# Questions tagged [linear-model]

Refers to any model where a random variable is related to one or more random variables by a function that is linear in a finite number of parameters.

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### Regressing on nuisance features as pre-processing

A friend recently told me about a technique to remove the effects of an unwanted feature $x$ in a response variable $y$. He mentioned an example from genetics. By regressing $y$ on $x$ (or a ...
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### A faster way of finding unbiased estimators for this linear model

No access to computers or calculators is available for this problem. Consider the following linear model Y_1 =\theta_1 + \theta_2 + \theta_3 + \theta_4 + \theta_5 + \theta_6 + \epsilon_1\\ Y_2 =\...
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### How do I obtain or calculate the value of theta in an Ornstein-Uhlenbeck PGLS model?

I'm using phylolm in R to run a phylogenetic least squares regression with an Ornstein-Uhlenbeck model of evolution. The model summary gives me the values for alpha and sigma squared but not theta (...
1 vote
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### Categorical linear-model coefficients from a pairwise competition experiment

I am presenting a question for which there may be a simple statistical answer, but I have prefaced it with perhaps a longer explanation, to err on the side of caution, in hopes that the data make more ...
51 views

### Re-using computations in several least squares problems

I have $K$ least squares problems of the form $Y_k = X_k\beta_k$ for $k = 1, \dots, n$. If the matrix $X_k$ is the same for each index $k$, we can rewrite the problem as $Y_k = X \beta_k$. How can I ... 17 views

### Have my assumptions been met?

I am running assumptions for multiple regression and scatterplots are a real bane of mine. Can anyone advise as to whether the following scatterplot provides a linear or non linear relationship ...
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### lme4/lmerTest nested mixed effect model output missing fixed effect with consistently significant penultimate t-value

I have a mixed effect model with the following fixed effect categories: Error: Y/N Groups: A/B And a random effect for each subject. I am interested in the difference in response variables due error ...
1 vote
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### How to calculate residuals from a given linear model

So I have been given a linear model, with the Beta0 = 0 as well as given equations. I have done several calculations needed in order to calculate residuals, as shown in my work below: I also went ...
1 vote
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### Binary variable in regression model (interview question)

I got this question, it may be easy but for some reason for me is not: you are given a binary variable $b\in [0,1]$, that has no predictive power on $y$, but has some on $X$. How would you use it to ...
1 vote
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### How to derive least squares estimators from normal equations with work shown

My last question was closed, so I made a new one that is more relevant and has my full calculations thus far. I have a scenario where I have been given some information, such as normal equations from ...
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### Is there an equivalent for an interaction term in linear models for non-linear regressions?

I’m working on how different temperatures affect the scaling of metabolic rate and gill area with body mass. It is commonly accepted that both metabolic rate and gill surface area increase with body ...
I am observing a strange (constant) residual error in my linear model. PROBLEM: I fitted a linear model (LM) $y=Ax$, where $A \in \mathbb{R}^{n \times p}$, with $n < p$. Hence, $A$ is ...