Questions tagged [regression-coefficients]

The parameters of a regression model. Most commonly, the values by which the independent variables will be multiplied to get the predicted value of the dependent variable.

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Relationship between β² and R² in regression?

I always thought that, in linear regression, R² is a measure of the proportion of variance of the criterion explained by all the predictors. As such, R² should always be equal to or larger than the ...
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Alternative to R$^2$ in linear regression without intercept

It has been extensively described in this website the reason why one cannot properly calculate the $R^2$ - neither the Adjusted $R^2$ - in regression models fitted without an intercept. What is a good ...
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Why are coefficient and standard errors zero?

I am having a problem with OLS regression. I am doing a relative time model (leads and lags model) to prove the robustness of my Difference in differences model. Problem is that some of my ...
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Total effect of main variable and it's interaction with dummy

I am going to estimate the following model: y=constant+b1(X)+b2(X)(Dummy) We have daily data from 1990 to 2000. Dummy variable is equal to one for the daily data of year 2000, else zero. b1 is the ...
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Coefficients for all levels of a categorical factor unchanged in lmer after adding variables

I was sent over here from stack overflow here: https://stackoverflow.com/questions/62635123/coefficients-for-all-levels-of-a-categorical-factor-unchanged-in-lmer-after-addi (sorry for posting there ...
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Interpreting a low phi-coefficient, but a high regression correlation coefficient

I'm conducting statistical analysis on two categorical binary variables. My phi-coefficient yields only 0.09 at a 0.01 significance level. However, when I conduct multiple logistic regression on the ...
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31 views

Can we bound $\frac{Cov(X,XY)}{Var(X)}$?

The question is can we bound $\beta = \frac{Cov(X,XY)}{Var(X)}$ with the help of the following assumptions : Y is a positive bounded random variable, let's assume $Y \in [0,1]$. X has an expectation ...
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Intercept interpretation in multi-level model when first-level predictor discrete

This is the experimental setup: 1 dependent variable (discrete, 4 levels) and 3 Independent variables: Time, measured within subject, 5 discrete levels Covariate, measured within subject, 5 discrete ...
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I am comparing the sex ratio of pheasants across Study Areas, (10), Release sites (26), and Years (13)

I am using Binary Logistic Regression and comparing Models using AIC. The Model is: sex ratio= study area + release site + years When I count the number of Parameters (K) in the Model -do I count ...
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To prove magnitude of regression coefficient is less in 1st model than in 2nd model

My intuition for solving the question is that when we regress the residual on X3 , we're basically regressing X1 after eliminating the Linear effect of X2 from it on X3. So the coefficient of X3 here ...
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How to interpret multiple interactions in lm

I'm wondering how to interpret the summary(lm) output in the context of multiple interactions. Here's some toy data with 2,000 observations, one dependent variable, ...
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What would be a good method to compare the results from my model to actual measurement data?

I have a complex physical model of an engine and I get certain outputs for a given set of inputs. However, these outputs are of course, not exact and deviate from the physically observed values for ...
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Regression for the dependent variable values given as intervals

What are optimal methods to find regression coefficients (I need many variable linear regression) when the information about values of the dependent variable is given in form of intervals? ...
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What is variance in coefficient in linear regression?

I would like to know why such uncertainty exists in linear regression exists? Why the parameters (or the regression coefficients) estimated can't be of certainty? Why there exist uncertainty such ...
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How to fit a sine regression curve of the form $f(x)=A\sin(Bx+C)$ to three data points?

Consider a sine function of the form: $$f(x)=A\sin(Bx+C)$$ Let's take a specific function: $$f(x)=2\sin(3x+4)$$ We can see that: $A=2$, $B=3$ and $C=4$ Let's take three random data points that would ...
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Resource for in depth “model checking” for multiple linear regression?

I'm looking for a book or resource that goes really in depth on the model checking and diagnostics for the multiple linear regression. Basically it goes into a lot of depth on how model assumption ...
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Relationship between Partial Correlation Coefficient and Coefficient of Determination

Let's consider multiple linear regression $E(Y|X)=\sum_i\beta_i X_i$. The only information I have is partial pearson correlation between $Y$ and every $X_i$, say $\rho_{Y,X_i}$. Now I want to estimate ...
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Regression: Simplifying Fama's test of UIP

Fama (1984) regresses the change in spot exchange rates in t and t+1 onto the difference of the spot and forward rate both in t and finds a significant negative association for most currencies. This ...
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How can a relationship be U-shaped when both linear and quadratic terms are positive and significant?

I have a predictor variable that ranges between 0-1, transformed to natural log due to multicollinearity and modeled with fixed effect negative binomial. Both the linear (B=9.9, St Error = 2.71, p<...
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Interpreting coefficients in Scikit-Learn

I'm experimenting with using SKLearn on some Spotify playlists. After doing the usual train_test_split I got these coefficients and am trying to draw conclusions from them: ...
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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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How to qualitatively understand interaction terms?

After many days of deliberation and looking up other similar posts I still feel that I'm missing something in my interpretation of interaction terms in regression. I want to double check to see if my ...
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Pooled OLS vs Fixed Effects regression

For my thesis, I'm currently comparing the effect of institutional ownership on the idiosyncratic volatility of stocks. My current approach has been to do a simple regression and including multiple ...
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Least squares fit of a bivariate quadratic-linear product to an oriented point set

As explained in this question, a bivariate quadratic has 6 DoF (coefficients), and a bivariate cubic has 10 DoF, while a bivariate quadratic-linear product has 8 DoF. The quadratic or the cubic models ...
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Coefficients not defined because of singularity - NOT because of dummy code error or multicollinearity

Variables are being removed from my analysis. I've looked at other questions for similar problems, but the answer always seems to be an error when creating dummy codes (i.e., not creating n-1 dummy ...
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Least-squares fit of explicit parabolic sheet to scattered data points [duplicate]

For a given set of data points $$\{(x_i, y_i, z_i)\}$$ there exists some $$f_{ABC}(x,y)=Ax^2+Bxy+Cy^2$$ that minimizes $$\sum_i(f_{ABC}(x_i,y_i)-z_i)^2$$ $A$, $B$, and $C$ can be found quickly ...
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How to improve Levenberg-Marquardt's method for polynomial curve fitting?

