# 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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### 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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### 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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### 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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### 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 ...
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 ...
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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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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### 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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### 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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### 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 ...
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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### 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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### 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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### 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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### 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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### 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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### 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 ...