Stat 1 - 13 Correlation Linear Regression.pptx

Perkuliahan Statistik - Pertemuan 13 - Regresi Linear

1. Statistics 1 13 Correlation & Linear Regression 2 Muhammad Rifqi Arviansyah

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4. Previously on Stat 1….

5. Correlation Analysis Group of techniques to measure the relationship between two variables . Regression Analysis Develop an equation that will allow us to estimate the value of one variable based on the value of another . Correlation Analysis & Regression Analysis

6. Correlation Coefficient Image from : Lind, Douglas A., Marchal, William G., Wathen, Samuel A., 2021

7. Correlation Coefficient Category Image from : Lind, Douglas A., Marchal, William G., Wathen, Samuel A., 2021 From Cohen 1988: Weak : 0.10 - 0.29 Medium : 0.30 - 0.49 Large : 0.50 - 1.00 From Evans 1996: Very weak : 0.00 - 0.19 Weak : 0.20 - 0.39 Moderate : 0.40 - 0.59 Strong : 0.60 - 0.79 Very strong : 0.80 - 1.00

8. Example Image from : Lind, Douglas A., Marchal, William G., Wathen, Samuel A., 2021

9. Regression Analysis Develop an equation that will allow us to estimate the value of one variable based on the value of another . Least Square Principle A mathematical procedure that uses the data to position a line with the objective of minimizing the sum of the squares of the vertical distances between the actual y values and the predicted values of y. Regression Analysis

10. Regression Analysis Image from : Lind, Douglas A., Marchal, William G., Wathen, Samuel A., 2021

11. Regression Analysis Image from : Lind, Douglas A., Marchal, William G., Wathen, Samuel A., 2021

12. Regression Analysis Image from : Lind, Douglas A., Marchal, William G., Wathen, Samuel A., 2021

13. Regression Analysis Image from : Lind, Douglas A., Marchal, William G., Wathen, Samuel A., 2021

14. Correlation Analysis & Regression Analysis

15. Correlation Analysis & Regression Analysis If the company has 100 employees, can we apply the correlation and regression equation?

16. Testing the Significance of the Correlation Coefficient 01 13 - Correlation & Linear Regression 2 Testing the Significance of the Regression Equation 02

17. If the company has 100 employees, can we apply the correlation and regression equation? We will use the concept of inferential statistics . Testing the Significance of the Correlation Coefficient

18. From the sample, the Sales Manager wants to know could there be zero correlation in the population from which the sample was selected? Develop the Hypothesis: H0 : ρ = 0 → The correlation in the population is zero. H1 : ρ ≠ 0 → The correlation in the population is different from zero. Testing the Significance of the Correlation Coefficient

19. Testing the Significance of the Correlation Coefficient Image from : Lind, Douglas A., Marchal, William G., Wathen, Samuel A., 2021

20. Known: r = 0.8646 n = 15 Determine the Test Statistics: Testing the Significance of the Correlation Coefficient

21. Determine the Critical Value: d f = n - 2 = 15 - 2 = 13 Testing the Significance of the Correlation Coefficient Image from : Lind, Douglas A., Marchal, William G., Wathen, Samuel A., 2021

22. Determine the Critical Value: Testing the Significance of the Correlation Coefficient Image from : Lind, Douglas A., Marchal, William G., Wathen, Samuel A., 2021

23. Make Decision: Test Statistics : 6.205088676 Critical Value : ± 2.160 6.2051 > 2.160 → (+) Test statistics > (+) Critical value Reject H0 Testing the Significance of the Correlation Coefficient

24. Interpretation: With 𝛼 = 5%, there is correlation with respect to the number of sales calls made and the number of copiers sold in the population of salespeople. Testing the Significance of the Correlation Coefficient

25. Testing the Significance of the Correlation Coefficient Make Decision: Test Statistics : 6.205088676 Check the Result from Data Analysis in GSheets / Excel:

26. How if the Sales Manager wants to know could there be a positive correlation in the population from which the sample was selected? Testing the Significance of the Correlation Coefficient

27. Testing the Significance of the Correlation Coefficient 01 13 - Correlation & Linear Regression 2 Testing the Significance of the Regression Equation 02

