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regression … Another interpretation of $R^2$ is that by square-rooting, we can find the multiple correlation coefficent $R$. …

This is such a common interpretation that you will often see a continuous variable transformed into two categories (low vs high blood pressure) to make this interpretation easier. … Overall, economists tend to look for strong interpretation of coefficients in their models. …

If you had a multiple logistic regression, there would be additional covariates listed below these, but the interpretation of the output would be the same. … (If you are not sufficiently familiar with log odds, it may help you to read my answer here: interpretation of simple predictions to odds ratios in logistic regression.) …

more features to choose from; some of them are better than others), but that also makes each tree more highly correlated with each other tree, somewhat mitigating the diversifying effect of estimating multiple … A regression is more easily interpreted, but interpretation might not be the most important goal for some tasks. …

), but have multiple meanings in different context. … and scale of the regression coefficients between marginal model and random-effects model would be different for nonlinear models (e.g. logistic regression). …

In the following I am referring to this PDF document: "Multiple Regression Analysis: Estimation", which has a section on "A 'Partialling Out' Interpretation of Multiple Regression" (p. 83f.). … weight for lmEC.resid (see column Estimate, $\beta_{lmEC.resid}=0.50$) in this simple regression is equal to the multiple regression weight for covariate, which also is $0.50$ (see @EpiGrad's answer …

(This is a somewhat free interpretation of the "possibility to see a value equal or greater than the one observed under the null hypothesis" and it is not meant to be a text-book definition.) … Clearly when ones starts adding multiple covariate in his regression model, a simple one-way ANOVA does not have a direct equivalence. …

Application to Multiple Regression This geometric process has a direct multiple regression interpretation, because columns of numbers act exactly like geometric vectors. … Fitting multiple regression coefficients is nothing more than projecting ("matching") vectors. …

All that follows is straightforward to extend to the multiple regression setting. … Thus this model is not the same as a bivariate multiple regression with four parameters. …

I went through stats.statexchange posts 1 and 2 that explain (a) difference between multiple and multivariate regression and (b) interpretation of multivariate regression results, but I am not able to … With respect to 1. and 2., can we compare the analysis when we do three univariate multiple regression versus one multivariate multiple regression? How to justify one over another? …

PCA: rotation/interpretation of components - sometimes (PCA is not enough realistic as a latent-traits model). FA: rotation/interpretation of factors - routinely. PCA: data reduction method only. … Similarly as in regression the coefficients are the coordinates, on the predictors, both of the dependent variable(s) and of the prediction(s) (See pic under "Multiple Regression", and here, too), in FA …

Additionally, overadjustment can cause multiple forms of bias in analyses. … You are right that the interpretation of effects from penalized regression are not easily interpreted for a non-statistical community, unlike estimates from an OLS, where 95% CIs and coefficient estimates …

GLMs include multiple regression but generalize in several ways: 1) the conditional distribution of the response (dependent variable) is from the exponential family, which includes the Poisson, binomial … Much of your multiple linear regression intuition will carry over if you keep the differences in mind. …

Kleiber/Zeileis, Applied Econometrics with R (2008, p. 59) claim it's "Theil's adjusted R-squared" and don't say exactly how its interpretation varies from the multiple R-squared. … I also looked at a related question on Stack Overflow (What is the difference between Multiple R-squared and Adjusted R-squared in a single-variate least squares regression?) …

In fact, there are several nice and convenient properties of linear regression that depend on there being a proper (unpenalized) intercept term. … (R)^2 = \text{cor}^2(\hat {\mathbf y}, \mathbf y) = \frac{\|\hat{\mathbf y}\|^2}{\|\mathbf y\|^2} = R^2,$$ see e.g. this thread for an explanation: Geometric interpretation of multiple correlation coefficient …