Some weeks ago I started coding the Levenberg-Marquardt algorithm from scratch in Matlab. I'm interested in the polynomial fitting of the data but I haven't been able to achieve the level of accuracy ...
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How to interpret brms output for binary logistic regression

So I have a binary response variable: $SP(0=\text{seronegative}, 1=\text{seropositive}, SP = \text{disease state})$ and I have just been playing around with my variables to understand what the output ...
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Telling which group's mean value is higher using lm()?

We have groups A,B,C and we try to see if their means are different. Below are the summary of the linear model fitted.Below you can see group A is the reference group.Can I say checking coefficient ...
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Techniques to estimate biasedness and sampling distribution of b0, b1, and $\sigma$ and confidence/prediction intervals when assumptions are violated?

This question is for the linear regression model. Let's say one or more of the assumptions are violated. For example, heteroskedasticity, autocorrelation, or non normality. I was wondering if there ...
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Linear regression changes in form when including other predictors

let $y_{i}$ be the response variable, and let $x_{i}$ be a predictor in a linear regression model. Suppose that we have the general model $y_{i}=B_{0}-B_{1}x_{1}$ now suppose that we include another ...
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Bias and variance calculation for Ridge estimator of β

I understand how bias and variance for ridge estimator of β are calculated when the model is Y=Xβ + ϵ. But I have the model Y=Xtβ + ϵ. I don't understand if a model like that makes sense, can someone ...
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OLS with multicollinear data and possible polynomial effects - what feature selection techniques would work?

I am new to regression modelling, have a dataset (vegetation health over time for ~250 sites) that I would like to model using OLS as a function of 5 continuous variables: light, pollution, humidity, ...
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Causal AR Model?

This questions is about necessary conditions (in form of inequality on coefficients) for the causality of autoregressive models. For instance, $|\phi_1| < 1$ is a necessary condition for an AR(1) ...
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Intercept and categorical variables

Suppose we have a linear model where ${variety_i}$ is an indicator for types of plant (A,B,C,D). $y_i = \mu + \beta{variety_i} + \beta_1 rain_i + \epsilon_i$ So we would have $\beta_A , \beta_B, \...
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Flip the sign of covariates in Cox model

I am just curious what will happen to beta (the coefficients) and its confidence interval when I flip the sign of the covariate (multiply all elements to -1) in Cox model for right censored data.
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Can the Poisson-Binomial distribution be used in a generalized linear modeling framework?

I recently came across the Poisson-Binomial distribution while doing some research for a modeling problem I have. I am trying to model the spread of an invasive species where I have county level ...
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How to Report a General Linear Model

I am currently analyzing whether several variables (age, gender, formal schooling, etc.) predict adults' understanding of the mathematical aspects of COVID-19 news coverage (n = 421). When I run a ...
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How calculate variance-covariance matrix of coefficients for multivariate (multiple) linear regression?

How to calculate a variance-covariance matrix of coefficients for multivariate (multiple) linear regression? Something like (equation below), but for the multivariate case. Being more specific I'm ...
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Rationale behind doing Regression + ARIMA(residuals) model?

I am looking at this model, which is used when the residuals of your typical least squares regression model is serially correlated. https://online.stat.psu.edu/stat510/lesson/8/8.1. I think on ...
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effect_plot, ggpredict, ggeffect: how to appropriately plot predicted values for a multiple linear regression?

I have a linear model with one main predictor of interest (GABA) and three covariates of no interest (BMI, Sex, Leg.Length): ...
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Interpretation of coefficients from multinomial logistic regression

I have run a multinomial logistic regression model with a four level response variable (walk, bike, bus and car) and two predictor variables being their gender (female/male) and where they live (urban/...
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Estimation of Parametric survival model in R [closed]

I fit an exponential survival model using flexsurv package. ...
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Transforming Logit to percentage and interpretation (Logistic Regression coefficients)

I have made a batch of Logistic Regression models concerning trends of plant species in a certain area. The model is as follows: ...
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If features are always positives why do we use RELU activation functions?

Sorry I'm a beginer. I understand the nature of non-linear vs linear activation functions, I know RELU basically filter the negatives inputs and only respond to the positive, but When does it happen ...
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Does the regression intercept capture the effect of the treatment year?

I read in a notes that runs the following regression $Y_{it}=\alpha+\beta_1D^{-1}_{it}+\beta_2D^{+1}_{it}+\gamma X_{it}+\epsilon_{it}$ $Y_{it}$ is some health index for individual $i$ in year $t$, $...
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How to conduct DFFITS and DFBETAS for a multiclass logistic regression problem?

Can anyone help me out how to conduct DFFITS and DFBETAS for a multiclass logistic regression problem? That is, do we have a software(preferably R) implementation of it? I also couldn't find the ...
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How can I compare coefficients in a Cox regression analysis from PCA features to the coefficients of categorical variables?

I am running an analysis on a Cox model where I used PCA features extracted from medical images to predict survival. However, when I examine the coefficients on these features they are very small. (...
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How to build a function with the result of arima in R?

I use: arima(y, order = c(3,1,1) in R to get ARIMA(3,1,1), result as follows: Call: arima(x = y, order = c(3,1,1)) Coefficients: ...

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