Questions tagged [regression]

Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.

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is it possible for odds ratios' or risk ratios' confidence interval to contain 1 and still be statistically significant?

my understanding is that if a 95% CI for odds ratios and risk ratios contains 1 then it is not statistically significant. However I have seen in studies such as https://pubmed.ncbi.nlm.nih.gov/...
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When does R-squared in multiple linear regression equals the sum of the R-squared from two simple linear regression?

I know that in the simple linear regression, the $R^2$ is just the sample correlation between the response and covariate. My question is that suppose I fit a linear regression by using two covariates, ...
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What estimation methods other than ordinary least squares guarantee the orthogonality of predictions and residuals?

From my question here, it is evident that estimation approaches to linear regression other than ordinary least squares can result in the predictions and residuals lacking orthogonality, despite the ...
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If residuals are serially correlated does that mean they are normally distributed

In linear regression if the residuals are serially correlated does that mean then that they are normally distributed
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Correction for multiple comparisons using sum contrasts with linear regression

I am computing the following model using the lme4 package in R: ...
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How to calculate variance of AR(1) process

I have a stationary AR(1) process: $Z_t = \alpha_{1}Z_{t-1} + \nu_{t}$, where $\nu_t$ is white noise and $|\alpha_1| < 1$. I have to show that the variance of $\Delta Z_t$ is $$V[\Delta Z_t] = 2\...
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Why same t-score for contrast pairs involve continuous x continuous interaction (emtrends)?

I want to calculate the difference in simple slope estimates for two-way interactions that involve two continuous variables. But I found the t-score is all the same for the contrast-pair results when ...
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regression plots for each group separately [closed]

I want to plot regression lines for each group separately. Each group's regression plot as 1 plot. I have around 100 groups. So it will be 100 plots. Can this be done automatically without selecting ...
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How I can choose best regression model on my data? [closed]

[I want to find the best fit curve or model for my data and my data follows the following pattern. I have tried the curve fitting tool on Matlab but no model fits precisely on the data. Could you ...
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Beyond R2: Is there a better way to assess my regression?

I wondered if someone could offer some advice on the following problem that I have been puzzling over. Sorry if this is a basic question. Problem: I have two sets of data and I need to build a linear ...
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Does multicollinearity among control variables matter?

I am conducting a regression analysis between X and Y, where X is the main independent variable. However, I want to control for several variables that are related to Y. For example if my dependent ...
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Why does the estimation of the variance of the outputs in linear regression include the fitted values?

I was revisiting my notes about the classical linear regression model, $Y = X \beta$. If we want to estimate the variance of the least squares estimator we usually suppose that the outputs $y_{i}$ are ...
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Derivation of the variance of the ${\hat{\beta}}$

First of all, thank you so much for all the input and for pointing out my mistakes. I made some corrections and try to add more details in my problem. Edit 1: I was trying to derive the variance of ${...
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Simple Linear Regression Question: How does correlation between X and Y affect MSE?

Suppose we know that the correlation between $X_1$ and $Y$ is $\rho_{X_1Y}$ and the correlation between $X_2$ and $Y$ is $\rho_{X_2Y}$. Furthermore, suppose $0 < \rho_{X_2Y} < \rho_{X_1Y}$. Now, ...
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Calculation of leave-one-out cross-validation statistic in linear regression when design matrix is square

Suppose we are performing a least-squares multiple linear regression of the form $$ \mathbf{Y}=\mathbf{X}\boldsymbol{\beta}+\boldsymbol{\varepsilon}\,, $$ where $\mathbf{Y}=(y_1,y_2,...,y_N)$ are the ...
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Understanding multiple linear regression residuals

I'm a bit confused whether residual vectors in OLS are orthogonal to every vector in X. The problem I have is: Which of the following are true statements for our multiple linear regression with ...
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Exercises for Linear Regression Models

I am looking for exercises (more theoretical than applied) about linear regression models. Maybe you can advice me where I can find such exercises. Here is what my linear models course deals with if ...
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Model validity for Ordinal logistic model

I am doing a study using OLR. The model tries to assess the satisfaction of ground level stakeholders (scale of 1(extremely dissatisfied) to 5(highly satisfied) in an urban area. The independent ...
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log of average or average of logs for regression?

