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MultipleRegression08B

# MultipleRegression08B - Regression with multiple...

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Regression with multiple independent variables ESM 206 Jan 10, 2008

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Multiple independent variables Dependent variable may be caused by more than one independent variable pH affected by both SO4 and NO3 Statistical model: β 0 : intercept (predicted value of y when both x and z are zero) β 1 : partial effect of x on y (effect of x on y while ‘controlling for’ z ) β 2 : partial effect of z on y (effect of z on y while ‘controlling for’ x ) 0 1 2 i i i i y x z β β β ε = + + +
pH in Norwegian Lakes In Excel, the independent variables (“X Range”) need to be in adjacent columns

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Regression Statistics Multiple R 0.487717 R Square 0.237868 Adjusted R Square 0.198785 Standard Error 0.516763 Observations 42 ANOVA df SS MS F Significance F Regression 2 3.250529 1.625264 6.086128 0.005007 Residual 39 10.41472 0.267044 Total 41 13.66525 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 5.721299 0.156296 36.60565 8.2E-32 5.405162 6.037437 SO4.1981 -0.00437 0.051012 -0.08565 0.932181 -0.10755 0.098812
Some questions Is pH~SO4+NO3 a “better” model than pH~SO4?

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MultipleRegression08B - Regression with multiple...

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