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1. Remember to pick up your homework http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man

2. MGMT 276: Statistical Inference in ManagementRoom 120 Integrated Learning Center (ILC)Fall, 2012 Welcome http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man

3. Screen Cabinet Cabinet Lecturer’s desk Table Computer Storage Cabinet Row A 3 4 5 19 6 18 7 17 16 8 15 9 10 11 14 13 12 Row B 1 2 3 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row C 1 2 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row D 1 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row E 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row F 27 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 28 Row G 27 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 29 10 19 11 18 16 15 13 12 17 14 28 Row H 27 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row I 1 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 1 Row J 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 28 27 1 Row K 26 2 25 3 24 4 23 5 6 22 21 7 20 8 9 10 19 11 18 16 15 13 12 17 14 Row L 20 1 19 2 18 3 17 4 16 5 15 6 7 14 13 INTEGRATED LEARNING CENTER ILC 120 9 8 10 12 11 broken desk

4. Exam 4 – Optional Final Time • Two options for completing Exam 4 • Thursday (11/29/12) • Tuesday (12/4/12) • Must sign up to take Exam 4 on Tuesday (12/4) • Only need to take one exam – these are two optional times

5. Readings for next exam (Exam 4: November 29th) Lind Chapter 13: Linear Regression and Correlation Chapter 14: Multiple Regression Chapter 15: Chi-Square Plous Chapter 17: Social Influences Chapter 18: Group Judgments and Decisions

6. MGMT 276: Statistical Inference in Management Welcome Please double check – All cell phones other electronic devices are turned off and stowed away http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man

7. Party with a purpose Extra Credit Opportunity Design a question/topic Gather Data (n<10) Present data in a memo Due November 27th

8. Extra Credit - Due November 27th • There are five parts • Five points possible • 1. A one page report of your design • Describe your study: what is your question / topic • Describe and define your constructs • Describe your assessment instrument (direct observation or survey) • How many participants did you measure, and how did you recruit (sample) them • Other information • 2. Gather the data • Try to get at least 10 people (or data points per level) • If you are working with other students in the class you should have 10 data points per level for each member of your group • 3. Input data into Excel (hand in data) • 4. Complete analysis hand in graph of results • 5. Summary of results

9. Homework due next class November 20th Assignment 20 Original Research Using Correlations Please clck in My last name starts with a letter somewhere between A. A – D B. E – L C. M – R D. S – Z Please double check – All cell phones other electronic devices are turned off and stowed away

10. Use this as your study guide By the end of lecture today11/15/12 Logic of hypothesis testing with Correlations Interpreting the Correlations and scatterplots Simple Regression Using correlation for predictions Regression uses the predictor variable (independent) to make predictions about the predicted variable (dependent)Coefficient of regression will “b” for each variable (like slope)

11. .92 3 270 .878 yes 240 210 yes Weekly Pay 180 The relationship between 150 the hours worked and weekly pay is a strong positive correlation. 120 This correlation is significant, r(3) = 0.92; p < 0.05 90 30 35 5 20 10 25 15 Hours Worked 29241 2565 225 41616 4080 400 24336 3120 400 68121 9135 1225 885 171,963 19,830 100 2,350 171,963 (5) (19,830) – (100)(885) =.9199711 10,650 (41.83)(276.75) (5) 171,963 – (885)2 (5) 2,350 – (100)2

12. -.73 3 400 3 380 .878 no 360 Wait Time no 340 The relationship between 320 wait time and number of operators working is negative and moderate.. 300 This correlation is not significant, r(3) = 0.73; p < 0.05 280 7 8 6 5 4 Hours Worked 1675 112225 25 2298 36 146689 2408 49 118336 2304 64 82944 30 608,419 10,225 190 1735 (5) (10,225) – (30)(1735) =-.73278 -925 (7.071)(178.52) (5) (608,419 – (1735)2 (5)(190) – (30)2

13. r = -.4 10 8 6 4 2 0 Amount Spent 10 20 30 40 50 Age weak negative down up r = -.292 weak negative more less

14. 8 -.632 -.292 8 8 No No This is a weak negative relationship that did not reach statistical significance r(8) = -.292; n.s.

