a425_mult - Multiple Regression APS 425- Advanced...

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Multiple Regression APS 425- Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 1 APS 425 – Winter 2010 Multiple Regression Review Instructor: G. William Schwert 275-2470 schwert@schwert.simon.rochester.edu Multiple Regression Model • We have studied the multiple regression model: Y i = 0 + 1 X 1 i + 2 X 2 i + e i Y i = 0 + 1 X 1 i + … + n X ni + e i • We don’t know the true values for 0 , 1 , …, n
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Multiple Regression APS 425- Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 2 Multiple Regression Model • Given a sample, we find, as before, estimators b 0 , b 1 , …, b n , by minimizing the sum of squared prediction errors: e i 2 = ( Y i –Y i ) 2 , where Y i = b 0 + b 1 X 1 i + … + b n X ni ^^ ^ • The estimators b 0 , b 1 , …, b n are unbiased, consistent, and efficient estimators of the population parameters 0 , 1 , …, n if the following six assumptions are satisfied Multiple Regression Model Si A ti • Six Assumptions –E ( e i ) = 0 – The model is correctly specified, i.e., Y i = 0 + 1 X 1 i + … + n X ni + e i – Corr( X ki , e i ) = 0 for all i , k e i Has a normal distribution –V a r ( e i ) = = a constant – Corr( e i , e j ) = 0 for all i , j • Hence, if these assumptions are satisfied, the estimators b 0 , b 1 , …, b n provide accurate information about the values of the population parameters 0 , 1 , …, n
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Multiple Regression APS 425- Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 3 Example: Wine Prices & Weather The Excel spreadsheet A425 WINE XLSX contains market • The Excel spreadsheet A425_WINE.XLSX contains market prices for a collection of 25 high quality Bordeaux wines (not including Château Petrus or Château Mouton Rothschild, both of which have prices that are often out of line with their “quality”) from different vintages (years). All prices (PRICE) are expressed relative to the prices of the 1961 vintage, which is renowned for being the best during this period. So, for is renowned for being the best during this period. So, for example, the portfolio of 25 1989 vintage Bordeaux wines costs 23% as much as the same wines from the 1961 vintage. Example: Wine Prices & Weather • The data were provided by Professor Orley Ashenfelter of Princeton University, publisher of Liquid Assets , a wine newsletter that provides current auction prices for wines and forecasts quality of new wine vintages [http://www.liquidasset.com]. There are no prices for wines after 1989 because these wines were not mature at the time these data were prepared. One of the goals of this i i t t t th d f f ti th i ( exercise is to construct a method of forecasting the prices (or values) of these wines.
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Multiple Regression APS 425- Advanced Managerial Data Analysis (c) Prof. G. William Schwert, 2001-2010 4 Example: Wine Prices & Weather • The weather variables for the Bordeaux region of France are some of the main determinants of the quality of wine. Harvest rainfall (HARVRAIN in mm) is important because if it rains too much during the harvest season then the wines will be too watery or too diluted. The better vintages have dry harvest periods and are said to be more concentrated.
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This note was uploaded on 03/03/2010 for the course APS 425 taught by Professor Schwert during the Spring '10 term at Rochester.

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a425_mult - Multiple Regression APS 425- Advanced...

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