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

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

Pseudoreplication & mixed effects with highly unbalanced dataset

I have a dataset with ~250 data points. When I regress Y on X1 and X2, X1 is a significant predictor of Y. However, about half the 250 points are pseudoreplicated; they come from locations with >1 observation and are not strictly independent. Normally, I would include a random slope for X1 and X2, but … Read more

Is there a multiple regression model with both percentage and unit changes in YY?

In a standard linear model, Y=β0+β1X1+β2X2, a unit increase in X1 leads to a β1 increase in Y (likewise for X2). In a log-level model, ln(Y)=β0+β1X1+β2X2, a unit increase in X1 leads to an exp(β1)×100% increase in Y (likewise for X2). Question: Is it possible to have a model where a unit increase in X1 … Read more