Coefficient of Determination

By F. Pyrczak, Deborah M. Oh. Making Sense of Statistics, 2018

200 citations recorded by the source corpus.

As with simple regression, in the multiple linear regression model, we can interpret ! SYY " RSS SYY as the fraction of the variability in Y explained by including the terms u 1 , u 2 , … , u k-1 in the mean function (as compared to the constant mean function). In the multiple regression context, ! SYY " RSS SYY is denoted as R 2 (with capital R). R 2 is called the coefficient of (multiple) determination or (misleadingly) the squared multiple correlation. • R alone (unsquared) has no meaning in multiple regression. • By convention, we use small r for the sample correlation in simple regression. • In multiple regression, we can talk about correlation between two variables (i.e,, just two at once). • In particular, in multiple regression, r ij is often used to denote the sample correlation coefficient between terms u i and u j. • R 2 is sometimes used for comparing models. But caution is needed: o It only makes sense to use for comparing models that are in the same units (e.g., submodels of the same full model). o A submodel of a model will always have a smaller R 2 than the larger model. o As discussed above and below, many other considerations should be taken to account in selecting a model.

Subfields: Statistics and Probability, Surgery

View Paper: https://www.semanticscholar.org/paper/5b1a0e6dd248e67f33d85f076513ab8a193daa06

Citations in the corpus

• The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation (2021, unknown): “…of studies about it has populated the scienti fi c literature of the last century, from general references detailing de fi nition and characteristics ( Di Bucchianico, 2008 ; Barrett, 2000 ; Brown, 2009 ; Barrett, 1974 ), to more re fi ned interpretative works ( Saunders, Russell & Crabb, 2012 ;…”