## Coefficient of partial determination versus R2R^2

In Applied Linear Statistical Models (Kutner, Nachtsheim, Neter, Li) one reads the following on the coefficient of partial determination: A coefficient of partial determination can be interpreted as a coefficient of simple determination. Consider a multiple regression model witht two X variables. Suppose we regress Y on X2 and obtain the residuals: ei(Y|X2)=Yi−ˆYi(X2) where ˆYi(X2) … Read more

## Standard error of the mean of several values of y predicted from a multiple regression

I have a multiple regression equation that predicts a trait of interest (\$y\$) from two measured traits (\$x_1\$ and \$x_2\$). I want to measure \$x_1\$ and \$x_2\$ for \$k\$ individuals of a certain plant species, and use this regression to estimate the mean and standard error of \$y\$ for this species. I know the standard … Read more

## Log and inverse Data transformation in Linear regression model

I am studying behaviour of particulate matters(pm10) concentration in respose to change in rain and tempretaure. my data was not normaly distributed so i have to transform data I did log transformation and inverse transformation.The Adjusted R-squared for log transformation is :0.07918 and Adjusted R-squared for inverse transform is :0.1002.Now according to rule i must … Read more

## Rescaling standardised parameters fitted through gradient descent

As a learning exercise, I have been implementing multiple linear regression from scratch using gradient descent to fit the parameters. Following the conventional approach to the algorithm, I have managed to dramatically speed up the convergence by standardising all of the features such that they have mean 0 and standard deviation 1 according to the … Read more

## Does entry-order in stepwise regression matter even if there is no colinearity between predictors?

I’m not sure I understand stepwise multiple regression, so I’ll first try to share my understanding of it: We use several IV to predict one DV. In forward selection, we first enter the IV that increases R2 the most. Then we enter the IV that increases R2 the second most etc., and we do so … Read more

## Multiple Regression, ‘Predict’ Independent variable?

I read that it is possible to use the multiple regression, and to interpret that we can predict the dependent variable using the historical independent variables. Y(t+1) = aX_1(t) + bX_2(t) + e(t) Is it also possible to use the multiple regression in this case?? Y(t-1) = aX_1(t) + bX_2(t) + e(t) Can I interpret … Read more

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## Best regression method for ratio of two binomial processes as response.

I have a situation where I have two binomial responses (A out of X and B out of Y). I have a binary categorical predictor C with a multilevel categorical covariate D. I basically want to find a way of doing the following regression (A/X / B/Y) ~ C + D while ideally not losing … Read more

## How to calculate Cohen’s effect size f squared for multiple linear regression?

For hypothesis testing, do I need to look at R2 of the model (multiple linear regression) when I want to calculate Cohen’s effect size F2 (F2= R2(1−R2))? I heard that P-value is not sufficient for hypothesis testing alone. Answer AttributionSource : Link , Question Author : Kamal Asasi , Answer Author : Community

## Quantifying uncertainty of regression models

I have built various different types of regression model (linear model, non-linear model, generalized linear model), and wish to determine the error/uncertainty of each one in order to compare them. I have built the three models in R, and understand that I am able to use the predict function to obtain a confidence interval around … Read more

## scale of one predictor affects significance of another

I have often read that predictors can or should be transformed to ease interpretation of the slope or intercept, or to standardize the coefficients. With this in mind, I attempted to rescale year in a data set, and met with unexpected behavior. The following reproducible example stemmed from data including a year effect and many … Read more