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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26 views

Do I accept or reject the null hypothesis?

M1 : Y ∼ β0 + β1x1 + β2x2 M2 : Y ∼ β0 + β1x1 anova(M1,M2) shows a p-value of 0.0001, so we prefer M1 at significance level 0.05. Would that be correct? I thought that if .0001<.05, I should reject ...
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1answer
42 views

How covariance matrix of the error term in linear regression can be NON-singular?

I don't understand linear regression. Assume the classic linear model: $$Y = X \beta + \epsilon,\\ \epsilon \sim \mathbb{N}(0, \sigma^2 I_n), $$ where $Y$ is a vector of length $n$, $X$ is a matrix of ...
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3answers
71 views

Regression in Causal Inference

I was recently introduced to the topic of causal inference in statistics and I am currently learning about the importance of the backdoor criterion (BDC), as applied to the following DAG. Interest ...
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1answer
128 views

Is the MSE of a vector a scalar or a matrix?

Suppose $Y = X\beta + \epsilon,$ where $Y$ is $n \times 1$, $X$ is $n \times p$, and $\beta$ is $p \times 1$, and $\epsilon$ is $n \times 1$ with mean 0 and variance $\sigma^2$. The OLS estimator of $\...
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0answers
16 views

Testing linear hypothesis with Wald test: unintuitive results

I have a question about testing the equivalence of two regression parameters. I know there are a lot of resources about how to test a linear hypothesis but I am confused about my results (and its been ...
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0answers
21 views

Multiplicity Correction for Coefficient Estimates in Linear Regression [duplicate]

When regressing a dependent variable y on some feature vector x with a standard linear regression, is there any correction in place for multiplicity or is this just not relevant in this case? The ...
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1answer
25 views

Checking the constant variance assumption for residuals vs fitted plots: What about for the same fitted values?

For a residuals vs fitted plot, we use the fitted values $\hat{Y} = \beta_0 + \beta_1 + \cdots + \beta_p x_p$ on the horizontal axis and the residuals on the vertical axis, and then compare the ...
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1answer
20 views

SPSS - Automatic Linear Modeling “Importance” Numbers

I have a large set of survey data. I'm looking at trying to find out which variables are the most important to impacting a DV (call it "happiness"). I'm not looking to find a beta number ...
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1answer
52 views

Assumptions of OLS and linear mixed models

I've only taken a few statistics courses, and so I apologize if any of my questions are rudimentary, however, I'm wondering if someone could explain/direct me to resources regarding the correct ...
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3answers
56 views

How to test if sum of two coefficients of ols model is greater than zero using R?

The regression model is: y = b0 +b1x1 + b2x2 + b3x3 + e I want to test if b1 + b2 > 0. the R package ...
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1answer
25 views

Linear model what is $p(x|y_0)$

If I have a linear model of the form: $$x_i = \beta y_i + \alpha + \epsilon_i$$ where $\epsilon_i$ are samples from $\epsilon$, an independent and identically distributed random variable. I can find ...
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1answer
44 views

Should I remove the trend of this data

I have time-series data. It includes a number of patients with series conditions due to car crashes. After I remove the trend, I found that some number of patients becomes negatives which is ...
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40 views

distance between two points (x,y) weighted by location (x)

a new on algebra. I am trying to create an indicator of the distance between two points (x,y) from a (0,1) scale, but I want to create a weight that reduces such distances as the point x is closer to ...
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2answers
47 views

Linear trend with time-series does not fit the data perfectly. Is that OK?

I am new to a time-series model. I try to improve my knowledge by practising. I understand the stationary for the time-series model. I read many papers and tutorials regarding removing the trends. ...
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0answers
17 views

Significance of datapoint outside prediction band

With linear regression I am plotting 25 bodies of text with their vocabulary count (independent variable X) and occurrence of a particular word (for example: "this"). I have a linear ...
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11 views

Can I use Helmert coding for two level categorical variables?

When I use Helmert contrast in R for two level categorical variables it codes the levels as -1 and 1. This is fine with me but I was not sure if I am doing this wrong because generally Helmert coding ...
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17 views

Why do different divisions of the same text corpus result in different regressions?

