It states that the estimated value of the dependent variable for a given value of t (Ŷ) is equal to the estimated intercept (Ý) plus the estimated slope ( ) times the value of the independent variable for a given value of t (X t). Equation 4–3 is the ordinary least squares estimate of Equation 4–1'. Equation 4–2' defines the error term as the difference between the observed value of the dependent variable (Y t) and the value of the dependent variable that is predicted by the estimated linear equation ( t)Įquations 4–3 to 4–5 define the components of the ordinary least squares model for simple linear regression. As a consequence, it is referred to as the random error in the equation. This third variable accounts for the fact that the dependent variable will not generally be exactly equal to the value that results from the calculation of a + bX for specific values of a, b, and X. This equation can be written in statistical form as Equation 4–1' by adding a subscript index (t) to identify specific observations and by adding a third variable (e t) that represents the influence of random factors on the dependent variable. It defines a straight line relationship between a dependent variable (Y) and an independent variable (X) in terms of the Y intercept (a) and the slope (b) of the line. The Appendix to this Study Guide includes information about these programs and sample problems that demonstrate their use.Įquation 4–1 is a linear function. The Regression Analysis Calculator, the Descriptive Statistics Calculator, and the Data Manager programs in Analytical Business Calculator are designed to perform these types of calculations. The problems in this chapter require calculations that involve statistical analysis. Consequently, it is crucial that you approach this chapter with the goal of developing a thorough knowledge of regression procedures. Regression analysis is an essential tool of managerial economics, not only for the estimation of demand, but for other applications as well. Primary among these is regression analysis, a statistical technique that is used to estimate the parameters of mathematical functions from empirical data. After working through this chapter, you should be conversant with the methods that can be applied to the estimation of demand.
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