# Questions tagged [linear]

For statistical topics which involve the assumption of linearity, for example, linear regression or linear mixed models, or for the discussion of linear algebra as applied to statistics.

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### How to solve the ARCH effect problem in estimating linear bivariate regression model?

I estimated a linear bivariate regression model by OLS method. I did the ARCH effect test. And there is the presence of ARCH effect in residuals. How can I deal with the presence of ARCH effect while ...
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### Shapley, cooperative games and linearity

Shapley values grant that the additivity property hold. However, I am in understanding cases where additivity in cooperative games does not hold. Specifically, I am looking for a practical example of ...
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### Does the linear regression fit follow the inverse relationship? [duplicate]

I fitted a X =logA, Y=logB with a weighted linear regression and I got the result as log B =(0.53 $\pm$ 0.054)logA + (17.41 $\pm$ 1.7). When I did the fit with X=logB, Y=logA, I expect the ...
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### swapping DV and IV in the presence of an interaction

I'm hoping someone could help with a problem that I'm sure has a simple explanation. I have conducted a visual test on 2 groups of people 1) healthy controls 2) patients (with a vision problem) using ...
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1 vote
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### If there are cubic polynomial features, then isn't this a polynomial regression, not a linear regression? [duplicate]

I have the following problem: Consider a Linear Regression problem with two features. Based on your visualisation of these 2D features, $x_1$ and $x_2$, on the training set, you noticed that using ...
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### Which analysis instead of linear regression?

I have collected data pertaining to suffering (scale from 0 to 8, higher is worse) and cognitive distortion (0 to 40, higher is worse) for a study with ~ 200 participants. My hypothesis is that there ...
1 vote
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### on a linear regression analysis, the determination coefficient is 0.99, but the residuals are not distributed normally. How do I interpret this?

So to preface I'd like to say that this is for homework and I am not very good at statistics. Please explain things to me like I am 5 years old.Also english is not my first language. So the homework ...
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### If R2 is not appropriate for non-linear ML algorithms such as Random Forests, can a Pearson or Spearman correlation be used as performance metric?

$R^2$ is not appropriate for non-linear models, such as Random Forest (RFs) models. https://arxiv.org/pdf/1611.03063 Is R-squared truly an invalid metric for non-linear models? https://...
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### Difference between regression methods

When to use logistic regression and when to use beta regression in statistical modeling for given data? How do know the difference between them? And when can I fit just a linear regression and not ...
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### Online updating of $t$-value for simple linear regression

Suppose I am regressing a dependent variable $y$ onto a single independent variable $x$ using a simple ordinary least squares regression model $y = \beta_1 x + \beta_0$. Suppose I start with $n$ data ...
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### Restricting the order in which variables are allowed to enter in the LARS algorithm

In the Least Angle Regression paper, in section 3, the authors refer to how you can restrict the order in which variables are allowed to enter the LARS Algorithm. In particular, having obtained some ...
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The maximum likelihood estimator for linear data $y_i = \beta x_i + \epsilon_i$ with i.i.d. normally distributed errors $\epsilon_i \sim \mathcal{N}(0,\sigma^2)$ is ordinary least squares, i.e. $$\... 0 votes 0 answers 22 views ### Running a Regression and Unclear How to Think About the Problem I am wanting to run a linear regression to better understand how force is a function of position in terms of delaminating/warping face frames. This is with respect to a product manufactured related to ... 1 vote 2 answers 94 views ### Covariance of Best Linear Unbiased Estimators and arbitrary LUE I'm working on a problem involving two linear unbiased estimators T and T' of a parameter \theta, defined from a sample \{X_1, \dots, X_n\} with mean \theta and finite variance. I aim to ... 0 votes 0 answers 28 views ### Dealing with Ratios in Linear Regression I am studying the relationship between X and Y using linear models. Both are composed of a left and right scalar value, and I'm interested in the relationship between both the totals and ratios for ... 1 vote 0 answers 169 views ### MLE of Linear Regression with heteroskedasticity Assume a linear regression model y = X \theta^{*} + \epsilon, where X represents a feature matrix and \theta represents a parameter vector. Here we assume heteroskedasticity where \epsilon \sim ... 1 vote 0 answers 19 views ### Regression when multiple observations per individual but final result is the same I'm very new to data analysis. I'm trying to find the causal effect of seating row and laptop use on grades at a specific university. I have data from 15 introductory economics lecture sessions ... • 11 2 votes 0 answers 62 views ### Constrained least squares where at least one of two coefficients is zero I have a linear model with a bunch of variables a number of linear constraints on these variables. I am currently using quadratic programming to solve this constrained least squares problem. However, ... • 121 3 votes 1 answer 146 views ### How to "see" the covariance matrix and mean vector? I am working with following model specifications (Regression, Modelle, Methoden und Anwendungen, Springer-Verlag Berlin Heidelberg (2009), p. 147):$$Y \sim MVN(X\beta, \sigma^2I)\beta|\sigma^2 \...
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Let be the linear model given by: $$y_i = x_i'\beta + \varepsilon_i$$ Using its matrix form, consider strictly exogenous assumption and spherical assumption, respectivelly: E[\varepsilon | X]=0, \...