2. Practice You collect data from 53 females and find the correlation between candy and depression is -.40. Determine if this value is significantly different than zero. You collect data from 53 males and find the correlation between candy and depression is -.50. Determine if this value is significantly different than zero.

3. Practice You collect data from 53 females and find the correlation between candy and depression is -.40. –t obs = 3.12 –t crit = 2.00 You collect data from 53 males and find the correlation between candy and depression is -.50. –t obs = 4.12 –t crit = 2.00

4. Practice You collect data from 53 females and find the correlation between candy and depression is -.40. You collect data from 53 males and find the correlation between candy and depression is -.50. Is the effect of candy significantly different for males and females?

5. Hypothesis H 1 : the two correlations are different H 0 : the two correlations are not different

6. Testing Differences Between Correlations Must be independent for this to work

7. When the population value of r is not zero the distribution of r values gets skewed Easy to fix! Use Fisher’s r transformation Page 746

8. Testing Differences Between Correlations Must be independent for this to work

9. Testing Differences Between Correlations

12. Note: what would the z value be if there was no difference between these two values (i.e., H o was true)

13. Testing Differences Z = -.625 What is the probability of obtaining a Z score of this size or greater, if the difference between these two r values was zero? p =.267 If p is <.025 reject H o and accept H 1 If p is = or >.025 fail to reject H o The two correlations are not significantly different than each other!

15. Remember this: Statistics Needed Need to find the best place to draw the regression line on a scatter plot Need to quantify the cluster of scores around this regression line (i.e., the correlation coefficient)

16. Regression allows us to predict!.....

17. Straight Line Y = mX + b Where: Y and X are variables representing scores m = slope of the line (constant) b = intercept of the line with the Y axis (constant)

18. Excel Example

19. That’s nice but.... How do you figure out the best values to use for m and b ? First lets move into the language of regression

20. Straight Line Y = mX + b Where: Y and X are variables representing scores m = slope of the line (constant) b = intercept of the line with the Y axis (constant)

21. Regression Equation Y = a + bX Where: Y = value predicted from a particular X value a = point at which the regression line intersects the Y axis b = slope of the regression line X = X value for which you wish to predict a Y value

22. Practice Y = -7 + 2X What is the slope and the Y-intercept? Determine the value of Y for each X: X = 1, X = 3, X = 5, X = 10

23. Practice Y = -7 + 2X What is the slope and the Y-intercept? Determine the value of Y for each X: X = 1, X = 3, X = 5, X = 10 Y = -5, Y = -1, Y = 3, Y = 13

24. Finding a and b Uses the least squares method Minimizes Error Error = Y - Y  (Y - Y) 2 is minimized

25. .....

26. ..... Error = 1 Error = -1 Error =.5 Error = -.5Error = 0 Error = Y - Y  (Y - Y) 2 is minimized

27. Finding a and b Ingredients COV xy S x 2 Mean of Y and X

28. Regression

30. Ingredients Mean Y =4.6 Mean X = 3 Cov xy = 3.75 S 2 X = 2.50

31. Regression Ingredients Mean Y =4.6 Mean X = 3 Cov xy = 3.75 S 2 x = 2.50

32. Regression Ingredients Mean Y =4.6 Mean X = 3 Cov xy = 3.75 S 2 x = 2.50

33. Regression Equation Y = a + bx Equation for predicting smiling from talking Y =.10+ 1.50(x)

35. Regression Equation Y =.10+ 1.50(x) How many times would a person likely smile if they talked 15 times?

36. Regression Equation Y =.10+ 1.50(x) How many times would a person likely smile if they talked 15 times? 22.6 =.10+ 1.50(15)

37. Y = 0.1 + (1.5)X.....

38. Y = 0.1 + (1.5)X X = 1; Y = 1.6......

39. Y = 0.1 + (1.5)X X = 5; Y = 7.60.......

40. Y = 0.1 + (1.5)X.......

41. Mean Y = 14.50; S y = 4.43 Mean X = 6.00; S x = 2.16 Quantify the relationship with a correlation and draw a regression line that predicts aggression.

