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Unformatted text preview: Click to edit Master subtitle style Professor Thomas R. Professor Thomas R. 11 Multiple Regression Professor Thomas R. Sexton College of Business Stony Brook University Professor Thomas R. Professor Thomas R. 22 Restaurant Example o Find the relationship between annual sales ($000) and n Floor area (in square feet) n Population of the service area (in 000s) n Number of competitors in the service area n Number of other stores in the shopping center n Average per capita income in the service area (in $000) Professor Thomas R. Professor Thomas R. 33 Several Independent Variables o We have one dependent variable, Y . o We have two or more independent variables, X 1, X 2, X 3,, Xk . o We have k +1 measurements on each of n observations: Yi , Xi 1, Xi 2, Xi 3,, Xik . o We want to find the best linear fit to these observations. Professor Thomas R. Professor Thomas R. 44 Multiple Linear Regression Model Professor Thomas R. Professor Thomas R. 55 Estimating the Coefficients o As in simple linear regression, we find the values of b 0, b 1, b 2, b 3,, bk , that minimize the sum of the squared deviations of the data points from the regression Professor Thomas R. Professor Thomas R. 66 The Normal Equations o Differentiate SSE with respect to b 0, b 1, b 2, b 3,, bk and set each derivative equal to zero. o This leads to k +1 linear equations in k +1 unknowns, b 0, b 1, b 2, b 3,, bk . o Solve these for b 0, b 1, b 2, b 3,, bk . o We calculate these values using SX. Professor Thomas R. Professor Thomas R. 77 Using SX Professor Thomas R. Professor Thomas R. 88 SX Output Unweighted Least Squares Linear Regression of SALES Predictor Variables Coefficient Std Error T P VIF Constant 122.653 48.1158 2.55 0.0124 FLOORAREA 0.43055 0.03691 11.67 0.0000 1.3 POPULATN 0.15888 0.10296 1.54 0.1262 3.0 COMPETIT 9.98324 2.99693 3.33 0.0012 1.1 OTHERSTOR 0.00471 1.59316 0.00 0.9976 1.0 PERCAPINC 4.50576 3.51646 1.28 0.2032 2.8 RSquared 0.7643 Resid. Mean Square (MSE) 4222.44 Adjusted RSquared 0.7517 Standard Deviation 64.9803 Source DF SS MS F P Regression 5 1286756 257351 60.95 0.0000 Residual 94 396909 4222 Total 99 1683665 Cases Included 100 Missing Cases 0 Professor Thomas R. Professor Thomas R. 99 Interpreting the Coefficients o The regression coefficient of Xi represents the n average change in Y associated with a n one unit change in Xi n holding all other independent variables constant ....
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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.
 Fall '09
 ThomasSexton
 Business, Sales

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