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Correlation Between Internet Cost and Customer Satisfaction Study

Investigating if the cost of internet service per month correlates with customer satisfaction level. Analyzing data using correlation coefficients and hypothesis testing. Excel regression example included.

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Correlation Between Internet Cost and Customer Satisfaction Study

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  1. 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 1 - 10 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.

  2. 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.

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

  4. Step 2 • Situation 1 • df = 98 • t crit = +1.985 and -1.984 • Situation 2 • df = 598 • t crit = +1.96 and -1.96

  5. Step 3 • Situation 1 • r = .15 • Situation 2 • r = .15

  6. Step 4 • Situation 1 • Situation 2

  7. 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 • 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

  8. 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.

  9. 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.

  10. 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

  11. 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?

  12. Hypothesis • H1: the two correlations are different • H0: the two correlations are not different

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

  14. 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

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

  16. Testing Differences Between Correlations

  17. Testing Differences Between Correlations

  18. Testing Differences Between Correlations

  19. 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)

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

  21. 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)

  22. Regression allows us to predict! . . . . .

  23. 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)

  24. Excel Example

  25. 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

  26. 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)

  27. 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

  28. 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

  29. 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

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

  31. . . . . .

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

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

  34. Regression

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

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

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

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

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

  40. 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)

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

  42. Y = 0.1 + (1.5)XX = 1; Y = 1.6 . . . . . .

  43. Y = 0.1 + (1.5)XX = 5; Y = 7.60 . . . . . . .

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

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