Some users of regression models may think that the only fitted value comparisons available to them are the ones that correspond to regression coefficients. 8 from 10 leaves b 2, which represents the change in the fitted value of Y for a one-unit increase in X 2 with X 1 held constant. 8 from 9 leaves b 1, which represents the change in the fitted value of Y for a one-unit increase in X 1 with X 2 held constant. 2, and Y′ X+1 the fitted value of Y when X + 1 is plugged into Eq. Starting with the single predictor model, let Y′ X be the fitted value of Y when some value of X is plugged into Eq. 3 and 4), letting j range from 1 to p, b j gives the change in the fitted value of Y for a one-unit increase in X j while controlling for all of the other explanatory variables in the model (i.e., while holding them all constant).Īs the phrase “change in the fitted value of Y” suggests, the b-coefficients from the single predictor model and the multiple regression model with no higher order terms represent the difference between two fitted values of Y. For the multiple linear regression model with first-order terms only (Eqs. 1 and 2), b gives the change in the fitted value of Y for a one-unit increase in X.
![spss code in unianova observed power spss code in unianova observed power](https://static.filehorse.com/screenshots/office-and-business-tools/ibm-spss-statistics-screenshot-04.png)
For the simple linear regression model (Eqs. In any regression model, the constant a gives the fitted value of Y when all explanatory variables are equal to 0. With Y′ once again representing the fitted value of Y. The output from the macros includes the standard error of the difference between the two fitted values, a 95% confidence interval for the difference, and a corresponding statistical test with its p-value. The !OLScomp and !MLEcomp macros are for use with models fitted via ordinary least squares and maximum likelihood estimation, respectively.
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We describe two SPSS macros that implement a matrix algebra method for comparing any two fitted values from a regression model.
#SPSS CODE IN UNIANOVA OBSERVED POWER SOFTWARE#
For many fitted value comparisons that are not captured by any of the regression coefficients, common statistical software packages do not provide the standard errors needed to compute confidence intervals or carry out statistical tests-particularly in more complex models that include interactions, polynomial terms, or regression splines. But the coefficients represent only a fraction of the possible fitted value comparisons that might be of interest to researchers. Therefore, each regression coefficient represents the difference between two fitted values of Y.
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In regression models with first-order terms only, the coefficient for a given variable is typically interpreted as the change in the fitted value of Y for a one-unit increase in that variable, with all other variables held constant.