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When to use partial regression and regression coefficient?


Asked by Owen Hahn on Dec 10, 2021 FAQ



Partial regression coefficient and regression coefficient When the independent variables are pairwise orthogonal, the effect of each of them in the regression is assessed by computing the slope of the regression between this independent variable and the dependent variable.
In respect to this,
Instead, it is common practice to interpret standardized partial coefficients as effect sizes in multiple regression. These coefficients are the unstandardized partial coefficients from a multiple regression where the outcome and predictors have been transformed to z-scores and the units are standard deviations.
One may also ask, "Partial regression coefficients" are the slope coefficients ($\beta_j$s) in a multiple regression model. By "regression coefficients" (i.e., without the "partial") the author means the slope coefficient in a simple (only one variable) regression model.
Accordingly,
P-values and coefficients in regression analysis work together to tell you which relationships in your model are statistically significant and the nature of those relationships. The coefficients describe the mathematical relationship between each independent variable and the dependent variable.
Thereof,
Multiple linear regression coefficient and partial correlation are directly linked and have the same significance (p-value). Partial r is just another way of standardizing the coefficient, along with beta coefficient (standardized regression coefficient)$^1$.