Multiple%20Linear%20Regression

Multiple%20Linear%20Regression - 4/24/11...

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Click to edit Master subtitle style 4/24/11 Multiple Regression and Correlation
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 4/24/11 The Multiple Regression Model Probabilistic Model yi  =  β 0 +   β 1 x 1 β 2 x 2 + ... + kxki  + ε i        where yi  = a value of the dependent variable,  y 0 = the  y -intercept x 1 i x 2 i , . .. ,  xki  = individual  values of the  independent variables,  x 1 , x 2 , . .. , xk 1,  2 ,. .. ,  k  = the partial regression  coefficients for the independent variables,  x 1 , x 2 , . .. , xk
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 4/24/11 The Multiple Regression Model Sample Regression Equation      =  b 0 +  b 1 x 1 b 2 x 2 + ... + bkxki        where       = the predicted value of the dependent  variable,  y , given the values of  x 1 , x 2 , . .. , xk b 0 = the  y -intercept x 1 i x 2 i , . .. ,  xki  = individual values of the  independent variables,  x 1 , x 2 , . .. , xk b 1,  b 2, . .. ,  bk  = the partial regression coefficients  ˆ y i ˆ y i
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 4/24/11 Assumptions For any given set of values for the  independent variables, the population of  errors will be normally distributed with a  mean of zero and a standard deviation of  σ The standard deviation of errors is the  same regardless of values taken on by the  independent variables. Errors are statistically independent of 
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 4/24/11 Multiple Regression Example Problem 16.11:  The owner of a large  chain of health spas has selected eight of  her smaller clubs for a test in which she  varies the size of the newspaper ad and  the amount of the initiation fee discount  to see how this might affect the number of  prospective members who visit each club 
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Problem 16.11, cont. Using Excel output: Regression Statistics Multiple R 0.846454 R Square 0.71648437 Adjusted R Square 0.60307812 Standard Error 3.374943 Observations 8 ANOVA df SS MS F Significance F Regression 2 143.9237987 71.9618994 6.31785614 0.04279987 Residual 5 56.95120128 11.3902403 Total 7 200.875 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 10.6873018 3.874981744 2.75802635 0.03992803 0.72636035 20.6482432 Ad Column Inches 2.15691421
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Multiple%20Linear%20Regression - 4/24/11...

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