Background I am comparing a small text of 169 words to a bigger text consisting of 19.000 words. I am trying to plot a linear regression of different texts that can result from the different ways of ...
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1answer
33 views

Choosing between Ordinal logistic Regression and Multiple linear regression

I have data in which the response variable (attitudes towards tourism) is scaled in nature ranging from -10 to +10 (calculated from the summation of scores of a few questions related to tourism). The ...
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1answer
12 views

What's the REAL difference between moderation and interaction, in ANOVA, in this case? And more

I think the people here will appreciate this. This is a reading assignment/puzzle. I don't see a difference between #1 and #6. This refers to the subject of my question here (moderation and ...
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0answers
28 views

What is the signfiance of “orthogonal” vectors in statistics?

So I am reading What does orthogonal mean in the context of statistics?, and there are contradictory answers. The most upvoted answer says that "Therefore, orthogonality does not imply ...
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1answer
56 views

How to choose between different methods of linear regression?

I find following commonly mentioned linear regression methods: OLS: ordinary least squares GLS: generalized least squares WLS: weighted least squaes RLM: robust linear model OLS is usually the default....
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1answer
34 views

Repeated measure clinical trial Linear mixed model

I am working on a clinical trial testing an innovative rehabilitation therapy on patients and I would like some suggestions on how to analyse the data. The study design is: 2-groups: conventional (n=...
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1answer
23 views

Why is Standard Error of Slope small when the data is spread out?

In the book " Introduction to Statistical Learning " , the standard error of the slope term of Linear Regression is given as follows : The book also says the Slope is more precise when the ...
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11 views

Fixing Autocorrelation in mini time series for a linear regression?

I have data with features that looks like this I am using ML regression in Sklearn to predict a final cost (in a separate df). Before fitting a linear regression I went to test the assumptions of ...
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1answer
38 views

All p-values of linear mixed models equal to 0

I am trying to model a varible (maximum depth) in function of type of dive and diel changes (day,night) with the individuals (whales in this case) as random factor in R. I tried to apply a linear ...
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4answers
136 views

Can we use linear regression to define the objective function in linear programming?

This is a general question about how linear programming is used in the analytics community. Is it common, or feasible to use linear regression (or perhaps even more complex models like regression ...
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2answers
51 views

Multiple regression, simple regression or other?

I'm attempting to put together a research proposal where area knowledge (Western Asia) is my speciality but where the statistical methodology I need to answer my research question is not and I'm ...
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1answer
16 views

How to test “nesting effects” in a linear model after you have reduced the IV by factor analysis?

I have a couple items (let's say 10) had run in a study and I want 1) to reduce the dimensions by factor analysis. Then I have two factors (let's say factor A has 3 and factor B has 7 items). After ...
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1answer
10 views

High correlation between linear regression residuals MSE and dependent variable's variance

I am building a linear regression model for 5000 gene expressions, and each gene has its own independent variables. So in total, there are 5000 linear models and for each model, I have 360 samples and ...
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1answer
68 views

Can anybody understand this specification of a feature for a horses preference to a condition?

I have become interested statistical analysis of sports and came across a horse racing paper: "Computer Based Horse Race Handicapping and Wagering Systems: A Report" (found at: https://www....
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9 views

How to run a Hierarchical multiple linear regression for impression management?

Thank you for your help! I am looking to run a Hierarchical multiple linear regression as part of my study. I am looking to see what if any impact impression management has on self report behaviours ...
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0answers
33 views

How can my confidence interval and p-value not be in line with each other in a linear difference-in-difference analysis in R?

I'm performing a linear difference-in-difference analysis with mental health care costs, log transformed (log10), as outcome measurement. Individuals are placed in a treatment or control group, and I ...
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1answer
63 views

Why can 'linear' regressions include non-linear transformations of the independent variables?

