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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 ...
volperossa's user avatar
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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 ...
Ashwin Aravindaraj's user avatar
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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 ...
holmes's user avatar
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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 ...
The Pointer's user avatar
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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 ...
David Capelle's user avatar
1 vote
1 answer
43 views

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 ...
Sofia V's user avatar
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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://...
JElder's user avatar
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2 votes
1 answer
51 views

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 ...
Anju's user avatar
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2 votes
1 answer
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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 ...
Sprotte's user avatar
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Simple Linear Regression, impact of standardizing data

Let's assume we have $(X_i, Y_i), 1 \le i \le n$ a series of $n$ observations. I want to explain $Y^T = (Y_1, \dots, Y_n)$ as a linear function of $X^T = (X_1, \dots, X_n)$. My model is: $$ Y = \...
jocelinbordet's user avatar
1 vote
1 answer
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Adding a confounder `Factor` vs. subtracting within-level mean

In order to account for a known confounder, one can add an additional factor (that describes the confounding effect) in linear regression. For example in R, we ...
Amin.A's user avatar
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Interpretation of linear regression results

I ran a linear regression model with 2 IVs (both are dichotomous) with an interaction: y = a + b1x1 + b2x2 + b3x1x2 The model and only x1 were significant....
user3315563's user avatar
4 votes
1 answer
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Making linear to logistic regression with sigmoid function - why is a transformation of predicted y needed?

I noticed that one can run a linear regression for binary outcomes and get the same predictions as from a logistic regression after using a sigmoid function. That is what I awaited. But the surprising ...
LulY's user avatar
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Target encoding in linear regression

I have a dataset with the loss rates of each contract as dependent variable. As independent variables I have country (four values), profession (5 values) and income (continous variable). I apply ...
Vit123's user avatar
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Linear regression results do not match expected ones [duplicate]

I am fitting a simple linear model. First I sample $X\sim\mathcal{N}(0,1)$ and $Y\sim\mathcal{N}(12,3)$. Then I impose the following linear model for $Z = 2+2X-\frac{1}{4}Y+\mathcal{N}(0,\frac{1}{2})$....
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Testing geometrical trend in a tail

I have a collection of values x1,x2,..., xm, ... xn, with n>>1. It has been observed that at 1<<m<n the points start following a geometric trend, i.e log(xi) -> linear. I need a ...
Jesús Castrejón's user avatar
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Determining when two slopes are different or not, given heteroskedasticity

My current experiment investigates substrate consumption at two different substrate concentrations. My question concerns whether the slope of consumption is equal. However, I obtain an F-value ...
simon vandenberghe's user avatar
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Is including all pair-wise interactions in a three-way interaction linear regression model necessary?

I am trying to assess the impact of X on Y with Z as a control and a dummy variable (D), which takes a value of 0/1. However, to test my hypothesis, I have interacted with XZD as I want to see the ...
Toshani Singh's user avatar
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Position in hierarchy as ordinal predictor in linear regression

I'm writing my thesis and I'm unsure about the analysis procedure. One of the hypotheses is: "A higher position of the deceased in the attachment hierarchy of the bereaved predicts a higher level ...
Sabina's user avatar
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1 answer
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Prove Wald statistic = number of linear restrictions times F statistics

I'm considering $F[J,n-k]= \displaystyle \frac{(e_{*}^{'}e_{*}-e'e) \backslash J}{e'e\backslash (n-k)}$, where $J$ stands for number of restrictions. I want to prove $W=(Rb-q)'(Rs^2(X'X)^{-1}R')^{-1}(...
Chang Henry's user avatar
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How to extrapolate/forcast data with a linear mixed model

I built a linear mixed model with data from a cohort of patients followed from 3 years before the start of the treatment to 24months after. The variable of interest in their blood pressure. I would ...
Jilano's user avatar
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Rank deficiency in a linear mixed model

I have a linear mixed model with 4 fixed factors and 1 random factor: V ~ A + B + C + D + (1|E). I want to compare this model with a model with an additional interaction term. When I add an ...
statuser's user avatar
3 votes
4 answers
88 views

Interpretation of high p value of a coefficient in linear regression [duplicate]

In a medical article, the multiple linear regression model included some coefficients with low p values but also some with p>0.05. How can I interpret these high p values and should they be be ...
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Using MMD for Feature Selection with Linear Regression: Valid Approach?

I'm using Maximum Mean Discrepancy (MMD) for feature selection (i.e., to select the features that minimize the dissimilarity between the training and testing datasets). I'm aware that MMD introduces ...
Adham Enaya's user avatar
1 vote
1 answer
21 views

Environmental variables explain hare weight - 80 traps in 4 zones where each trap caught unequal number of hares - Linear mixed effects model best?

