Lecture 6_regression

Lecture 6_regression - 9/2/2010 Regression Analysis Making...

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9/2/2010 1 Regression Analysis Making Predictions 1 Review • Last week we looked at analyzing the relationship between two variables – Covariance was a measure of how two variables change together – Correlation was a standardized measure to describe the relation between two variables: illustrating both direction and magnitude – Scatterplots provided a visual aid to further illustrate the relation 2 Review • All of the measures previously covered to assess relationship specified no direction between the variables – Made no a priori assumption as to which variable is responsible for the other… just examine whether they were interdependent – Thus the measures were/are symmetric: SP XY =SP YX , R XY =R YX – This is why you always hear that correlation does not mean causation 3
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9/2/2010 2 Introduction to Regression • There are statistical tools to aid in the prediction of one variable from another – Regression analysis attempts to predict one variable from another, thus implicitly assuming a directional relationship – Because regression analysis involves prediction and is directional, the relationship between the variables is no longer symmetric • You cannot interchanging the X and Y variables in analysis and get the same result 4 5 Regression Applications • The owner of a professional baseball team is thinking about increasing ticket prices – S/he would like to know by how much will attendance decrease (if at all) given the price increase? • University admissions committees want to choose the best possible candidates for acceptance into their schools – They would like to predict a student’s college GPA given their high school GPA Strategy of Regression Analysis • The strategy for making predictions requires that you start with a group of individuals on whom you have measured both X and Y • Using the observed data, you develop a regression equation that summarizes the relationship between scores on X and scores on Y 6
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9/2/2010 3 Strategy of Regression Analysis • The regression equation is a probabilistic function based on the conventional equation for a straight line: Y = mx + b – We will use the regression equation in such a way that when a new subject comes along, we can simply measure him/her on X and come up with a predicted value for them on Y – Regression analysis will allow us to compute specific numerical values for the slope and intercept of the equation using the data 7 Strategy of Regression Analysis • The regression equation is probabilistic because there are more than two points in the data, making it impossible to perfectly fit a straight line through all of the data • You will not be able to form a line that
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Lecture 6_regression - 9/2/2010 Regression Analysis Making...

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