214 views

### standardised random variable least square regression $X$ against $Y$, $Y$ against $X$ [duplicate]

Let $X$ and $Y$ be mean 0 and variance 1 random variables such that we choose $\alpha$ and $\beta$ to minimise $$\mathbb{E}(X-\beta Y)^2$$ and $$\mathbb{E}(Y-\alpha X)^2$$ after not so difficult ...
45 views

### Are the statistical results of a linear regression affected if I swap IV and DV with each other? [duplicate]

Context: The linear regression Y = mX + c Intuitively, it seems to me that swapping the independent variable and dependent variables won't change the test statistic for the significance of the ...
48 views

### Inverse linear model doesn't seem exact inverse [duplicate]

I'm dealing with a quantity that diminishes over time from 100% to 0%. I'm trying to plot the values, a lm abline, and large indicative points where the graph intersects ...
27 views

### Basic Linear Regression in R: Dependent and Independent Variables [duplicate]

This is probably a very basic question but I cannot find the answer after experimenting a lot with it. I am using the Davis dataset from https://vincentarelbundock.github.io/Rdatasets/datasets.html (...
11 views

29k views

### Choosing between LM and GLM for a log-transformed response variable

I'm trying to understand the philosophy behind using a Generalized Linear Model (GLM) vs a Linear Model (LM). I've created an example data set below where: $$\log(y) = x + \varepsilon$$ The ...
16k views

### Why do we say the outcome variable “is regressed on” the predictor(s)?

Is there some intuitive explanation for this terminology? Why is it this way, and not the predictor(s) being regressed on the outcome? Ideally I'm hoping that a proper explanation of why this ...