Behaviour of Statistical
Measures of Goodness of Fit Subject to Variation in
Sample Size and Number of Regressors
Nirmali Borah
Abstract
R² (Adj. R²) is the most widely pursued statistical measure in judging the goodness of the fit of the model as well as in explaining the total variation of the explained variable via explanatory variables, especially in applied scientific fields. As regards the application of R² (Adj. R²) there is a variation of its interpretation across linear models with and without Intercept along with equally spaced and unequally spaced sample observations. In this paper, an attempt has been made to see the behaviour of R² (Adj. R²) on varying sample sizes from small to moderate. What has been observed in this paper is that R² is relatively large for a small sample compared to a moderate (and large) sample. The results obtained are found to corroborate those of the prominent work by Gerald J. Hahn and Others. In addition, this paper aims to study the behaviour of R² (Adj. R²) on varying numbers of regressors. The inferences are that R² (Adj.R²) is an increasing function of regressors.
Keywords: Coefficient of determination, adjusted regression coefficient of determination, Regression analysis.
