07.whatisregression

# 07.whatisregression - Lecture 7 What is Regression Analysis...

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Lecture 7:  What is Regression Analysis? BUEC 333  Summer 2009 Simon Woodcock

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To this point we’ve focused on a single random variable, X. We’ve talked about population quantities (e.g., μ and σ 2 ). We’ve discussed how to compute sample statistics to estimate population quantities, the properties of estimators (e.g., bias and efficiency), and how to test hypotheses about the population. Things get much more interesting when we consider two or more random variables. we care about the relationship between variables we can use one or more variables to predict a variable of interest, etc. We can get a lot of mileage out of studying the conditional expectation of a variable of interest ( Y ) given another variable (or group of variables) X. That is, studying E( Y|X ). Recall that another name for E( Y|X ) is the regression function . We’ll spend the rest of the semester talking about regression analysis, which is a very powerful tool for analyzing economic data. Regression analysis is based on E( Y|X ).
What is Regression Analysis? Regression analysis is a very common statistical/econometric technique We use it to measure/explain relationships between economic variables Example: casual observation will reveal that more educated individuals tend to have higher incomes. regression methods can be used to measure the rate of return of an extra year of education or, use regression methods to estimate the relationship between income and education, gender, labour market experience, etc. Example: economic theory tells us that if the price of a good increases, individuals will consume less of it. that is, demand curves slope down but economic theory doesn’t predict how big the change in consumption will be for a given price change we can use regression analysis to measure how much individuals reduce their consumption in response to a price increase (i.e., we can estimate the elasticity of demand)

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The Regression Model The goal of regression analysis is to explain the value of one variable of interest (the dependent variable ) as a function of the values of other variables (the independent or explanatory variables ) Usually, the dependent variable is denoted Y The independent variables are X 1 , X 2 , X 3 etc. Sometimes we say we want to explain “movement” in Y as a function of “movement” in the X variables. That is, how much does Y change when the X variables change? In this context, a better word for “movement” is variation . We use an equation (sometimes more than one) to specify the
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## This note was uploaded on 06/21/2009 for the course BUEC BUEC333 taught by Professor Simonwoodcock during the Summer '09 term at Simon Fraser.

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07.whatisregression - Lecture 7 What is Regression Analysis...

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