systems Isabella Jacob They should sell 43.68 systems If they sell more  over performing If they sell fewer  underperforming

29. Step 2: State the regression equation Y’ = a + bx Y’ = 20.526 + 11.579x Step 3: Solve for some value of Y’ Y’ = 20.526 + 11.579(3) Y’ = 55.263 Regression: Predicting sales Step 1: Predict sales for a certain number of sales calls What should you expect from a salesperson who makes 3 calls? If make three sales call You should sell 55.263 systems Ava Emma They should sell 55.263 systems If they sell more  over performing If they sell fewer  underperforming

30. Step 2: State the regression equation Y’ = a + bx Y’ = 20.526 + 11.579x Regression: Predicting sales Step 1: Predict sales for a certain number of sales calls What should you expect from a salesperson who makes 4 calls? Step 3: Solve for some value of Y’ Y’ = 20.526 + 11.579(4) Y’ = 66.842 If make four sales calls You should sell 66.84 systems Emily They should sell 66.84 systems If they sell more  over performing If they sell fewer  underperforming

31. Regression: Evaluating Staff Step 1: Compare expected sales levels to actual sales levels What should you expect from each salesperson They should sell x systems depending on sales calls If they sell more  over performing If they sell fewer  underperforming Madison Isabella Ava Emma Emily Jacob Joshua

32. Regression: Evaluating Staff Step 1: Compare expected sales levels to actual sales levels How did Ava do? Ava sold 14.7 more than expected taking into account how many sales calls she made  over performing Ava 14.7 Difference between expected Y’ and actual Y is called “residual” (it’s a deviation score) 70-55.3=14.7

33. Regression: Evaluating Staff Step 1: Compare expected sales levels to actual sales levels How did Jacob do? Jacob sold 23.684 fewer than expected taking into account how many sales calls he made  under performing Ava -23.7 Difference between expected Y’ and actual Y is called “residual” (it’s a deviation score) Jacob 20-43.7=-23.7

34. Regression: Evaluating Staff Step 1: Compare expected sales levels to actual sales levels Madison Isabella Ava Emma Emily Jacob Joshua 14.7 Difference between expected Y’ and actual Y is called “residual” (it’s a deviation score) -23.7

35. Residuals: Evaluating Staff Step 1: Compare expected sales levels to actual sales levels Madison Isabella Ava Emma Emily Jacob Joshua 14.7 Difference between expected Y’ and actual Y is called “residual” (it’s a deviation score) -23.7 -6.8 7.9

36. 14.7 Difference between expected Y’ and actual Y is called “residual” (it’s a deviation score) Does the prediction line perfectly the predicted variable when using the predictor variable? The green lines show how much “error” there is in our prediction line…how much we are wrong in our predictions How would we find our “average residual”? No, we are wrong sometimes… How can we estimate how much “error” we have? Exactly? -23.7

37. 14.7 Difference between expected Y’ and actual Y is called “residual” (it’s a deviation score) Does the prediction line perfectly the predicted variable when using the predictor variable? The green lines show how much “error” there is in our prediction line…how much we are wrong in our predictions No, we are wrong sometimes… How can we estimate how much “error” we have? -23.7 Perfect correlation = +1.00 or -1.00 Each variable perfectly predicts the other No variability in the scatterplot The dots approximate a straight line Any Residuals?

38. Difference between expected Y’ and actual Y is called “residual” (it’s a deviation score) How do we find the average amount of error in our prediction The green lines show how much “error” there is in our prediction line…how much we are wrong in our predictions How would we find our “average residual”? Step 1: Find error for each value (just the residuals) Y – Y’ Ava is 14.7 Emily is -6.8 Madison is 7.9 Jacob is -23.7 Residual scores The average amount by which actual scores deviate on either side of the predicted score N ΣxΣx Big problem Σ (Y – Y’) = 0 2 Square the deviations Step 2: Add up the residuals Σ (Y – Y’) 2 Divide by df n - 2 Σ (Y – Y’) Square root

39. Difference between expected Y’ and actual Y is called “residual” (it’s a deviation score) How do we find the average amount of error in our prediction The green lines show how much “error” there is in our prediction line…how much we are wrong in our predictions How would we find our “average residual”? Step 1: Find error for each value (just the residuals) Y – Y’ Step 2: Find average ∑(Y – Y’) 2 n - 2 √ Diallo is 0” Mike is -4” Hunter is -2 Preston is 2” Deviation scores N ΣxΣx Sound familiar??

40. The Standard Error of Estimate The standard error of estimate measures the scatter, or dispersion, of the observed values around the line of regression A formula that can be used to compute the standard error:

41. These would be helpful to know by heart – please memorize these formula Standard error of the estimate (line) =

42. These would be helpful to know by heart – please memorize these formula Standard error of the estimate (line) =

43. Slope doesn’t give “variability” info Intercept doesn’t give “variability info Correlation “r” does give “variability info How well does the prediction line predict the predicted variable when using the predictor variable? Residuals do give “variability info Standard error of the estimate (line) What if we want to know the “average deviation score”? Finding the standard error of the estimate (line) Standard error of the estimate: a measure of the average amount of predictive error the average amount that Y’ scores differ from Y scores a mean of the lengths of the green lines

44. Shorter green lines suggest better prediction – smaller error Longer green lines suggest worse prediction – larger error Why are green lines vertical? Remember, we are predicting the variable on the Y axis So, error would be how we are wrong about Y (vertical) How well does the prediction line predict the Ys from the Xs? Residuals A note about curvilinear relationships and patterns of the residuals

45. 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.

46. 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 (explanatory) power for the data should be drawn to provide minimum predictive error - what is it good for? r2r2

47. Regression Analysis – Least Squares Principle When we calculate the regression line we try to: minimize distance between predicted Ys and actual (data) Y points (length of green lines) remember because of the negative and positive values cancelling each other out we have to square those distance (deviations) so we are trying to minimize the “sum of squares of the vertical distances between the actual Y values and the predicted Y values”

48. Some useful terms Regression uses the predictor variable (independent) to make predictions about the predicted variable (dependent) Coefficient of correlation is name for “r” Coefficient of determination is name for “r 2 ” (remember it is always positive – no direction info) Standard error of the estimate is our measure of the variability of the dots around the regression line (average deviation of each data point from the regression line – like standard deviation)

49. Pop Quiz - 5 Questions 2. What is a residual? How would you find it? 1. What is regression used for? Include and example 3. What is Standard Error of the Estimate (How is it related to residuals?) 4. Give one fact about r 2 5. How is regression line like a mean? r2r2

50. Writing Assignment - 5 Questions Regressions are used to take advantage of relationships between variables described in correlations. We choose a value on the independent variable (on x axis) to predict values for the dependent variable (on y axis). 1. What is regression used for? Include and example

51. Writing Assignment - 5 Questions 2. What is a residual? How would you find it? Residuals are the difference between our predicted y (y’) and the actual y data points. Once we choose a value on our independent variable and predict a value for our dependent variable, we look to see how close our prediction was. We are measuring how “wrong” we were, or the amount of “error” for that guess. Y – Y’

52. Writing Assignment - 5 Questions 3. What is Standard Error of the Estimate (How is it related to residuals?) The average length of the residuals The average error of our guess The average length of the green lines The standard deviation of the regression line

53. Writing Assignment - 5 Questions 4. Give one fact about r 2 5. How is regression line like a mean?