This preview shows page 1. Sign up to view the full content.
Unformatted text preview: fine X= lg(Z), Z2, or eZ. Note that Y = α + X β + u is not a linear regression model. Quiz: Are the following linear regressions? a. log(Y ) = α + β (
b. Y = 1
+u α +βX c. Y = α + eβ X + u 1
)+u X α and β , and hence the true regression line is unknown. 3 Our Objective: given a sample of data (from the population) on Y and X, we try to estimate this unknown true regression line, i.e., to estimate α and β . Once we estimate α and β , we can see how X can affect Y or predict Y using X. Examples: Y=housing price, X=housing characteristics (number of rooms, lot size etc), or local amenities, such as pollution level, weather etc. Y=wage, X=education level Y= unemployment rate X= GDP growth rate Notational convention 1: Use X, Y, Z etc capital letters to denote r.v.’s, and use x, y, z etc small letters to denote specific values, or realizations, or observations. Further, we use subscript to denote different observations. Assume that we have a sample of n observations ( yi , xi ), for i = 1, 2,..., n , on Y and X, then we can write yi = α + β xi + ui , for i = 1,...
View Full Document