Refers to any model where the 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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21 views

Inflation as an independent variable

Assume a model like this, basically explaining stock market returns with a bunch of stuff: ...
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22 views

Help interpreting R linear model fit [duplicate]

I have observed variables power$values. I am trying to model this process using a second set of observations, such that $P = M\cdot X + B$. $P$ is the function ...
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0answers
12 views

Transforming / Evaluating (Probably) Normal Data from Sample with Linear Probability Distribution

I have a sample of data for which the count of a given value increases roughly in proportion to the actual value. For example, the value 22 will occur around 22 times and the value 30 will occur ...
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3 views

Liblinear types of solver

There is many variants of type of solver in liblinear but I don't understand their differences.Which one I must choose? Also why data must be scaled? duo to some numerical issues? ...
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1answer
37 views

Multiple linear regression through orthogonal matrices

An example of linear regression could look like: $min \sum_{i=0}^{m}||x_i A - y_i||_2^{2}$, where ${x_i, y_i} \in \mathbb{R}^n$ and $A \in \mathbb{R}^{n\times n}$. I am interested in knowing how do ...
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1answer
50 views
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1answer
21 views

Dummies instead of the Chow test

I have found somewhere a mention to the possibility of using dummies variables instead of the Chow test to test whether the coefficients in two linear regressions on different data sets are equal. ...
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1answer
26 views

Interaction: ignore two-level if three-level is significant in every case?

I am using lmer in R to run LMM. My DV is continuous and my IVs are categorical. Many statistician said if the three-level parameter is significant, I cannot interpret the two-level parameter. Does it ...
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1answer
50 views

Interpreting the “coefficient” output of the lm function in R

I have created a linear model (which has multiple predictors) using the lm() function and I would like to interpret the "coefficients" that I get when I use the summary() function on the linear model. ...
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3answers
145 views

Question about the error term in a simple linear regression

Suppose we have a linear regression model $Y_{it} = \beta_0 + \beta_1 X_{it} + \epsilon_{it}$, many times in literature it is assumed that $\epsilon_{it} \sim N(0,\sigma^2).$ This assumptions makes ...
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1answer
34 views

Linear regression on grouped data

I'm new in stats..I hope to write something that makes sense. I have a sample composed by 200.000 projects, each project is defined according to its size (S) and the presence of active users (U). The ...
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34 views

Random model selection and validity of significance tests

Suppose we have some data, $\{y_i, x_{1i}, \dots, x_{ki}\}_{i=1}^n$ and we want to build a linear model of the form $y_i = \beta_0 + \beta_{1'i}x_{1'i} + \dots + \beta_{k'i}x_{k'i} + \epsilon_i$, ...
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14 views

Interpretation of three-way interaction in an output of lmer

I am using lme4 to run a three-way interaction model. I have three independent variables: animal (rat, lion, dog), color (red, green, blue) and sex (male, female). The baselines are as follows: ...
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14 views

Do I need a planned contrast or post-hoc analysis when doing LMM in R?

I am doing a LMM in R and would like to know if I need to do a planned contrast or a post-hoc analysis. From my understanding, the LMM in R already provideds me a planned contrasts and if I have ...
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0answers
15 views

Including squared predictors in model matrix [migrated]

I have the following code x <- c(1, 2, 3) y <- c(2, 3, 4) z <- c(3, 4, 5) df <- data.frame(x, y, z) model.matrix(x ~ .^4, df) This gives me a model ...
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33 views

k-means + linear regression: How to split the data for validation

I want to cluster my data first using k-means and then determine a regression model for each cluster. Then I want to evaluate the performance of this approach using split validation. I can think of ...
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0answers
9 views

Goodness of Fit tests in a linear model (lin-log)

I am using a lin-log model and am currently doing tests for goodness of fit of the regression. I already used the R-squared test, Q-Q plot and Shapiro test. Are there any other tests i could use in R ...
2
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34 views

Effect of each parameter on a Monte Carlo Simulation

I was wondering what is the best way to determine the effect of each random parameter on the result obtained from a Monte Carlo Simulation. I realise I have asked a similar question here, but this ...
2
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1answer
62 views

Interaction term in a linear log model

I am using a linear-log model to test whether overseas development assistance and remittances positively affect FDI in cases of good governance and financial market development. Let's say I want to ...
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1answer
28 views

Explanatory variables in a Lin-log model

I have a data set and I want to fit a Lin-log model. Is it possible to apply the log transformation only to some of the explanatory variables or should the log ...
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21 views

When are multiple linear regressions independent?

I'm doing many pairwise linear regressions on a set of variables. For example x as the dependent variable vs y, ...
4
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1answer
64 views

Statistical significance for comparison of linear regression models

I have two linear regression models (with the same predictors) that try to estimate two different (although related) features of the same population. I am analyzing the hypothesis that these ...
2
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1answer
20 views

When no model comparison, should I use REML vs ML?

I'm running LMM, and I will make no comparison of models. Could I ask which one should I use between REML and ML?
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71 views

Difficult interpreting linear mixed model result - R lme function

I'm fitting an harmonic regression model on data from different plants separately as follows: ...
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20 views

Power analysis in a linear model - pooled vs individual samples

I'm interested in how many samples are required to see a relationship between allele frequencies (proportions of alleles) and environmental gradients, such as temperatures and water quality. ...
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1answer
53 views

Residual Vs. Fitted Plot with Outliers

I have a model relating fuel consumption to other vehicle parameters, which produces the following Residuals Vs. Fitted plot. My Question: Is the skew to the right simply an indication of outliers ...
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1answer
52 views

R: multiple linear regression model and prediction model

Starting from a linear model1 = lm(temp~alt+sdist) i need to develop a prediction model, where new data will come in hand and predictions about ...
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11 views

So the interpretation of 2-way interaction cannot be interpreted if it is significant in 3-way interaction?