28. Y’ = 19,98 + 0,2606 x This is the regression equation of the sample . How about the regression equation of the population ? Testing the Significance of the Regression Equation

29. Y’ = 19,98 + 0,2606 x We identified the intercept value as a . We use “A” to represent the population intercept . Testing the Significance of the Intercept

30. Where: a = sample intercept A = population intercept sa = the standard error of the intercept estimate Testing the Significance of the Intercept

31. Testing the Significance of the Intercept

32. the Sales Manager wants to know could the intercept in the population is not 0 from which the sample was selected? Develop the Hypothesis: H0 : A = 0 → The slope in the population is zero. H1 : A ≠ 0 → The slope in the population is different from zero. Testing the Significance of the Intercept

33. Known: a = 19.98 s a = 4.38967553266198 Determine the Test Statistics: Testing the Significance of the Intercept

34. Determine the Critical Value: df = n - 2 = 15 - 2 = 13 Image from : Lind, Douglas A., Marchal, William G., Wathen, Samuel A., 2021 Testing the Significance of the Intercept

35. Make Decision: Test Statistics : 4.551589258 Critical Value : ± 2.160 4.552 > 2.160 → (+) Test statistics > (+) Critical value Reject H0 Testing the Significance of the Intercept

36. Interpretation: With 𝛼 = 5%, the intercept of the number of sales calls made and the number of copiers sold in the population of salespeople is significant. Testing the Significance of the Intercept

37. Y’ = 19,98 + 0,2606 x We identified the slope (kemiringan) value as b . We use “β” to represent the population slope . Testing the Significance of the Slope

38. Develop the Hypothesis: H0 : β = 0 → The slope in the population is zero. The regression line is horizontal and there is no relationship between the independent variable ( X ) and dependent variable ( Y ). H1 : β ≠ 0 → The slope in the population is different from zero. Testing the Significance of the Slope

39. Testing the Significance of the Slope

40. Testing the Significance of the Slope

41. the Sales Manager wants to know could there be a positive slope in the population from which the sample was selected? Develop the Hypothesis: H0 : β <= 0 → The slope in the population is zero. H1 : β > 0 → The slope in the population is different from zero. Testing the Significance of the Slope

42. Known: b = 0.260625 s b = 0.0420018171539133 Determine the Test Statistics: Testing the Significance of the Slope

43. Determine the Critical Value: df = n - 2 = 15 - 2 = 13 Image from : Lind, Douglas A., Marchal, William G., Wathen, Samuel A., 2021 Testing the Significance of the Slope

44. Make Decision: Test Statistics : 6.205088676 Critical Value : 1.771 6.2051 > 1.771 → (+) Test statistics > (+) Critical value Reject H0 Testing the Significance of the Slope

45. Interpretation: With 𝛼 = 5%, the slope of the number of sales calls made and the number of copiers sold in the population of salespeople is positive / significant. Testing the Significance of the Slope

46. Testing the Significance of the Slope & Intercept

47. Y’ = 19.98 + 0.2606 X (Number of products sold) = 19.98 + 0.2606 (number of sales calls) Is the regression equation is a good predictor? Finding the exact outcome is practically impossible . Therefore, we know the standard error of estimate . Standard Error of Estimate is a measure of dispersion of the observed values around the line of regression. Standard Error of Estimate

48. Standard Error of Estimate

49. Standard Error of Estimate

50. The interval of estimated value of products sold (Y) could be determined by calculating the upper and lower bound. Interval Y’ = Y’ ± s y.x Standard Error of Estimate

51. Standard Error of Estimate

52. Interval of the Intercept & Slope

53. The proportion of the total variation in the dependent variable Y that is explained by the variation in the independent variable X . Symbol : r^2 (R Square) The Coefficient of Determination

54. The Coefficient of Determination

55. r square = 0.7475 Interpretation: 74.75% variance of products sold has been explained by sales calls. The other 25.25% could be explained by other factors. The Coefficient of Determination

56. https://docs.google.com/spreadsheets/d/1Pj0mP5M6sJbnMFU75nHSKypt9VUZYa_qjCIQYRX8sAo/edit?usp=sharing Exercise

57. References Lind, Douglas A., Marchal, William G., Wathen, Samuel A.. (2021). Statistical techniques in business & economics

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