3. With the growth of internet service providers, a researcher decides to examine whether there is a correlation between cost of internet service per month (rounded to the nearest dollar) and degree of customer satisfaction (on a scale of with a 1 being not at all satisfied and a 10 being extremely satisfied). The researcher only includes programs with comparable types of services. Determine if customers should be happy about paying more.
dollars
satisfaction 11 6 18 8 17 10 15 4 9 5 12 3 19 22 2 25

5. Practice
Situation 1
Based on a sample of 100 subjects you find the correlation between extraversion is happiness is r=.15. Determine if this value is significantly different than zero.
Situation 2
Based on a sample of 600 subjects you find the correlation between extraversion is happiness is r=.15. Determine if this value is significantly different than zero.

6. Step 1 Situation 1 H1: r is not equal to 0 H0: r is equal to zero
The two variables are related to each other
H0: r is equal to zero
The two variables are not related to each other
Situation 2

7. Step 2 Situation 1 df = 98 t crit = +1.985 and -1.984 Situation 2

8. Step 3
Situation 1
r = .15
Situation 2

9. Step 4
Situation 1
Situation 2

10. Step 5 Situation 1 If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0
Situation 2

11. Step 6
Situation 1
Based on a sample of 100 subjects you find the correlation between extraversion is happiness is r=.15. Determine if this value is significantly different than zero.
There is not a significant relationship between extraversion and happiness
Situation 2
Based on a sample of 600 subjects you find the correlation between extraversion is happiness is r=.15. Determine if this value is significantly different than zero.
There is a significant relationship between extraversion and happiness.

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

13. 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

14. 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?

15. Hypothesis H1: the two correlations are different
H0: the two correlations are not different

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

17. 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

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

19. Testing Differences Between Correlations

20. Testing Differences Between Correlations

21. Testing Differences Between Correlations

22. Testing Differences Between Correlations
Note: what would the z value be if there was no difference between these two values (i.e., Ho was true)

23. 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 < reject Ho and accept H1
If p is = or > .025 fail to reject Ho
The two correlations are not significantly different than each other!

25. 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)

26. Regression allows us to predict!. . . . .

27. 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)

28. Excel Example

29. 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

30. 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)

31. 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

32. 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

33. 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

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

35. . . . . .

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

37. Finding a and b
Ingredients
COVxy
Sx2
Mean of Y and X

38. Regression

40. Regression
Ingredients
Mean Y =4.6
Mean X = 3
Covxy = 3.75
S2X = 2.50

41. Regression
Ingredients
Mean Y =4.6
Mean X = 3
Covxy = 3.75
S2x = 2.50

42. Regression
Ingredients
Mean Y =4.6
Mean X = 3
Covxy = 3.75
S2x = 2.50

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

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

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

47. Y = (1.5)X . . . . .

48. Y = (1.5)X X = 1; Y = 1.6 . . . . . .

49. Y = (1.5)X X = 5; Y = 7.60 . . . . . . .

50. Y = (1.5)X . . . . . . .

51. Mean Y = 14.50; Sy = 4.43 Mean X = 6.00; Sx= 2.16
Quantify the relationship with a correlation and draw a regression line that predicts aggression.

52. ∑XY = 326
∑Y = 58
∑X = 24
N = 4

53. ∑XY = 326
∑Y = 58
∑X = 24
N = 4

54. COV = -7.33
Sy = 4.43 Sx= 2.16

55. COV = -7.33
Sy = 4.43 Sx= 2.16

56. Regression Ingredients Mean Y =14.5 Mean X = 6 Covxy = -7.33
S2X = 4.67

57. Regression Ingredients Mean Y =14.5 Mean X = 6 Covxy = -7.33
S2X = 4.67

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

59. Y = (-1.57)X . 22 20 . 18 16 . 14 . 12 10

60. Y = (-1.57)X . . 22 20 . 18 16 . 14 . 12 10

61. Y = (-1.57)X . . 22 20 . 18 16 . 14 . 12 . 10

62. Y = (-1.57)X . . 22 20 . 18 16 . 14 . 12 . 10

63. 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

64. 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

65. 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

66. 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)

67. Practice Candy Depression Charlie 5 55 Augustus 7 43 Veruca 4 59 Mike
108
Violet 65

68. Step 1
H1: b is not equal to 0
H0: b is equal to zero

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

70. Step 3 Candy Depression Charlie 5 55 Augustus 7 43 Veruca 4 59 Mike 3
108
Violet 65
COV = N = 5
r = Sy = 24.82
Sx = 1.52

71. Step 3 Y = 127 + -13.26(X) b = -13.26 COV = -30.5 N = 5 r = -.81
Sx = 1.52
Sy = 24.82

72. Step 4
Calculate t-observed
b = Slope
Sb = Standard error of slope

73. Step 4
Syx = Standard error of estimate
Sx = Standard Deviation of X

74. Step 4
Sy = Standard Deviation of y
r = correlation between x and y

75. Note

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

77. Step 4
Sy = Standard Deviation of y
r = correlation between x and y

78. Step 4
Syx = Standard error of estimate
Sx = Standard Deviation of X

79. Step 4
Syx = Standard error of estimate
Sx = Standard Deviation of X

80. Step 4
Calculate t-observed
b = Slope
Sb = Standard error of slope

81. Step 4
Calculate t-observed
b = Slope
Sb = Standard error of slope

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

83. Step 5 If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0

84. t distribution
tcrit =
tcrit = 3.182

85. t distribution
tcrit =
tcrit = 3.182
-2.39

86. Step 5 If tobs falls in the critical region:
Reject H0, and accept H1
If tobs does not fall in the critical region:
Fail to reject H0

88. Practice

89. Practice
Page 288
9.18

90. 9.18
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.

91. Practice
Page 290
9.23

92. 9.23
r = r1 = .829
r = r1 = .563
Z = .797
p = .2119
Correlations are not different from each other

93. SPSS Problem #3 Due March 14th
Page 287
9.2
9.3
9.10 and create a graph by hand