Goodness-of-fit: Desirable Properties of a Regression Model

In interpreting the quality of a regression model, the following aspects are taken into consideration.

High adjusted R²: R² is proportion of variation in the dependent variable explained by the independent variables. R_adj² adjusts for number of explanatory terms in a model relative to the number of data points (i.e., df associated with the sums of squares).

Significant F-statistic: The null hypothesis that all coefficients (b₁, b₂ …) are zero can be conclusively rejected.

Significant t-statistics: The individual coefficients are statistically significant.

Residuals are random, normally distributed, with mean 0, and their variance does not vary significantly, over the values of the independent variables.