15. r = -.4 35 30 25 20 15 10 5 This Year 3 6 9 12 15 18 21 24 27 Last Year moderate positive larger smaller r = .5313 strong positive larger smaller

16. .482 .53 15 15 15 Yes Yes This is a strong / moderate relationship between this year and last year portfolio returns r(15) = .53; p<.05

17. r = .75 8 7 6 5 4 3 2 Shipping Cost 6 7 8 9 10 11 Number of Orders(in hundreds) strong positive larger smaller r = .8196 strong positive larger smaller

18. .576 .8196 10 10 10 Yes Yes This is a strong / moderate relationship between Number of orders and shipping costs r(10) = .82; p<.05

19. Hand in yourhomework http://www.thedailyshow.com/video/index.jhtml?videoId=188474&title=an-arab-family-man

20. 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 What are we predicting? What are we predicting? Dependent Variable Dependent Variable Independent Variable Independent Variable

21. What are we predicting? Correlation Positive correlation: as values on one variable go up, so do values for the other variable Negative correlation: as values on one variable go up, the values for the other variable go down Yearly income by expenses per year YearlyIncome Positive Correlation Expenses per year

22. What are we predicting? Correlation Positive correlation: as values on one variable go up, so do values for the other variable Negative correlation: as values on one variable go up, the values for the other variable go down Temperatures by time spent outside in Tucson in summer Temperature Negative Correlation Timeoutside

23. What are we predicting? Correlation Positive correlation: as values on one variable go up, so do values for the other variable Negative correlation: as values on one variable go up, the values for the other variable go down Height by average driving speed Height Zero Correlation Average Speed

24. What are we predicting? Correlation Positive correlation: as values on one variable go up, so do values for the other variable Negative correlation: as values on one variable go up, the values for the other variable go down Amount Healthtex spends per month on advertising by sales in the month Amountof sales Positive Correlation Amount spent On Advertising

25. YearlyIncome Expenses per year Correlation - What do we need to define a line If you probably make this much Y-intercept = “a” (also “b0”)Where the line crosses the Y axis Slope = “b” (also “b1”)How steep the line is If you spend 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

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

27. Correlation - the prediction line - what is it good for? 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

28. Yearly Income Yearly Income YearlyIncome Expenses per year Expenses per year Expenses per year Correlation - What do we need to define a line Y-intercept = “a”Where the line crosses the Y axis Slope = “b” How steep the line is Y-intercept is good…slope is wrong Y-intercept is wrong…slope is good

29. BrushingTeeth BrushingTeeth BrushingTeeth NumberCavities NumberCavities NumberCavities Correlation - What do we need to define a line Y-intercept = “a”Where the line crosses the Y axis Slope = “b” How steep the line is Y-intercept is wrong…slope is good Y-intercept is good…slope is wrong

30. 5 4 Number of times per day teeth are brushed 3 2 1 0 0 1 2 3 4 5 Number of cavities Correlation - let’s do another one Does brushing your teeth correlate with fewer cavities? Step 1: Draw scatterplot Step 2: Data table X Y XY X2 Y2 1 5 5 1 25 3 4 12 9 16 2 3 6 4 9 3 2 6 9 4 5 1 5 25 1 Σ 14 15 34 48 55 Step 3: Estimate r and prediction line Step 4: Find r

31. Correlation - Let’s do one Step 1: Find n n = 5 (5 pairs) Step 2: Find ΣX and ΣY Step 3: Find ΣXY Step 4: Find ΣX2 and ΣY2 Step 5: Plug in the numbers X Y XY X2 Y2 1 5 5 1 25 3 4 12 9 16 2 3 6 4 9 3 2 6 9 4 5 1 5 25 1 Σ 14 15 34 48 55 The formula:

32. r = r = [√[(5)(55)-(15)2] [√[(5)(48)-(14)2] - 40 (170 - 210) = [√50 ] [√44 ] 46.90 Correlation - Let’s do one Step 1: Find n n = 5 (5 pairs) Step 2: Find ΣX and ΣY Step 3: Find ΣXY Step 4: Find ΣX2 and ΣY2 Step 5: Plug in the numbers (5)(34)-(14)(15) X Y XY X2 Y2 1 5 5 1 25 3 4 12 9 16 2 3 6 4 9 3 2 6 9 4 5 1 5 25 1 Σ 14 15 34 48 55 r = -.85 The formula:

33. X Y XY X2 Y2 . 1 5 5 1 25 3 4 12 9 16 2 3 6 4 9 3 2 6 9 4 5 1 5 25 1 Σ 14 15 34 48 55 Find r r = -0.85

34. X Y XY X2 Y2 . 1 5 5 1 25 3 4 12 9 16 2 3 6 4 9 3 2 6 9 4 5 1 5 25 1 Σ 14 15 34 48 55 Draw a scatterplot

35. X Y XY X2 Y2 1 5 5 1 25 3 4 12 9 16 2 3 6 4 9 3 2 6 9 4 5 1 5 25 1 Σ 14 15 34 48 55 Draw a scatterplot

36. Draw a regression line

37. Draw a regression line

38. r = -0.85 b= - 0.91(slope) a= 5.5 (intercept) Draw a regression line and regression equation

39. Prediction line Y’ = a+ b1X1 Y’ = 842 + (-37.5)X1 Interpreting regression equation Y-intercept a) Interpret the slope of the fitted regression line:Sales = 842 – 37.5 Price Slope Notice in this case it is negative A slope of “37.5” suggests that raising “price” by 1 unit will reduce “sales” by 37.5 units b) If “price” = 20, what is the prediction for “Sales”?Sales = 842 – 37.5 Price Sales = 842 - 37.5 Price Sales = 842 - (37.5) (20) Sales = 842 - (37.5) (20) = 842 – 750 = 92 Sales price of product