I have to perform regression for product prices over a period of time and I have to do so for multiple categories. For eg. Category_1 includes prices of item_1, item_2 and item_3 over a period of time,...
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Detection of Multivariate Outliers (in a multiple linear regression problem) [duplicate]

In a multiple regression problem, suppose we have responses $Y_1, Y_2, \cdots , Y_n$ corresponding to data $\mathbf{X}_1, \mathbf{X}_2, \cdots, \mathbf{X}_n$ where each $\mathbf{X}_i$ is a $d$-...
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on the rank condition of regression model with cross validation

Consider a standard linear regression model in a matrix form given by \begin{equation} y=X\beta+u \end{equation} where $y$ is $n \times 1$, $X$ is $n \times k$ with $n>k$. Assume that $X$ has full ...
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Zeros in Dependent Variable : Bad- Zeros in Independent Variables: Not Bad?

I am an MBA Student taking courses in statistics. We have been learning about regression models for count data. Recently, our professor has been talking about situations in which there are a lot of ...
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Do I need to include the information (Pvalue) of confounders in the final table?

I was wondering if I need to provide a regression table including the estimation of all main varibales + confounders? Can I just present the final result (coefficeint and pvalues) of the main ...
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Performing deconfounding using multilinear regression for select number of variables

I'm trying to perform a correction on my data so I can use deconfounded residuals in later analyses. My data object is a subject by observation matrix (each subject has i observations - if it helps ...
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calibration according to Kuleshov

i was reading this paper https://arxiv.org/pdf/1807.00263.pdf in which Kuleshov gives a definition of a well calibrated neural network in a regression task I would like to ask one thing: why does he ...
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Interpretation of coefficient in log-level regression [duplicate]

The result of my panel study with log-transformed dependent variable l_passengers results in a coefficient of 1.15076 of my independent variable lccshare. I'm not quite sure how to interpret this as ...
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Classification email newsletter imbalanced

I'm given a case to determine the best time to send an email newsletter based on whether the email is opened. The problem is that over 70% of the emails are sent on Tuesday and the dataset is ...
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How to perform multilevel regression on Y?

We know multiple linear regression has the equation $$ Y_1 = \beta_0 + \beta_1x_{11} + ... + \beta_k x_{1k} + \epsilon_1 \\ Y_2 = \beta_0 + \beta_1x_{21} + ... + \beta_k x_{2k} + \epsilon_2 \\ \dots \...
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One of the main effects not significant, but interaction term significant

A is significant B is not significant A x B is significant Do I say that (1) There exists a ...
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For ecological data, when is a gaussian distribution appropriate?

This may seem like a very basic question, but is something I have become more confused about the more I read. Say I have a dataset with morphological measurements of various plant traits (e.g. leaf ...
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How to determine if the log likelihood of logistic regression is too large or not?

I am running a logistic regression on STATA with binary response variable, and 2 predictor variable that are discrete, as such one is in % (but takes only 2 values strictly i.e., 5% or 10%) and ...
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Prove that the sample covariance between observation and OLS fittings are nonnegative

I am trying to show that $$\frac{1}{n} \sum_{i = 1}^n (y_i - \overline{y})(\hat{y}_i - \overline{\hat{y}}) \geq 0$$ where $y_i$s are the observations, $\hat{y}_i$s are corresponding LS fitting values, ...
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Build three models in one study

I build three models. First model has two mediators, one is not significant, then I removed it from the second model. The second one has one moderator and one mediator. The third one has another ...
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What is the best model selection method for high-dimensional linear regression?