42. ∑XY = 326 ∑Y = 58 ∑X = 24 N = 4

43. ∑XY = 326 ∑Y = 58 ∑X = 24 N = 4

44. COV = -7.33 S y = 4.43 S x = 2.16

45. COV = -7.33 S y = 4.43 S x = 2.16

46. Regression Ingredients Mean Y =14.5 Mean X = 6 Cov xy = -7.33 S 2 X = 4.67

47. Regression Ingredients Mean Y =14.5 Mean X = 6 Cov xy = -7.33 S 2 X = 4.67

48. Regression Equation Y = a + bX Y = 23.92 + (-1.57)X

49. .... 10 12 14 16 18 20 22 Y = 23.92 + (-1.57)X

50. .... 10 12 14 16 18 20 22 Y = 23.92 + (-1.57)X.

51. .... 10 12 14 16 18 20 22 Y = 23.92 + (-1.57)X..

52. .... 10 12 14 16 18 20 22 Y = 23.92 + (-1.57)X..

53. Hypothesis Testing Have learned –How to calculate r as an estimate of relationship between two variables –How to calculate b as a measure of the rate of change of Y as a function of X Next determine if these values are significantly different than 0

54. Testing b The significance test for r and b are equivalent If X and Y are related (r), then it must be true that Y varies with X (b). Important to learn b significance tests for multiple regression

55. Steps for testing b value 1) State the hypothesis 2) Find t-critical 3) Calculate b value 4) Calculate t-observed 5) Decision 6) Put answer into words

56. Practice You are interested in if candy consumption significantly alters a persons depression. Create a graph showing the relationship between candy consumption and depression (note: you must figure out which is X and which is Y)

57. Practice CandyDepression Charlie555 Augustus743 Veruca459 Mike3108 Violet465

58. Step 1 H 1 : b is not equal to 0 H 0 : b is equal to zero

59. Step 2 Calculate df = N - 2 –df = 3 Page 747 –First Column are df –Look at an alpha of.05 with two-tails –t crit = 3.182 and -3.182

60. Step 3 CandyDepression Charlie555 Augustus743 Veruca459 Mike3108 Violet465 COV = -30.5N = 5 r = -.81Sy = 24.82 S x = 1.52

61. Step 3 COV = -30.5N = 5 r = -.81 S x = 1.52 S y = 24.82 Y = 127 + -13.26(X) b = -13.26

62. Step 4 Calculate t-observed b = Slope S b = Standard error of slope

63. Step 4 S yx = Standard error of estimate S x = Standard Deviation of X

64. Step 4 S y = Standard Deviation of y r = correlation between x and y

65. Note

66. ..... Error = 1 Error = -1 Error =.5 Error = -.5Error = 0 Error = Y - Y  (Y - Y) 2 is minimized

67. Step 4 S y = Standard Deviation of y r = correlation between x and y

68. Step 4 S yx = Standard error of estimate S x = Standard Deviation of X

69. Step 4 S yx = Standard error of estimate S x = Standard Deviation of X

70. Step 4 Calculate t-observed b = Slope S b = Standard error of slope

71. Step 4 Calculate t-observed b = Slope S b = Standard error of slope

72. Step 4 Note: same value at t-observed for r

73. Step 5 If t obs falls in the critical region: –Reject H 0, and accept H 1 If t obs does not fall in the critical region: –Fail to reject H 0

74. t distribution t crit = 3.182 t crit = -3.182 0

75. t distribution t crit = 3.182 t crit = -3.182 0 -2.39

76. Step 5 If t obs falls in the critical region: –Reject H 0, and accept H 1 If t obs does not fall in the critical region:If t obs does not fall in the critical region: –Fail to reject H 0

78. Practice

79. Page 288 9.18

80. The regression equation for faculty shows that the best estimate of starting salary for faculty is $15,000 (intercept). For every additional year the salary increases on average by $900 (slope). For administrative staff the best estimate of starting salary is $10,000 (slope), for every additional year the salary increases on average by $1500 (slope). They will be equal at 8.33 years of service.

81. Practice Page 290 9.23

82. r =.68r 1 =.829 r =.51r 1 =.563 Z =.797 p =.2119 Correlations are not different from each other

83. Discuss 9.38

84. SPSS Problem #3 Due March 15th Page 287 –9.2 –9.3 –9.10 and create a graph by hand