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Unformatted text preview: lecture 23, Linear Regression I Simple Linear Regression Model Form of The Simple Linear Regression Model Assumptions Least Square Estimates Standard Error lecture 23, Linear Regression I Outline 1 Simple Linear Regression Model Form of The Simple Linear Regression Model Assumptions 2 Least Square Estimates 3 Standard Error lecture 23, Linear Regression I Simple Linear Regression Model Form of The Simple Linear Regression Model Assumptions Least Square Estimates Standard Error lecture 23, Linear Regression I Motivation • Managers often make decisions by studying the relationship between variables, and improvements can often be made by understanding how changes in one or more variables affect the output • Regression analysis is a statistical technique in which we use observed data to relate a variable of interest (dependent variable or response), to one or more variables (independent variables or predictors). • The objective is to build a regression model , or prediction equation, that can be used to describe, predict, and control the dependent variable on the basis of the independent variables. lecture 23, Linear Regression I Simple Linear Regression Model Form of The Simple Linear Regression Model Assumptions Least Square Estimates Standard Error lecture 23, Linear Regression I Simple Linear Regression Model An Example of Two Dimensional Data, Background • Natural gas companies purchase natural gas from marketers and periodically (perhaps daily, weekly, or monthly) place orders for natural gas to be transmitted to their cities. • To place an order (nomination), a natural gas company makes its best prediction of the city’s natural gas needs for that period. Then the company instructs its marketer(s) to deliver this amount of gas to its pipeline transmission system. • A natural gas company is charged a transmission fine if it substantially undernominates or overnominates natural gas. Natural gas companies want to predict their cities’ natural gas needs with reasonable accuracy. lecture 23, Linear Regression I Simple Linear Regression Model Form of The Simple Linear Regression Model Assumptions Least Square Estimates Standard Error lecture 23, Linear Regression I Simple Linear Regression Model An Example of Two Dimensional Data • Experience suggests that weekly fuel consumption ( y , in millions of cubic feet (MMcf)) depends on the (average hourly) temperature ( x , in degrees Fahrenheit). • Data is collected and we hope to find the relationship between the two variables, which hopefully can be helpful in making predictions. Week Temperature x (deg F) Fuel Consumption y (MMcf) 1 28.0 12.4 2 28.0 11.7 3 32.5 12.4 4 39.0 10.8 5 45.9 9.4 6 57.8 9.5 7 58.1 8.0 8 62.5 7.5 lecture 23, Linear Regression I Simple Linear Regression Model Form of The Simple Linear Regression Model Assumptions Least Square Estimates Standard Error lecture 23, Linear Regression I Simple Linear Regression Model A Graphical Tool: Scatter Plot ● ● ● ● ● ● ● ● 20 30 40 50 60 70 6 8 10 12 14 TEMP FUEL lecture 23,...
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 Fall '09
 AnthonyChan
 Linear Regression, Regression Analysis, Errors and residuals in statistics, linear regression model, The Simple Linear Regression

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