# Tag Info

### correlation range between y and two variables x1 and x2

Let's assume, without loss of generality, all data are standardised into z-scores. The data generating equation for y can then be written as: $y = b_1*x_1 + b_2*x_2 + e$ using more common notation. ...
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1 vote

### Regression using unordered combinations, sign of predictor depends on order

This doesn't strike me as hopeless or deeply flawed. I however think you'd want to account for the pairwise structure of your data. I.e. any error/noise in measuring $f_i$ is going to affect all pairs ...
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### Standard error of estimated coefficient

To complete the answer by @MaartenBuis, Standard deviation is the measure of variability of a sample with individual values (observations). Standard error is the measure of variability of a sample ...
Accepted

### Why are error properties in linear regression assumptions if they are true by construction?

Distinctions First let us differentiate two levels. The true model. We can also call this the data generating process or a structural model. It is structural in the sense that it reflects how each ...
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### Why are error properties in linear regression assumptions if they are true by construction?

Why are error properties in linear regression assumptions if they are true by construction? $E(\epsilon) = 0$ $cov(X, \epsilon) = 0$ ... However, both of these are just results of fitting a least ...
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1 vote

### Linear Regression on data with seasonality

You could try linear regression with three explanatory variables, time, sin(c$\times$time) and cos(c$\times$time) where c is a constant chosen to correctly represent the period of the seasonality. ...
Accepted

### What's the justification for comparing two separate models built on subsets of data versus using one model that uses the whole dataset?

Running two models lets you compare the model for the two subsets -- e.g. in your example, control and disease subsets. Also, when you have specifically "control" and "disease" ...
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### ANOVA comparison different subsets of same data frame

It's because they are two different subsets. When you use anova for model comparison, the models have to be on the same data with different models, usually nested models. If you want to see if there ...
• 117k
1 vote
Accepted

### Can I use an autoregressive (AR1) model to determine if longitudinal data can be treated as individual single time points?

I'm not a time series expert, but I don't think four time points is enough to estimate a AR(1) model. Usually, the label "time series" is for much longer time series. You could run ...
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### Can I violate assumptions of normality for categorical linear regression models?

I think we need to back up. Questions of normality are -- in my opinion -- the least important when it comes to linear regression. That being said, your model and data are showing other signs that ...
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### Linear regression with overlapping observations

Not a full answer unfortunately, but I am thinking in the context of linear regression with just one predictor, you can use the correction outlined in: "Long-run predictability tests are even ...

### The effect of the order of observations on the distribution of $\hat{\beta}$ in Linear Regression

To make the same point as Glen_b but in a different way, we can prove that if $Z$ is a reordered $X$ then $Z^T Z = X^T X$. Specifically, if $Z$ can be obtained from $X$ by permuting $X$'s rows then ...

### linear Combination of Normal and T-Distributions

What you have is a mixture distribution, and that the components of the mixture are normal and t is irrelevant. Let $F$ and $G$ be two cdfs (cumulative distribution functions) and consider the mixture ...
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### Confusion regarding the criteria for defining a ML model as a linear model

In statistics, we call a model linear when the outcome is a linear combination of the parameters, meaning that you can write $\hat y_i = \sum_j x_{ij}\hat\beta_j$ (second definition). We could have ...
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Accepted

### Weighted least squares for a linear model

I don't get this cancellation ...
• 37.1k
Let's focus on Step 2, where you have $$R^2_\text{adj}=1-\frac{SS_\text{res}}{SS_\text{tot}}\cdot\frac{(n-1)}{(n-p-1)}$$ As you have mentioned, $R^2=1-\frac{SS_\text{res}}{SS_\text{tot}}$. We want to ...