Chapter 12 Bivariate Regression

# Chapter 12 Bivariate Regression - Click to edit Master...

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Unformatted text preview: Click to edit Master subtitle style Professor Thomas R. Professor Thomas R. 11 Bivariate Regression Professor Thomas R. Sexton College of Business Stony Brook University Professor Thomas R. Professor Thomas R. 22 The New Restaurant How large should a new restaurant be? Your company currently has n = 100 restaurants. You have data for each restaurant: floor area (in square feet) total sales (\$000) for last year What is the relationship between floor area and total sales? We begin by examining the data in a scatter Professor Thomas R. Professor Thomas R. 33 Scatter Plot in SX Professor Thomas R. Professor Thomas R. 44 Finding a Relationship Regression analysis examines the relationship between two (or more) continuous random variables. Simple linear regression looks for a linear relationship between 2 variables. Professor Thomas R. Professor Thomas R. 55 The Data We make n pairs of observations on n items ( Xi , Yi ), i =1, 2, , n . Y is called the dependent variable (sales). X is called the independent variable (floor area). We hypothesize that Y is a linear function of X . Professor Thomas R. Professor Thomas R. 66 The Linear Regression Model slope estimated the is intercept- estimated the is ..., , 2 , 1 n observatio for term error random the is slope the is intercept- the is ..., , 2 , 1 1 1 1 1 b Y b n i X b b Y i Y n i X Y i i i i i i = + = = + + = Professor Thomas R. Professor Thomas R. 77 The Estimation Problem [ ] ( 29 [ ] = = +- =- = n i i i n i i i b b X b b Y Y Y SSE b b b b 1 2 1 1 2 , 1 1 Minimize to and Choose (OLS) Squares Least Ordinary : fit" best " Define ? fit" best " the provide and of s What value 1 Professor Thomas R. Professor Thomas R. 88 Finding b 0 and b 1 Normal Equations Professor Thomas R. Professor Thomas R. 99 Solve the Normal Equations Professor Thomas R. Professor Thomas R. 1010 Using SX for Linear Professor Thomas R. Professor Thomas R. 1111 Unweighted Least Squares Linear Regression of SALES Predictor Variables Coefficient Std Error T P Constant 55.9687 36.2409 1.54 0.1257 FLOORAREA 0.52956 0.03693 14.34 0.0000 R-Squared 0.6773 Resid. Mean Square (MSE) 5544.77 Adjusted R-Squared 0.6740 Standard Deviation 74.4632 Source DF SS MS F P Regression 1 1140278 1140278 205.65 0.0000 Residual 98 543388 5545 Total 99 1683665 Cases Included 100 Missing Cases 0 Coefficient Estimates in SX Professor Thomas R. Professor Thomas R. 1212 Scatter Plot with Regression Professor Thomas R. Professor Thomas R....
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## This note was uploaded on 09/17/2009 for the course BUS 215 taught by Professor Thomassexton during the Fall '09 term at SUNY Stony Brook.

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Chapter 12 Bivariate Regression - Click to edit Master...

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