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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. ...
BenP's user avatar
  • 577
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 ...
Martin Modrák's user avatar
0 votes

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 ...
Happy Cretine's user avatar
4 votes
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 ...
Kuku's user avatar
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3 votes

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 ...
markowitz's user avatar
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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. ...
Dikran Marsupial's user avatar
0 votes
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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" ...
Peter Flom's user avatar
  • 117k
2 votes

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 ...
Peter Flom's user avatar
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1 vote
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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 ...
Peter Flom's user avatar
  • 117k
2 votes

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 ...
Demetri Pananos's user avatar
2 votes

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 ...
user406363's user avatar
2 votes

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 ...
Jamie Ballingall's user avatar
3 votes

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 ...
kjetil b halvorsen's user avatar
6 votes

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 ...
Dave's user avatar
  • 60.9k
4 votes
Accepted

Weighted least squares for a linear model

I don't get this cancellation ...
Thomas Lumley's user avatar
2 votes
Accepted

Converting Adjusted R²

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 ...
Javier's user avatar
  • 66

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