Study design So I have put out 80 hare traps in a forest area of 50 km^2. There forest area is split into 4 zones. Each zone is expected to be different because of different pollution input levels. In ...
Cordex's user avatar
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1 answer
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If IV and DV shares a component, can you simplify the linear regression between them?

If y = a - b, x = c - b, for a simple linear regression y ~ x, is it still (c-b) ~ (a-b), or can you simplify it into c ~ a? Is it even correct to run a regression if you know they share a component?
PPNA's user avatar
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Needing to rank order correlations from highest to lowest

Hello I have a very large data set in excel with many different variables. Some of the examples of independent variables are moisture percent at the time of harvesting corn, temperature the dryer when ...
user410357's user avatar
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2 answers
68 views

Linear Regression switch in sign when including intercept [closed]

I am running a simple regression of y on x. When I include the intercept the beta for x is negative and significant and when I don't include the intercept the beta is positive and significant. What to ...
acooper's user avatar
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7 votes
2 answers
435 views

Questions about how to proceed when residuals of linear regression are not exactly normally distributed

I have done a linear regression analysis on some data and I want to construct confidence intervals on the coefficients. I have read that it is necessary for the residuals to be normally distributed to ...
fj34ifj3ljfk3fj43jfk3jf's user avatar
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0 answers
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Mathematical rigorous approach to linear regression [duplicate]

I'd like a book or any PDF that teaches about linear regression in a complete way. That is, I want something that, for instance, doesn't use any random variable without stating its domain or the $\...
rfloc's user avatar
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regression wtith t scores

I have performed a study in which I converted performance on a cognitive test to z statistics and from that derived t scores. We would like to examine the relationship between t-scores and various ...
user287446's user avatar
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0 answers
9 views

Which variables should I include/exclude in my regression analysis for GDP? [duplicate]

I am wanting to establish the impact mobile money has on Kenyan economic growth. I am building my regression model and have collected data for GDP, consumption, government spending, investment, net ...
Georgia's user avatar
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0 answers
13 views

False negative B coefficient following multiple linear regression? [duplicate]

I'm running a linear regression in SPSS to test for effects of a binary variable (X) on cost of hospital admission. The variable is correlated with a cost increase of around $3000W When the model has ...
James's user avatar
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Does a Fixed Effect necessarily mean a Fixed-Slope model in a Mixed Effects Model for Repeated Measures?

I'm trying to understand what "fixed effects" means in the following paragraph. "The SF-36v2 PCS score change from baseline to month 9 was analyzed as prespecified, using a restricted ...
Mandem's user avatar
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0 votes
1 answer
30 views

Understanding the significance of a few results derived in the course of linear regression

I am reading up on linear regression from 18.650 MIT. In the way of explaining it, the professor derives a few results and I have attached them in the image The first result gets used along with the ...
figs_and_nuts's user avatar
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1 answer
59 views

Obtaining P value in LASSO regularized linear regression showing that the model is generalizable

I have a problem. I am a biologist working in machine learning. Recently I am dealing with LASSO regularized linear regression. Very nice RMSE, MSE, R^2 values under all kinds of cross-validation. But ...
Mátyás Bukva's user avatar
3 votes
0 answers
52 views

Isn't $f(\mathbf{x}; \mathbf{\theta}) = b + \mathbf{w}^T \mathbf{x} = b + w_1 x_1 + w_2 x_2 + \dots + w_D x_D$ the linear regression model?

Chapter 1.2.1.5 Uncertainty of Probabilistic Machine Learning: An Introduction by Kevin P. Murphy says the following: We can capture our uncertainty using the following conditional probability ...
The Pointer's user avatar
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1 vote
1 answer
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What is the intuition for estimating residuals when boosting linear regression models?

So basically the title is my question. lin-reg model: $$y_i = x^{T}_i\beta + \epsilon_i, i = 1,...,n$$ Initalize $\hat{\beta^{[0]}}$ and the number of iterations $m_{stop}$. Compute: $$u = y - X\hat{\...
BlankerHans's user avatar
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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 ...
hahnbanach123's user avatar
3 votes
2 answers
89 views

How to select the "best" distribution of the errors in linear data?

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. $$\...
Justin Furlotte's user avatar
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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 ...
Joseph H.'s user avatar
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 ...
Taha Rhaouti's user avatar
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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 ...
Celongar's user avatar
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 ...
basementGenius's user avatar
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 ...
Abdul's user avatar
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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, ...
galpo's user avatar
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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 \...
BlankerHans's user avatar
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0 answers
32 views

Advantages of GLS Estimator for OLS in the Presence of Violated Spherical Assumption

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, \...
user346624's user avatar
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0 answers
32 views

How does correlation give better model predictability?

Does correlation give better model predictability. In case of using regression models, typically OLS, how does it help with the model predictability and what are its limitations. Any articles or other ...
user402101's user avatar

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