So the definition of linear regression is that the response variable is a linear function of the estimators. If we consider univariate regression (for ease of visualization), we have $$ y = \beta_1x + ...
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34 views

log transform in linear regression

Assume we have a data set and the theory suggests to model $Y \sim X$. We apply a simple linear regression and get the following: Next, let us make a log transform of both $X$ and $Y$. The result is ...
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0answers
9 views

Combined Variance through Several Linear Functions

Apologies in advance if my terminology isn't correct for everything I'm about to write I am dealing with a corner-cased problem and I'm trying to figure out if my derivation is correct. I have a large ...
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1answer
14 views

How can I interpret the residualplots

I have this plot and need some interpretation. The response variable of my data is Salary and the predictors are, Education, experience, age, kids, GPA, and Assets.
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1answer
34 views

lmer reports “fixed-effect model matrix is rank deficient so dropping 1 column / coefficient” and doesn't show one interaction"

So I'm trying to run a mixed-effects model looking at the relative intensity of Arabic and English fricatives produced by bilingual Arabic-English speakers; for context, I'm looking at /f/ and /v/, ...
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1answer
38 views

Linear regression | is it wise to convert all categorical variable to numerical variable to perform linear regression?

I would like to know whether if it is recommended to convert the categorical variable into a numerical variable to perform linear regression or to rather perform a logit regression instead. Dependent ...
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1answer
23 views

Violation of multiple linear regression assumptions after adding interactions

I am working with a data set and properly fitted a model that satisfied the assumptions of lienar regression in a multi-variate setting. I have 8 predictors, and proceeded to test for significance of ...
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1answer
32 views

Are these scatterplots violating linearity? (multiple regression)

I'm aiming to run a linear regression for some data so I'm testing assumptions. I have a few scatterplots that I'm finding it hard to read. It looks somewhat linear but I can't tell whether they ...
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0answers
9 views

How do you calculate cohen's L so that you can plug it into a power calculation for multiple linear regression?

I am reviewing a book called Statistical Methods for Healthcare Research so I can learn how to do a power calculation for my sample size for multiple linear regression. This book says that cohen ...
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0answers
13 views

R2 scores when the output is a 2D value

Based on my readings, R2 is used to calculate the closeness of fit for regression models where As a beginner in the field, I have only encountered 1D values of <...
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0answers
9 views

Set up and analyse planned contrasts in lmer() from lme4

I would like to analyse planned contrasts in my lmer() model from the lme4package. I have three factors: group (levels: trt, ...
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0answers
18 views

When assessing fixed effects in LME for statistical significane do I leave interaction terms in?

I'm trying to assess the statistical significance of some fixed effects and interactions in a linear mixed effects model I'm building. I'm essentially following the tutorial laid out by Bodo Winter (...
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0answers
15 views

Testing for inclusion or exclusion of interactions in multiple linear regression

I am working with a multiple linear regression model in a r setting. The model is model2<-lm(strength~blast+flyash+water+superplast+coarseagg+fineagg+age) where ...
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0answers
6 views

Parallel model form

Suppose that we have a categorical variable with 4 types, we use $x_{i1},x_{i2},x_{i3}$ to be predictors that take the value of 1,2,3, and 0 otherwise depending on corresponding type(1 of 4) from ...
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8 views

Change in baseline for covariates for linear regression

I am new to linear regression and have a question about how to incorporate follow-up time into my linear regression. I'm interested in exploring the relationship between childhood systolic blood ...
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0answers
8 views

Quantify error introduced by window used for linear fit?

It is often necessary to perform linear fits to experimental data to estimate an extrapolated x-intercept. I've found that the precise choice of range of x-values used in the fit can often have a ...
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1answer
29 views

Order of operations for multiple linear regression diagnosis and application?

I am working with a data set and trying to fit a model to it. I transformed, the data and satisfied the assumptions of multiple linear regression. After doing this using regsubsets() in r and backward ...
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4answers
494 views

What is limiting about a linear model?

I've read that a linear model means linear in the parameters, and not necessarily in the predictors. For example, both: $$Y=\beta_0+\beta_1x_1+\cdots+\beta_kx_k+\epsilon$$ and $$Y=\beta_0+\...

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