3_multiple_regression - THE MULTIPLE REGRESSION MODEL: A...

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RESEARCH METHODS IN ECONOMICS ECO 4451 Slide # 1 THE MULTIPLE REGRESSION MODEL: A REVIEW y = β 0 + 1 x 1 + 2 x 2 + 3 x 3 + ε Slide # 2 I. INTRODUCTION ´ A. Definition « 1. Previously: simple two-variable model « 2. Now: more realistic « 3 Multiple regression mode Slide # 3 3. Multiple regression model « 4. Multiple IVs (X 1 , X 2 , . . . X k ) INTRODUCTION (CONT.) ´ B. The Model « 1. Y = β 0 X 0 + β 1 X 1 + β 2 X 2 + . . . + β k X k + ε « 2. NOTE: ² a β is intercep Slide # 4 a) 0 is intercept ² b) X 0 is constant term (column of 1's ) « 3. Y = β 0 + β 1 X 1 + β 2 X 2 + . . . + β k X k + ε « 4. coefficients to estimate ² Excluding intercept , K ² Including intercept , K+1 X 0 IS CONSTANT TERM (COLUMN OF 1'S) PROFIT Constant MKTSIZE WINS 33.4 1 3 57 22 1 3 63 16 1 3 46 8.7 1 2 42 Slide # 5 5.4 1 2 44 4.7 1 2 55 -1.5 1 1 35 -2.1 1 1 13 -4 1 1 28 NOTE: NBA market size = 3 for large, 2 for medium, 1 for small PROFIT is in millions of $ WHO USES THIS The fuel economy of engine designs can be predicted by multiple regression models . The Building Owner Management Association of Chicago uses a multiple regression model to predict Slide # 6 downtown commercial rental rates. Their report not only presents the multiple regression coefficients but also the t-ratio of each coefficient. (Source: Professor John McDonald Department of Economics, University of Illinois at Chicago.)
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WHO USES THIS COLORADO STATE HURRICANE FORECAST TEAM SEES INCREASED HURRICANE ACTIVITY Colorado State Press Release: May 23, 2002 FORT COLLINS-After six years that set a record for Atlantic Basin tropical storms and hurricane activity William Gray and Slide # 7 Basin tropical storms and hurricane activity, William Gray and his associates at Colorado State University are calling for a season slightly above the long-term average. For 2002, they forecast twelve named storms, seven hurricanes and three major (Saffir-Simpson category 3-4-5) hurricanes. Gray and co-authors . . . apply statistical regression . . . to make their forecasts. Remember summer of 2004?? INTRODUCTION (CONT.) ´ C. Interpreting each β k Y = β 0 + β 1 X 1 + β 2 X 2 + . . . + β k X k + ε Slide # 9 ´ When X k changes by one of its units, Y changes by β k (in Y's units). . . holding all other Xs fixed INTERPRETING EACH Β K (CONT.) PROFIT = β 0 + β 1 MKTSIZE + β 2 WINS + ε « PROFIT = NBA team annual profit ($M), « MKTSIZE= market size (1=small, 2=medium, 3= large), « WINS= number of wins in one season Slide # 10 PROFIT = -20.8 + .185 WINS + 11.2 + .185 WINS + 11.2 MKTSIZE MKTSIZE ´ As market size increases by one category, profit rises $11,200,000, even if number of wins stay the same. (average rise) INTERPRETING EACH Β K (CONT.) PROFIT = β 0 + β 1 MKTSIZE + β 2 WINS + « PROFIT = NBA team annual profit ($M), « MKTSIZE= market size (1=small, 2=medium, 3= large), « WINS= number of wins in one season Slide # 11 PROFIT = -20.8 + .185 WINS + 11.2 + .185 WINS + 11.2 MKTSIZE MKTSIZE ´ As team wins one more game, profit rises $????, even if ???? stays the same.
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3_multiple_regression - THE MULTIPLE REGRESSION MODEL: A...

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