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Interpretation in Multiple Regression - Duke University

Interpretation in Multiple and Adjusted of parameter combinations of parameter estimates variance-covariance matrix standard errors of combinations standard error for the meanWe will use the final model from last time to illustrate these concepts. Summaries of themodel - least squares estimates with standard errors given below in parentheses: logit proportion log duration I .14 = with 44 degrees of freedomR-squared = :TheR-squaredvaluemeansthat61% ,theadjustedR-squaredisoftenusedtosummar izethefitasit takes into account the the number of variables in the model. Adjusted R-squared = 1 - Mean Square Error /Total Mean SquarewhereMeanSquareErroris 2fromtheregressionmodelandtheTotalmeansq uareisthesamplevarianceoftheresponse(sY2 2isagoodestimateifalltheregressioncoeffi cients are 0).

2 from the regression model and the Total mean square is the sample variance of the response ( sY 2 2 is a good estimate if all the regression coefficients are 0). For this example, Adjusted R-squared = 1 - 0.65^2/ 1.034 = 0.59. Intercept: the intercept in a multiple regression model is the mean for the response when

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