I use LMM to analyse my data and my variables are as follows: DV: continuous IV: 1) color(red, blue, green), height(low, tall, medium), and sex (male, female) Then for color, "red" is baseline, and ...
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1answer
32 views

R: Explanation of a multiple linear regression summary [duplicate]

I am quite new with R and while i am able to perform the basics i am not yet able to understand the output results. For example: summary(lmodel) generates the ...
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1answer
144 views

The main effect will be non-significant if the interaction is significant? [duplicate]

I am using linear mixed models to identify important factors, and it turns out that: A: significant B: not significant ...
2
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1answer
88 views

How to define weights when testing an exponential trend?

In a linear model including ANOVA one can test a trend (e.g., linearity, quadratic effect, etc.) among the ordered effects (regression coefficients or factor levels) through assigning proper weights. ...
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1answer
77 views

Is it necessary to exclude all nonsignificant parameters to choose the best model?

I'm running LMM models and could I ask if I can just report the model after comparing random intercept with random intercept and slope model without excluding nonsignificant factor?
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2answers
70 views

Should the outcome variable be measured at least twice for a longitudinal study?

I am trying to find the association between BMI and onset age of a condition with linear regression model. I have multiple records of BMI measurement. But the outcome variable, onset age of condition, ...
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31 views

Best Regression with Binary Features

I'm seeking to do a linear regression for an evaluation function in a board game. My features are all (signed) binary 1 0 0 1 -1 1 0 0 0. Mostly zeros. Around 200 to an observation. I have 10 million ...
2
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1answer
91 views

What type of multivariate linear regression is this?

I'm trying to reproduce a result from a book (see bottom) and it doesn't work. I would like to do some further readings about this method but he doesn't specifically give the method other than a ...
4
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1answer
39 views

Linear regression: Evaluate probability of $Y>y| X=x$

Given a linear regression model with all the assumptions checked and validated, I would like to obtain the probability that $Y>y|X=x$. For example for the iris dataset, I would do the following to ...
2
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0answers
37 views

creating contrast matrix (limma) for two factorial in R

I am attempting to construct a contrast matrix that I can run in R, using the limma bioconductor package, but I am not sure that I have coded the contrast matrix correctly. A previous post and the ...
2
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1answer
43 views

Positive linear regression coefficient

I am trying to use R to find the optimal solution for my problem with positive coefficients. Here are my data: ...
3
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1answer
150 views

Analysis of the Residuals vs Fitted

I have a model for which I gathered 10 observations from each person, a total of 25 people, then 250 observations. Well, this is part of my summary of the model, ...
7
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1answer
104 views

Linearized exponential regression by lm() vs. non-linear nls() regression

Disclaimer I am new to this site, relatively new to R (two weeks of learning), have just a really basic knowledge in statistics so sorry if I'm doing a dumb mistake there or asking bad question or ...
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0answers
22 views

Three-way interaction in LMM: Can I write interpretation in this way?

I have a couple of questions regarding to the interpretation of LMM: Question 1: If I have three independent factors and two of them have three categories, I will have to run at least four models to ...
3
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1answer
59 views

What happens in linear regression when observations are not independent in time

Let's consider the example of whether a person's weight is correlated with their height (simple linear regression). What is the difference between running this correlation on the following two data ...
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1answer
50 views

Code for conditional linear regression [closed]

I've just run a linear regression on an entire data set, but now I need to run the regression with data just from females within the data. Females are denoted under the ...
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1answer
46 views

Can univariate linear regression be used to identify useful variables for a subsequent multiple logistic regression?

Does the $R^2$ (or some other statistic) from a univariate linear regression tell me anything about how it would work in a logistic model? What if I normalized the data to mean zero? I'm doing ...
4
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1answer
127 views

Derive Variance of regression coefficient in simple linear regression

In simple linear regression, we have $y = \beta_0 + \beta_1 x + u$, where $u \sim iid\;\mathcal N(0,\sigma^2)$. I derived the estimator: $$ \hat{\beta_1} = \frac{\sum_i (x_i - \bar{x})(y_i - ...
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2answers
46 views

Linear regression with group-dependent intercept and variance

This is my first question on CrossValidated and I'm not a professional statistician (although I am trained in theoretical probability) so please be indulgent. I have data of the form $(X_i, Y_i, ...
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1answer
109 views

Reproducing the Table 3.2 from the Elements of Statistical Learning

I was able to reproduce table 3.1 from ESL. However, when I tried to reproduce table 3.2, my estimated coefficients were way off (shown below): ...
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2answers
136 views

Does Principle of Marginality apply to interactions of categorical variables?

Suppose we have factor X with n levels, factor M with p levels, then $\hat{Y} = X+M+X\cdot M$ and $\hat{Y} = X \cdot M$ will give us two parametrizations of the same model, since we can only get ...
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1answer
40 views

Reason for not shrink the bias term

For linear model, $y=\beta_0+x*\beta+\varepsilon$, the shrinkage term is always like $P(\beta) $. What's the reason we do not shrink the bias term $\beta_0$? Comparatively, should we shrink the bias ...
4
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1answer
102 views

Normality assumption in linear regression

As an assumption of linear regression, the normality of the distribution of the error is sometimes wrongly "extended" or interpreted as the need for normality of the y or x. Is it possible to ...