# Tagged Questions

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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### Linear discriminant analysis posterior not giving expected values in R

I have two normal distributions fg and bg with mean (mu) and standard deviations (sd) as follows: ...
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### Impact of spurious regressors on out of sample prediction error

The true DGP is $$y=\alpha_0 + \alpha_1 x_1 + \dots + \alpha_k x_k +\epsilon, \quad \epsilon\sim \mathcal{N}(0,1)\label{eq:1}$$ but we instead estimate y=...
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### What are periodic version of splines?

In this What's wrong to fit periodic data with polynomials? post, I tried to use Fourier basis expansion and Polynomial basis expansion to fit a toy periodic data (daily temperature data set). I ...
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### Effect of quadratic term when variable's range is negative

I am running a Linear Model where I want to include a quadratic term. The dependent and the explanatory variables are all in logarithmic terms. Further, due to Log transformation the range of X is ...
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### Relation linear regression and ARMA models

I have data from a time series which I am currently fitting with a linear model. For that Im using the data as cross-sectional data, where each response corresponds to the value of each variable on ...
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### What are common ill-conditioned matrices in linear system? [closed]

Matrix condition number is very important because many problems are ill-conditioned and cannot be reliably solved using double precision computer systems. Here is what I know that could happen in ...
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### regression of a level vs a change variable

This question has likely been asked already but due to the lack of proper terminology I might not have been able to find google up the relevant questions. We have data for several years: 2000, 2001, ....
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### Using differences or ratios in regression

Is it always wrong to use ratios in linear regression? For example, If I am trying to fit a linear model and I have a predictor given by: average age of team A / average age of team B should i ...
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### Help understanding Linear Model in ESL book

Also known as "Nate slowly deciphers ESL to conceptual understanding/plainer language", part two (see part one) Help me understand this (bullets added) The term $\hat{β}_0$ is the intercept, also ...
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### Missing rows ANOVA in R [closed]

Why does the S:x1 column disappear (presumably S:x1 goes into ID but I dont know why)? S is a factor, x1 is a covariate and ID is a factor. ...
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### Linear model for testing a ratio of ratios

Our experimental design is as follows: For each of two genotypes (wt and ko), we perform two different gene expression assays (Assay1 and Assay2), and do 4 replicates of each assay. We are interested ...
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### Performing limma on residuals or including batch and other covariates in the model?

I am trying to analyse a gene expression dataset of about 240 samples (Illumina microarray). There are multiple questions I need to ask (healthy vs diseased, effect of treatment in diseased, ...
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### Design/Contrast Matrices and Unestimable Coefficients

I am trying to analyse microarray data from samples with the following characteristics: one of two genotypes, a procedure either carried out or not carried out, and, in the case that the procedure is ...
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### Constrained optimization algorithm in linear regression

I am interested in the following constrained parameter estimation in linear regression, $$\min_\beta\sum_{i=1}^{n}(y_i-x_i\beta)^2 + \lambda \sum_{j}^{p}f(\beta_j)$$ where the model is $y=x\beta+e$, ...
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### Residuals in a linear model are independent but sum to zero; isn't it a contradiction?

The sum of the residuals in a linear model equals zero. The residuals in a linear model are independent. Isn't it a contradiction?
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### ReLUs and Gradient Descent for Deep Neural Nets

I understand that ReLUs are used in Neural Nets generally instead of sigmoid activation functions for the hidden layer. However, many commonly used ReLUs are not differentiable at zero. Gradient ...
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### What is the relationship between the function $\mathbb{E}(Y \mid X = x)$ and linear regression?

Consider the function $$r(x) = \mathbb{E}(Y \mid X = x)$$ This has been called the regression function in a textbook I'm using. I'm trying to figure out the relationship between this function ...
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### Circularity in Linear Regression: Independent variable used as dependent in the same model

I have a dataset with at Customer-Date level. I want to fit a line on the data estimating spend of a customer on a certain date. One of the covariates I am using in the model is historical sales of ...
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### Linear “self” regression, terminology and references?

Suppose that $X_i, i=1,\ldots,n$ are some random variables. I'd like to do multiple linear regression to learn to predict any of these variables from the others. My model for the reconstructed ...
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### Predict results of Elections

I have information on the votes in my town and in the country. I want to predict the results in the country's elections knowing the results in my town. What methods I can use? I have thought of ...
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### Regression with some observations having more than one factor level

I have data I want to analyze using multiple regression or machine learning: the response is cells for which I measured viability (a continuous response) and the independent variables are the genes in ...
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### Correlation of 2 categorical variables in linear model

I have this dataframe with two categorical variables (Sex and Ethnicity (only Asian or European)) and I need to fit a linear model to estimate the weight of a fetus given the day of the echography and ...
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### What is a good way to know if a variable adds value to an existing regression model without its components

Suppose someone gives you the fitted values to a regression model with $k$ terms, along with the fitted coefficients. If this is all you have, and you are investigating an additional "term" or set of ...
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### Orthogonal projection onto additive subspace (normal linear model)

It is known that in a normal linear model $X \sim N(\xi, \sigma^2 I) \in \mathbb{R}^N$, if we group our observations using a factor $F$, i.e we claim that $\xi$ lies in the subspace $L_F$ where ...
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### Covariance-residual technique for linear regression feature selection

When doing forward feature selection for linear regression, it is a well known trick that to select the next feature to add, we can compute the covariance of each candidate feature against the current ...
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### Regression with a ratio as an independent variable

I'm regressing a response versus a ratio between two measurements as an independent variable. I'm getting a significant positive effect and I'd like to test whether the contribution of the increase in ...
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