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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Reporting non-significant regression analysis?

As a result of attached regression analysis I found non-significant results and I was wondering how to interpret and report this. I am a self-learner and checked Google but unfortunately almost all of ...
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Removing NAs from multiple logistic regression coefficients in R (tidymodels)

I am running a logistic regression with about 60 variables. And some of my variables have NAs in their coefficients. There are no NAs in data though. I read this question and it makes sense for me, ...
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Include or discard non-significant coefficients in the total Y estimate/calculation?

In Y= b0 + b1x1 + b2x2 + b3 x1 * x2 where e.g. b1 is not significant. What is the correct estimate (calculation) for Y? Since b1 is not significantly different from 0, wouldn't a correct ...
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Where does this formula for the OLS estimate as a function of the true parameters come from?

Suppose that in the population: $$ y = \alpha + \beta_1 x_1 + \epsilon $$ We now estimate the model: $$ \hat{y} = \hat{\alpha} + \hat{\beta_1} x_1 $$ I have seen the following formula which writes the ...
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Writing OLS estimates as a function of real parameters in case of multivariate regression

Suppose that in the population: $$ y = \alpha + \beta_1 x_1 + \epsilon $$ We now estimate the model: $$ \hat{y} = \hat{\alpha} + \hat{\beta_1} x_1 $$ If we try to estimate $\beta$ using OLS, we have ...
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Variance of regression coefficients difference - approximating covariance

I have a following question. Let’s assume that we have a following linear model: $y = b_1x_1 + b_2x_2 + … + b_nx_n + b_m$ I would like to find a difference between coefficients with its accompanying ...
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If X^2 is not significant but X is significant, do I have to remove X^2 and run again the regression analysis?

Model DV ~ W+PDSR+Corr+(FAGDP1+FAGDP2)+log(PCGDP)+Exp+Pop+Health FAGDP2=FAGDP1^2 Result: After removing FAGDP2(FAGDP1^2) from the model, FAGDP1 turns to be insignificant Am I right in removing FAGDP^...
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Why T-test used in linear regression doesn't consider sample size

In case of hypothesis test we usually use z-test for larger sample size and t-test for smaller sample. but in linear regression analysis why do we always use t-test for individual coefficient even if ...
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Adding a constant to predictors for Log transformation

I have a dataset to predict customers' Churn that contains categorical and numeric variables. I intend to perform a Logistic regression. I want to apply log transformation to some of the numeric ...
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Explained variance score vs $R^2$ score

I came across explained variance score and $R^2$ score in scikit learn docs. Docs defines exaplained variance score as: $\text{explained variance} (y,\hat{y})=1-\frac{Var\{y-\bar{y}\}}{Var\{y\}}$ ...
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Directional derivative in regression (coefficients, after all, are partial derivatives)

The coefficients in a (let's stick with linear for now) regression are the partial derivatives. A regression equation is a function of several variables, so all of the multivariable calculus tricks ...
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The Frisch-Waugh-Lovell Theorem and a Regression Coefficient

I am wondering how the following statement holds. There is a two-way fixed effects model: $$ y_{it}=\alpha_i + \gamma_t + \beta D_{it}+e_{it} $$ where $\alpha_i$: individual-fixed effects, $\gamma_t$: ...
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Combining two slopes of linear regression

Let's say we have two linear regression results Y = a + bX + error X = c + dZ + error Why can't we just use 1) and 2) to deduce that slope of Y~Z = bd without having to do actual regression between ...
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Could a nomogram be built from meta-regression coefficients?

I'm trying to build a nomogram from meta-regression co-efficients. The meta-regression model is done using the metafor package. However, I would like to represent the results into a nomogram. The RMS ...
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Linear Regression: Multiplying the coefficient by the mean

I have a coefficient that represents per minute of watching videos. I am measuring against the dependent variable of exam scores. I also have the mean of the minutes of watching videos from ...
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(Why) Are stepwise regression coefficients biased?

Issues with stepwise regression are known to statisticians. It yields R-squared values that are badly biased to be high. The F and chi-squared tests quoted next to each variable on the printout do ...
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fit-coefficient for non-linear function

I have a sigmoid (growth) function, in python: def sigmoid(x, centroid, k, amplitude = 1): y = amplitude / (1 + np.exp(k*(centroid-x))) return y It is ...
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Coef and Polynomial equation

I have a problem about the coef of polynomial, from machine learning. ...
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1answer
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Logistic Regression - Feature Interpretation [duplicate]

I have fit a logistic regression to predict a given binary outcome, and the estimated coefficient associated with one of the features, feature $x$ let's say, has a value $\theta$. The interpretation ...
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Transform regression model with all logged terms to 'unlogged' form [duplicate]

