1. Techniques of Data Analysis Assoc. Prof. Dr. Abdul Hamid b. Hj. Mar Iman Director Centre for Real Estate Studies Faculty of Engineering and Geoinformation Science Universiti Tekbnologi Malaysia Skudai, Johor

7. Examples of “abstraction” of phenomena

8. Examples of “abstraction” of phenomena % prediction error

10. Examples of relationship Dep=9t – 215.8 Dep=7t – 192.6

13. Common mistakes (contd.) – “Abuse of statistics” Many – a.o.t. Box-Cox  2 test for model equivalence Using R 2 To evaluate whether a model fits data better than the other Simple regression coefficient Multi-dimensional scaling, Likert scaling Finding the “relationship” between one variable with another Using a regression parameter Using partial c orrelation (e.g. Spearman coeff.) Measure the “influence” of a variable on another Many – a.o.t. two-way anova,  2 , Z test Multi-dimensional scaling, Likert scaling “ Compare” whether a group is different from another Hold-out sample’s MAPE Using R 2 and/or F-value of a model To evaluate accuracy of “prediction” Many – a.o.t. manova, regression Multi-dimensional scaling, Likert scaling To determine whether a group of factors “significantly influence” the observed phenomenon Correct technique Example of abuse Data analysis techniques Issue

19. Principles of data analysis (contd.) More female shoppers than male shoppers More young female shoppers than young male shoppers Young male shoppers are not interested to shop at the shopping complex 10 15 Female Old Young 6 4 Male Old Young Number Shoppers

28. Central Tendency – “Median” (contd.)

29. Central Tendency – “Quartiles” (contd.) Upper quartile = ¾(n+1) = 19.5 th . Taman UQ = 145 + (3/7 x 5) = RM 147.1/month Lower quartile = (n+1)/4 = 26/4 = 6.5 th. Taman LQ = 135 + (3.5/5 x 5) = RM138.5/month Inter-quartile = UQ – LQ = 147.1 – 138.5 = 8.6 th . Taman IQ = 138.5 + (4/5 x 5) = RM 142.5/month

35. “ Probability Distribution” (contd.) 12 11 10 9 8 7 6 11 10 9 8 7 6 5 10 9 8 7 6 5 4 9 8 7 6 5 4 3 8 7 6 5 4 3 2 7 6 5 4 3 2 1 6 5 4 3 2 1 Dice1 Dice2

36. “ Probability Distribution” (contd.) Values of x are discrete (discontinuous) Sum of lengths of vertical bars  p(X=x) = 1 all x Discrete values Discrete values

37. “ Probability Distribution” (contd.) ▪ Many real world phenomena take a form of continuous random variable ▪ Can take any values between two limits (e.g. income, age, weight, price, rental, etc.)

38. “ Probability Distribution” (contd.) P(Rental = RM 8) = 0 P(Rental < RM 3.00) = 0.206 P(Rental < RM7) = 0.972 P(Rental  RM 4.00) = 0.544 P(Rental  7) = 0.028 P(Rental < RM 2.00) = 0.053

40. “ Probability distribution” μ ± 1 σ = ? = ____% from total observation μ ± 2 σ = ? = ____% from total observation μ ± 3 σ = ? = ____% from total observation

41. “ Probability distribution” * Has the following distribution of observation

55. Correlation and regression – matrix approach

56. Correlation and regression – matrix approach

57. Correlation and regression – matrix approach

58. Correlation and regression – matrix approach

59. Correlation and regression – matrix approach

62. Test yourselves! Q5: Find:  (AGE > “30-34”)  (AGE ≤ 20-24)  ( “35-39”≤ AGE < “50-54”)

65. Thank you