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 Regression Model

A Critical Examination of Hedonic Analysis of a Regression Model (HARM) and META-ANALYSIS Albert R. Wilson BSSE, MBA, CRE (Ret).  Regression Model. A model intended to allow an exploration of the hypothetical relationship between possible explanatory variables and the sales price.

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 Regression Model

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  1. A Critical Examination ofHedonic Analysis of a Regression Model (HARM) and META-ANALYSISAlbert R. WilsonBSSE, MBA, CRE (Ret)

  2.  Regression Model A model intended to allow an exploration of the hypothetical relationship between possible explanatory variables and the sales price

  3. Regression Model • Reflection of reality • The touchstone of that reality? Actual market participants

  4. “Estimated” versus “Predicted” • Estimated = Sale IN database • Predicted = Sale NOT IN database

  5. Predicted Sales Prices At the mean predicted sales price variance is larger than estimated variance by σ2 (variance in the data)

  6. Mean Confidence Intervals (MCI)Estimated and Predicted MCI FOR PREDICTED 4.38 TIMES MCI FOR ESTIMATED

  7. DATABASE EDITING  GARBAGE IN => GARBAGE OUT (GIGO) 

  8. Case ExampleInfluence on the Removal of “Flipping Transactions” on the Predicted Prices for 33 Properties

  9. Editing and Confirmation of Data STEP 1: Edit to identify obvious issues (the desk edit) Case Example Assessor’s Data 4,325 Removed 747 17.3% R-Squared 0.79 0.83 MLS Data 1,888 Removed 779 44.3%

  10. Editing and Confirmation of Data STEP 2: Identify sales that are not appropriate to the analysis

  11. Editing and Confirmation of Data STEP 3: Sales confirmation • A values-neutral interview of sale participants • OBJECT: to elicit the primary factors motivating the conclusion of the sale price MUST NOT INTRODUCE ANALYST OPINION THIS IS THE ONLY MEANS OF IDENTIFYING/CONFIRMING THE REASONS FOR A CONCLUDED PRICE

  12. Regression Model Considerations Faithfully represent: • Identified concerns of actual market participants • Restrictions imposed by the data Estimates of prices the ONLY VERIFIABLE OUTPUT

  13. Coefficient Calculation Result of iterative calculations designed to provide the most accurate estimates of sales prices in database

  14. Coefficient Calculation Goodness of Fit • Measures of the Goodness of Fit apply only to the relationship between the estimated and actual sales prices in the database • They do not apply to the coefficients

  15. Most commonly-cited Goodness-of-Fit Measure R-Squared (Coefficient of Determination)

  16. R-Squared • Generally-applied interpretation: • R-Squared is the amount of variance “explained” by the model

  17. Low R-Squared Models Mathematically, as the R-Squared approaches 0.30, it becomes more likely that the model is only measuring random effects

  18. The Omitted and Additional Variable Problem • Omitting generally increases magnitude and statistical significance of the remaining coefficients • Adding generally decreases the magnitude and statistical significance of the remaining variable coefficients

  19. Illustration of Omitting or Adding a Variable

  20. Consequences of Variable Selection Including the Assessor’s Parcel Number APN Coefficient Value 0.023 t-statistic 8.98 Mean Value 30,834,360 R-Squared 0.83 Mean Sale Price $211,000 Results in an incremental increase in the sales price of 0.023 x 30,834.360 = $709,190 (APN Coef.) x (Mean Value) = (Incremental Increase)

  21. Consequences of Variable Selection Omission of a Variable: • Removal of “Pool”; present in 38% of properties • SQFT Cofficient changed from $40.79 to $41.79 • Approximately the same t-statistic • Removal of “Fixtures”; present in 100% of properties • SQFT Coefficient changed from $40.79 to $46.50 • T-statistic = 50.94

  22. Coefficients Coefficients are simply multipliers for the explanatory variable

  23. Causation in Real Estate From the Real Estate Appraiser’s perspective: • Causation demonstrated through sales confirmation interviews. • Causation NEVER proven through a regression.

  24. Strengths and Weaknesses • Can never be better than the data • Requires significant amount of data: five to 15 or more sales • Upper limit to the amount of data: too much may be worse than too little • Guide: Are the sales competitive to the subject? • Estimate of sales prices most accurate at the mean value of the data • Variance of a predicted sales price larger than variance of estimated • Thousands of possible regression models

  25. Further Considerations • Absent standards, the “Rubber Ruler” may apply • When recognized and published standards are not used, author must demonstrate the accuracy and reliability of his/her work

  26. Hedonic Analysis

  27. The Hedonic Assumption The coefficient accurately and only represents the contribution of the declared meaning of the explanatory variable to the sale price

  28. Hedonic Analysis The validity of the hedonic assumption must be demonstrated

  29. “Revealed Preference” Idea cannot be supported for real estate

  30. Supporting Literature Not a single paper demonstrated the validity of the hedonic assumption PLUS • NO indication of confirmation of raw data • NO indication of adherence to any recognized / published standards • NO indication of confirmation of results with the normal or typical market participant THE RUBBER RULER EFFECT IS MUCH IN EVIDENCE.

  31. Regression Model Accuracy If the regression model is inaccurate, then there is no reason to expect the coefficients to be accurate or meaningful. Therefore the HARM cannot be accurate.

  32. CASE EXAMPLETO POOL OR NOT TO POOL • Using the data from the previous case. • Does a pool influence value? • By how much? • The Hedonic Approach, the coefficient is the marginal contribution to value.

  33. TO POOL OR NOT TO POOL (CONT.) • What are the coefficients if there is no pool?

  34. Comparision • Orig Fixt 2,805 3,088 • Orig-nopatio -14,116 -14,725 • Orig-no pool 9,162 NA • Orig-sqf 41.52 42.40 • Orig-garage 16,213 16,925 • SY2000 5,980 5,728 • ESP $184,513 $184,059 • R-sq 0.88 0.88

  35. POOL OR NOT TO POOL (CONT.) • WHAT HAPPENS IF WE CONSIDER A DATABASE WITH POOLS, AND SEPARATELY A DATABASE WITHOUT POOLS?

  36. POOLS AND NO POOLS SEPARATELY • ESTIMATED SALE PRICE WITH POOL $204,954 • R-SQUARED 0.87 • ESTIMATED SALE PRICE W/O POOL $170,805 • R-SQUARED 0.89

  37. The Coefficient – What Counts? ALL THAT STATISTICAL SIGNIFICANCE CAN TELL US IS THAT FOR THIS MODEL AND DATABASE THE COEFFICIENT IS A SIGNIFICANT (OR INSIGNIFICANT) MULTIPLIER FOR THE EXPLANATORY VARIABLE. NOTHING MORE.

  38. The Appropriate Standard:Economic Significance For us, economic significance is determined by what the normal or typical participant considers important to the conclusion of the transaction.

  39. A Criticality: NOT ONE hedonic analysis encountered to date has actually asked this question: “What was important to you in concluding your transaction?”

  40. Hedonic Analysis of a Regression Model (HARM) is: • Highly inaccurate and unreliable method • Not appropriate for appraisal work Observations apply to hedonic analysis NOT regression models!

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