multiregress1 - Multiple Regression Multiple Regression...

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Multiple Regression Multiple Regression Model Least Squares Method Multiple Coefficient of Determination Model Assumptions Testing for Significance
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The equation that describes how the dependent variable y is related to the independent variables x 1 , x 2 , . . . x p and an error term is called the multiple regression model . Multiple Regression Model y = b 0 + 1 x 1 + 2 x 2 + . . . + p x p + e where 0 , 1 , 2 , . . . , p are the parameters , and is a random variable called the error term
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The equation that describes how the mean value of y is related to x 1 , x 2 , . . . x p is the deterministic portion of the model Multiple Regression Equation E ( y ) = b 0 + 1 x 1 + 2 x 2 + . . . + p x p Remember in simple regression, the equation that described how the mean value of y is related to x is the deterministic portion of the model E ( y ) = 0 + 1 x
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Assumptions About the Error Term e The error is a random variable with mean of zero. The variance of , denoted by 2 , is the same for all values of the independent variables. The values of are independent. The error is a normally distributed random variable
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A simple random sample is used to compute sample statistics b 0 , b 1 , b 2 , . . . , b p that are used as the point estimators of the parameters b 0 , 1 , 2 , . . . , p . Estimated Multiple Regression Equation ^ y = b 0 + b 1 x 1 + b 2 x 2 + . . . + b p x p The estimated multiple regression equation is:
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Estimation Process Multiple Regression Model E ( y ) = b 0 + 1 x 1 + 2 x 2 +. . .+ p x p + e Multiple Regression Equation E ( y ) = 0 + 1 x 1 + 2 x 2 +. . .+ p x p Unknown parameters are 0 , 1 , 2 , . . . , p Sample Data: x 1 x 2 . . . x p y . . . . . . . . 0 1 1 2 2 ˆ ... pp y b b x b x b x Estimated Multiple Regression Equation Sample statistics are b 0 , b 1 , b 2 , . . . , b p b 0 , b 1 , b 2 , . . . , b p provide estimates of 0 , 1 , 2 , . . . , p
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Least Squares Method Least Squares method Computation of Coefficient Values The formulas for the regression coefficients b 0 , b 1 , b 2 , . . . b p involve the use of matrix algebra.
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This note was uploaded on 09/28/2011 for the course STAT METHO 33:623:385 taught by Professor Faridalizadeh during the Spring '11 term at Rutgers.

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multiregress1 - Multiple Regression Multiple Regression...

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