1. Statistical methods for real estate data prof. RNDr. Beáta Stehlíková, CSc. 2013

2. Beáta Stehliková, Bratislava 2 Information is currently besides financial, energy, material resources the main factor of progress.

3. Beáta Stehliková, Bratislava 3 How to obtain new knowledge? We want to answer the question: How to obtain new information, new knowledge from data?

4. Talk only about one method of spatial statistics Why spatial statistics ? Methods of spatial statistics are for spatial data Real estate data contain very often information about the geographic location – there are spatial data Beáta Stehliková, Bratislava 4

5. Variable and data A variable - a characteristic of population or sample that is of interest for us. Data - the actual values of variables Beáta Stehliková, Bratislava 5

6. 6 Different kinds of data Cross-sectional data are data on one or more variables collected at a single point in time Time series data data are collected over a period of time on one or more variables Panel data – the same cross-section over time in real estate

7. Types of data (scale) We have said that data - the actual values of variables Types of data: Interval data are numerical observations Ordinal data are ordered categorical observations Nominal data are categorical observations Beáta Stehliková, Bratislava 7

8. Types of data (scale) Knowing the type of data (scale) is necessary to properly select the technique to be used when analyzing data. Beáta Stehliková, Bratislava 8

9. 2.9 Descriptive statistics involves arranging, summarizing, and presenting a set of data in such a way that useful information is produced. Descriptive statistics

10. graphical techniques (histogram) numerical descriptive measures Mean (average) Median (middle value) Mode (most frequently ) Variance Standard deviation Beáta Stehliková, Bratislava 10

11. Beáta Stehliková, Bratislava 11 Descriptive statistics are not enough Average (17,8) Standard deviation (4,7) Coefficient of variation (26,4 %) n=25 It is necessary to know the probability distribution Consider two data sets A and B A B

12. Beáta Stehliková, Bratislava 12 Second example Consider two large data sets A and B

13. Beáta Stehliková, Bratislava 13 The location information It is not possible to identify differences between data sets without we take into account the location information

14. Beáta Stehliková, Bratislava 14 The location information Variograms quantify changes in values ​​ in the space there is no there is spatial autocorrelation small distances correspond to small changes in values small distances correspond to large changes in values

15. Spatial autocorrelation The degree to which near and more distant things are interrelated Measures of spatial autocorrelation attempt to deal with similarities in the location of spatial objects and their attributes

16. Spatial autocorrelation Positive (objects similar in location are similar in attribute) Negative (objects similar in location are very different) Zero (attributes are independent of location)

17. Spatial autocorrelation - measures. Several measures available: Moran’s coefficient I, Geary’s C coefficient, Getis-Ord coefficient G. These measures may be “global” - they apply to the study region or “local” - autocorrelation may exist in some parts of the region but not in others.

18. Moran’s coefficient I varies between –1.0 and + 1.0 0 indicates no spatial autocorrelation [1/(n-1)] (indicate random pattern) When autocorrelation is high, the I coefficient is close to 1 or -1 Negative values I indicate negative autocorrelation Positive values I indicate positive autocorrelation (indicate a tendency toward clustering)

19. Regression analysis is a technique for using data to identify relationships among variables and use these relationships to make predictions. Beáta Stehliková, Bratislava 19

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21. Regression analyses that ignore spatial dependency can have unstable parameter estimates and unreliable significance tests. Solution: Spatial Autoregressive Models Lag model Spatial Error model Beáta Stehliková, Bratislava 21

22. Spatial Models 22 SPATIAL LAG SPATIAL ERROR Ordinary Least Squares No influence from neighbors Dependent variable influenced by neighbors Residuals influenced by neighbors Y = β 0 + Xβ Y = β 0 + λ WY + Xβ + εY = β 0 + Xβ + ρWε + ξ Lag model controls spatial autocorrelation in the dependent variable Error model controls spatial autocorrelation in the residuals, thus it controls autocorrelation in the dependent and the independent variables

23. Software GeoDa Beáta Stehliková, Bratislava 23

24. Compare different spatial models Neither R 2 nor Adjusted R 2 can be used to compare different spatial regression models We can used Akaike Information Criteria (the smaller the AIC value the better the model) 24

25. Example Beáta Stehliková, Bratislava 25 dependent variable y – price of dwelling independent variable x – living area Classical regression analysis

26. Residuals Beáta Stehliková, Bratislava 26 Moran´s I = 0.193022 Significance: P value= 0.03140<0.05 This indicate positive spatial autocorrelation between residuals.

27. Spatial error model Beáta Stehliková, Bratislava 27

28. Local Moran’s coefficients Beáta Stehliková, Bratislava 28 Which values produce spatial autocorrelation ?

29. Spatial statistics Methods of spatial statistics very use full for data with the location information The art of looking for beauty, and science looking for true. Spatial statistics will help us find the true when we use the right methods Beáta Stehliková, Bratislava 29

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