Simple Linear Regression

Simple Linear Regression - C22.0103: Statistics for...

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Unformatted text preview: C22.0103: Statistics for Business Control: Regression and Forecasting Hong Luo Section 003, Spring 2009 Tue/Thu/Fri, 11:00 - 12:15pm, Tisch 200 Stern School of Business New York University (SIMPLE) LINEAR REGRESSION Introduction Least Squares Estimators Fitted Value and Residuals R 2 Prediction Other Aspects Introduction Least Squares Estimators Fitted Value and Residuals R 2 Prediction Other Aspects Relationship between Two Variables I Often, we wish to study the relationship between two variables, the purpose of which include: I describe and understand how they are related, I help us make predictions , and I adjust or control a process. e.g. I a countrys per capita health expenditure and life expectancy I daily Pepsi consumption and consumers age I fat content of ice cream, and its sales I movie genre and its box office performance Scatterplot: a useful tool I The first thing to do is to make a scatterplot : a graphical display of each data point using two axes represent the two variables. I The variable that might cause or influence the other is called X , and defines the horizontal axis. I Some common names for X include: Independent Variable, Predictor Variable, Explanatory Variable, Exogenous Variable, Regressor, and Factor I The variable that might respond or be influenced is called Y , and defines the vertical axis. I Some common names for Y are: Dependent Variable, Response Variable, and Endogenous Variable. I Keep in mind (always) that Correlation 6 = Causation Descriptive Relationship I Education and life expectancy. (WHO-HealthStudy.mpj) I DALE: disability adjusted life expectancy I EDUC: average education level of a country I Which do you think should be X , and which should be Y ? I Does more education make people live longer? I Is there a hidden drive for both? like how wealthy the country is Descriptive Relationship I US gasoline market, 1953-2004. Per capita gasoline usage and gasoline price. (GasolineMarket.mpj) I Which do you think should be X , and which should be Y ? I Does this relationship make sense to you? I Remember the demand and supply curves in Micro 101? Note that the graph shows the equilibrium points, not the demand curve nor the supply curve. Increasing income (over time) shifts the demand curve to the right, when holding the supply curve fixed. Descriptive Relationship? I Gross weight of ingested drugs and age of a sample of arrested smugglers at JFK airport. (shonubi.mtp) I Which do you think should be X , and which should be Y ? I What do we learn from the figure? (Not much) Help Predict I Scatterplot of Overseas Box Office and Domestic Box Office for the biggest movies. (Movies.mtp) I Which do you think should be X , and which should be Y ?...
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Simple Linear Regression - C22.0103: Statistics for...

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