Model selection (best subset selection) in linear regression is quite important in many applications. Among the methods belonging to different frameworks such as information criterion, hypothesis ...
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Simulated data for logistic regression

I used the code below to create the random variable x1 and binary variable y, and fit the regression with y and x1. My questions are: Why regression coefficient estimates are not close to 2 and 10 (...
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What is better OMP or LASSO?

Variable selection in linear regression models is quite important. In this regard, the orthogonal matching pursuit (OMP) is a classical greedy approach to variable selection. On the other hand, LASSO ...
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Calculate uncertainty of surface normal based on points uncertainty

How to calculate angular variation of fitted plane from points that has positional uncertainty with normal probability distribution? For example, I have 4 points P1 = 102.0000 84.0000 139.5443 P2 = ...
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Knockoff filters simple explanation and importance!

Knockoff filters are new in the field of variable selection. Can someone provide (or refer to) a slightly simple understanding of the topic? Also, what is the fuzz about this new method compared to ...
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Controlling for Variables in Binary Logistic Regression

How do you control for variables such as gender within a binary logistic regression? I have a yes/no dependent variable with several variables that are also either yes/no. I'd like to control for ...
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Why linear mixed effect regression over multiple linear regressions for individual random effect?

I have a dataset on green-up days pan-Arctic and relate this to weather variables. I therefore want to use a linear mixed effect model where region (e.g. Alaska, ...
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Expression of $\hat{\beta}_1$ in term s of $\beta_1$ in simple linear regression

I'm reading a pdf document about simple linear regression, and it gave an expression of the least square estimator $\hat{\beta}_1 = \beta_1 + \frac{\sum^n_{i=0} \epsilon_i (x_i - \bar{x})}{\sum^n_{i=0}...
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I want to plot regression lines for each group separately in different plots. I have around 100 groups [closed]

I want to plot regression lines for each group separately. Each group's regression plot as 1 plot. I have around 100 groups. So it will be 100 plots. Can this be done automatically without selecting ...
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1 vote
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Multicollinearity Market mix modeling

I want to know what can be the best approach to handle multicollinearity. I am building a regression model with just 4 independent but all important variables and am not able to control the VIF. ...
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Is it incorrect to calculate residuals directly from a phylogenetically-controlled linear regression?

I would like to calculate the residuals from a regression of log body mass and log brain mass, controlling for phylogeny. I originally used phylolm in R to run this regression, under a Brownian Motion ...
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How to train a ML pipeline with a classification model followed by a regression model for a given class

I am trying to create a pipeline that has 2 distinct models: a multiclass-classifier and a regressor. The main goal is to predict for 3 different classes using the classifier and if the output belongs ...
3 votes
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How can I compute correct standard errors after implementing the FWL Theorem?

I am trying to implement the FWL theorem for some sample data in Stata. This theorem tells us that given a multivariate regression of the form $y = \beta_{1}x_{1} + \beta_{2}x_{2} + \varepsilon$, the ...
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Does one need consistent estimate of "$S$" in ordinary least squares for unbiased, consistent fixed-effects level-one estimate and correct inference? [closed]

What is a complete list of the usual assumptions for linear regression? says that one obtains a Consistent Estimate of $S$ when the regressors have finite fourth moments. $$ \hat{S}=\frac{1}{n} \sum_{...
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Reasoning about modelling uncertainty w.r.t input

I am trying to build up my reasoning about uncertainty modelling and ways of modelling it. What I am trying to essentially get at is how changes in input variables results in different posteriors(...
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What parameters of a neural network should be changed when increasing the number of training samples?

I was testing a DL model (GNN with two GCN layers and one linear layer) on a small dataset for a regression purpose, the resulted MAE and the scatter plot showed some really good results. However, ...
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For linear regression, why do people usually standardize the X variables and log transform Y variables to make them normally distributed?

In many Kaggle competitions where linear regression has been applied, I see people plot the y distribution and then take the log of (or other transformation of) the dependent variable to make y normal ...

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