Chapter 4 - Basic estimation techniques. After completing this unit, you should be able to: Set up a regression equation that can be estimated using a computerized regression routine, interpret and understand how to use the computer output to investigate problems that are of interest to managers of a firm, specify a relation or model between a dependent variable and the appropriate independent variable(s) that can be estimated using regression techniques,. | Chapter 4: Basic Estimation Techniques McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. Basic Estimation Parameters The coefficients in an equation that determine the exact mathematical relation among the variables Parameter estimation The process of finding estimates of the numerical values of the parameters of an equation Regression Analysis Regression analysis A statistical technique for estimating the parameters of an equation and testing for statistical significance Intercept parameter (a) gives value of Y where regression line crosses Y-axis (value of Y when X is zero) Slope parameter (b) gives the change in Y associated with a one-unit change in X: Simple Linear Regression Simple linear regression model relates dependent variable Y to one independent (or explanatory) variable X Random Effect Firm expects $10,000 in sales from each agency plus an additional $5 in sales from each additional $1 of advertising. Simple Linear | Chapter 4: Basic Estimation Techniques McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. Basic Estimation Parameters The coefficients in an equation that determine the exact mathematical relation among the variables Parameter estimation The process of finding estimates of the numerical values of the parameters of an equation Regression Analysis Regression analysis A statistical technique for estimating the parameters of an equation and testing for statistical significance Intercept parameter (a) gives value of Y where regression line crosses Y-axis (value of Y when X is zero) Slope parameter (b) gives the change in Y associated with a one-unit change in X: Simple Linear Regression Simple linear regression model relates dependent variable Y to one independent (or explanatory) variable X Random Effect Firm expects $10,000 in sales from each agency plus an additional $5 in sales from each additional $1 of advertising. Simple Linear Regression Parameter estimates are obtained by choosing values of a & b that minimize the sum of squared residuals The residual is the difference between the actual and fitted values of Y: Yi – Ŷi The sample regression line is an estimate of the true regression line Sample Data Time series data – values taken by a variable over time Cross sectional data – values for multiple occurrences of a variable at a point in time Sample Regression Line (Figure ) A 0 8,000 2,000 10,000 4,000 6,000 10,000 20,000 30,000 40,000 50,000 60,000 70,000 Advertising expenditures (dollars) Sales (dollars) S • • • • • • • Sample regression line Ŝi = 11,573 + Ŝi = 46,376 ei Si = 60,000 Population regression line – true regression line Sample regression line – estimate of the true regression line The Method of Least Squares Statistical Output - Excel Y= + Three Kinds of Correlation Unbiased Estimators The distribution of values the estimates might take is centered around the
