Bivariate regression Student version

Bivariate regression Student version - ECO 6416 Bivariate...

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1 ECO 6416 Bivariate Regression ± Statistical model to study relationship between dependent variable and one or more independent variables. ± Flexible modeling approach ± Widely used statistical method in business & economics ± Can do anything that analysis of variance can do, plus more ± Illustrative example ± Framework and regression model ± Estimation ± Inferenc Inference ± Simple regression ± Examples ± Transition to multiple regression ± To study the influence of advertising on profits, the Boston Celtics compiled annual data on Ad expenditures in $100,000s and profits in millions of dollars . The sample (for each of the Slide #4 last five years) is: ± Year 1 2 3 4 5 ± Ad Expenditures (x) 2 3 4.5 5.5 7 ± Profit (y) 3 6 8 10 11 ± Ad Expenditures (x) 2 3 4.5 5.5 7 ± Profit (y) 3 6 8 10 11 ± The Celtics need answers to these question Slide #5 The Celtics need answers to these questions ± 1. Does advertising increase profit? ± 2. How much does another $100,000 spent on advertising increase profit? ± 3. What will our profit be if we spend $800,000 on advertising? ± 4. How much will we need to spend on ads to generate $12,000,000 in profit? Slide #6
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2 ± Surprisingly, one statistical decision-making tool can provide answers to all of these questions -- and more. ± The tool is called regression analysis . Slide #7 ± Note: You would never really use a regression with only five observations! ± Regression analysis is a statistical technique ± A ttempts to "explain" movements in one variable, the dependent variable . . . Slide #8 ± as function of movements in a set of other variables, the independent variables . . . ± through the quantification of one or more equations Slide #9 equations. Northwestern Memorial Hospital, which has the largest birthing facility in the Midwest, uses a simple regression model to forecast delivery volume based on previous delivery volumes. Slide #10 (Source: Jerry Lassa, Northwestern Memorial Hospital, Chicago, IL.) IRI, the largest market research firm in the United States uses simple regression on adjusted weekly sales data to determine baseline sales when there is no special promotion. (Source: Doug Slide #11 Honnold, IRI, Inc., Chicago, IL.) 01 value of dependent variable for population element i. X value of independent variable for population ii i i i YX u Y β = ++ = = element i. , population parameters governing X, Y relationship. a random i u ββ = = "error" for population element i.
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3 01 , vary across population elements and are observable. varies across population elements, but is ii i YX u u β =+ + varies across population elements, but is unobservable. , are the same for all population elements but are unobservable. i ββ Our goal is to make inferences about these parameters based on a sample drawn from the population. ± Disturbance or error term needed in model for combination of four reasons ² 1. variables omitted from model Slide #14 ² 2. captures effects of nonlinearities in model ² 3. errors in measuring X and Y ² 4. random effects.
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This note was uploaded on 11/15/2010 for the course ECO 6416 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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Bivariate regression Student version - ECO 6416 Bivariate...

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