Introduction to Statistical Methods in Pathology by Amir Momeni Matthew Pincus & Jenny Libien

Author:Amir Momeni, Matthew Pincus & Jenny Libien
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Assessing Utility of the Fitted Model

The next question to ask is how good the predictor function fits the observed data. Assessing the goodness of fit is done using the R 2 statistics. The “R-squared ” is also known as the “coefficient of determination.” This statistic determines the proportion of the variability in the dependent variable that is explained from the independent variable(s). For simple linear regressions with intercept, the r-squared statistic is the square of the correlation coefficient (r 2). For multiple correlations, the R 2 is the sum of all correlation coefficients adjusted for correlations between the input variables. R 2 statistic can have values between 0 and 1. As the statistic nears one, the prediction power of the model increases, with 1 being the perfect score (meaning that all the variations in the response variable are explained by the input variable).

The calculation of R-squared is done through calculation of the “residual sum of squares” (SSresidual) and “total sum of squares” (SStotal) as discussed in Chap. 4, Eq. 4.​19:

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