40. Prediction line Y’ = a+ b1X1 Y’ = 842 + (-37.5)X1 Interpreting regression equation Y-intercept a) Interpret the slope of the fitted regression line:Sales = 842 – 37.5 Price Slope A slope of “37.5” suggests that raising “price” by 1 unit will reduce “sales” by 37.5 units b) If “price” = 20, what is the prediction for “Sales”?Sales = 842 – 37.5 Price Sales = 842 - 37.5 Price Sales = 842 - (37.5) (20) Sales = 842 - (37.5) (20) = 842 – 750 = 92 (20, 92) Sales probablyabout 92 units Sales price of product If Price = 20

41. Prediction line Y’ = a+ b1X1 Y’ = 2.277 + (.0307)X1 Interpreting regression equation a) The regression equation: NetIncome = 2,277 + .0307 Revenue Interpret the slope Y-intercept Slope Notice in this case it is positive A slope of “.0307” suggests that raising “Revenue” by 1 dollar, NetIncome will raise by 3 cents b) If “Revenue” = 1,000, what is the prediction for “NetIncome”? NetIncome = 2,277 + .0307 Revenue NetIncome = 2,277 + (.0307 )(1,000) NetIncome = 2,277 + 30.7 = 2,307.7 (1,000, 2,307.7) NetIncome Revenue

42. Prediction line Y’ = a+ b1X1 Y’ = 2,277 + (.0307)X1 Interpreting regression equation a) The regression equation: NetIncome = 2,277 + .0307 Revenue Interpret the slope Y-intercept Slope A slope of “.0307” suggests that raising “Revenue” by 1 dollar, NetIncome will raise by 3 cents b) If “Revenue” = 1,000, what is the prediction for “NetIncome”? NetIncome will be about 2,307.70 NetIncome = 2,277 + .0307 Revenue NetIncome = 2,277 + (.0307 )(1,000) NetIncome = 2,277 + 30.7 = 2,307.7 (1,000, 2,307.7) NetIncome Revenue If Revenue = 1000

43. Prediction line Y’ = a+ b1X1 Other Problems Cost will be about 95.06 Cost Y-intercept The expected cost for dinner for two couples (4 people) would be $95.06Cost = 15.22 + 19.96 Persons People Slope If People = 4 If “Persons” = 4, what is the prediction for “Cost”? Cost = 15.22 + 19.96 Persons Cost = 15.22 + 19.96 (4) Cost = 15.22 + 79.84 = 95.06 If “Persons” = 1, what is the prediction for “Cost”? Cost = 15.22 + 19.96 Persons Cost = 15.22 + 19.96 (1) Cost = 15.22 + 19.96 = 35.18

44. Prediction line Y’ = a+ b1X1 Other Problems Rent will be about 990 Cost Y-intercept Slope Square Feet If SqFt = 800 The expected cost for rent on an 800 square foot apartment is $990Rent = 150 + 1.05 SqFt If “SqFt” = 800, what is the prediction for “Rent”? Rent = 150 + 1.05 SqFt Rent = 150 + 1.05 (800) Rent = 150 + 840 = 990 If “SqFt” = 2500, what is the prediction for “Rent”? Rent = 150 + 1.05 SqFt Rent = 150 + 1.05 (2500) Rent = 150 + 840 = 2,775

45. Prediction line Y’ = a+ b1X1 Frequency of Teeth brushing will be about Other Problems Y-intercept If number of cavities = 3 Slope The expected frequeny of teeth brushing for having one cavity is Frequency of teeth brushing= 5.5 + (-.91) Cavities If “Cavities” = 3, what is the prediction for “Frequency of teeth brushing”? Frequency of teeth brushing= 5.5 + (-.91) Cavities Frequency of teeth brushing= 5.5 + (-.91) (3) Frequency of teeth brushing= 5.5 + (-2.73) = 2.77 (3.0, 2.77)

46. Draw a regression line and regression equation Prediction line Y’ = b1X1+ b0 Y’ = (-.91)X 1+ 5.5 b0 = 5.5 (intercept) b1 = - 0.91(slope) r = - 0.85

47. 5 4 Number of times per day teeth are brushed 3 2 1 0 0 1 2 3 4 5 Number of cavities Prediction line Y’ = b1X 1+ b0 Y’ = (-.91)X 1+ 5.5 Correlation - Evaluating the prediction line Does the prediction line perfectly predict the Ys from the Xs? No, let’s see How much “error” is there? Exactly? Residuals The green lines show how much “error” there is in our prediction line…how much we are wrong in our predictions

48. Thank you! See you next time!!