I have two independent variables to predict my independent variable. For both theoretical and practical reasons, it made sense to log all of the three variables. In R formula: ...
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1answer
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Trouble with obtaining constant matrix to find variance-covariance matrix of regression parameters

I have been working on an exercise from Applied Linear Statistical Models - 5th edition- by Kutner. The question is asking me to obtain the variance-covariance matrix for a polynomial regression of ...
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Meta-analysis effect size conversion: regression coefficient to correlation coefficient (r)

I am trying to extract data from an article for a meta-analysis. I would like to convert the following information into a correlation coefficient (r): Pre-covid period: Nov 19 2019 - March 2 2020 (...
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Combine multiple regression models to create a new model, without having the original data

Suppose I have these linear regression models: Y given A (p-value=p1 << p2) Y given B (p-value=p2) Y given A, B, C (With A having a big p-value that shows A is meaningless in this regression, ...
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A coefficient test of poisson regression

I have a question for a coefficient test of poisson regression. That test uses a Wald statistic defined as; $$ W = \frac{\hat{\beta}-\beta_0}{\hat{se}(\hat{\beta)}} $$ where $\hat{\beta}$, $\hat{se}(\...
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Variance of coefficients in linear regression when responses are correlated

I have a linear regression problem given by: $Y = X\beta+\epsilon$, where $Y\in R^n, X\in R^{n\times k}, \text{and }\beta \in R^k$. Rather than assuming that the error is independently distributed, i....
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Predictor variable with opposite relationship than expected

I have run a GLM (negative binomial family) to test the effect of environmental factors on the longevity/duration (days) of turtle tracks left on beaches. Looking at the "Estimate" values in ...
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Calculating Pearson's CC from output of Dynamic Time Warping

I'm currently doing some hierarchical clustering of time series using correlation coefficient as a distance measure (or, a dissimilarity matrix based on 1 - absolute pearsons CC). However, I know ...
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Interpretation of coefficients in multivariate Poisson regression in terms of expectation

If I have a regression model $Y = \beta_0 + \beta_1 A + \beta_2 B$, where $A$ and $B$ are treatment indicators. Firstly, if I frame the definition of $\beta_1$ in terms of expectations, how do you ...
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what exactly does correlation mean [duplicate]

what exactly is a correlation of zero meant to be, does that mean that changes in x does not affect y, if that is the case, from the scatter plot That is completely false, as sometimes as x increases,...
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negative Coefficient interpretation

I have the following regression equation: deathrate=0.237 (incidencerate)-0.0006(medincome)+0.201(pctpublicoverage)+0.0002(popest2015)-1.044(Private coverage )+0.777(private employeecovarge)+ ԑ My ...
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Use dummy in the regression or not

I have the following data: The data shows information about prices for different kinds on different days (days are the same across the kinds). The volume shows the number of spare parts bought by the ...
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Comparing coefficients across segmented regression models given aggregated, heterogenous data

My goal is to compare $\beta_1$ across $7$ models: \begin{align*} Y^1_t &= \beta_0 + \beta_1 X^1_t + \epsilon_t \\ Y^2_t &= \beta_0 + \beta_1 X^1_t + \epsilon_t \\ &\vdots \\ Y^7_t &= \...
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Is there a way to use the covariance matrix to find coefficients for multiple regression WITHOUT intercept?

Given: $$ y=\alpha + \beta x $$ The problem on how to get regression coefficients $\alpha, \beta_0, \beta_1,...,\beta_n$ from the covariance matrix is solved here: Is there a way to use the covariance ...
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Difference between two coefficients

I have an unbalanced panel dataset for a list of firms for the period extending from 2000-2015. Set of standards issued in 2003, and the adoption is voluntary. Firms started to adopt in different ...
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Estimates from MCMCglmm multivariate regression

I'm running a multivariate regression on two response variables (X and Y) using MCMCglmm in R. X is a continuous variable (family = Guassian) while Y is a binary response variable (family = threshold)....
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Simulating slope coefficient for linear regression

I'm currently reading an article: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4302277/#S5title And in Section 5 I've come across a simulation for a few estimators of the slope $\beta_1$. I wanted to ...
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Interpreting mixed effects model results. Why are my coefficients for mixed effects model are so large?

I am an economics grad student and I am in the process of writing a paper disproving using the Gini coefficient as a solitary measure of income inequality in migration determinants analysis. I have ...
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Calculating the effect of trustworthiness on obtaining bank loan and on loan rate (interpretation question)

I am reading a paper that discusses how people's perception of borrower's trustworthiness affects his/her probability of loan approval, and also loan rate. This is from a RFS paper on page 2474 (2.1) (...
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MLE of regression coefficients depends only on correlation matrix and single-predictor z-scores

Assume a standard linear model $$ \boldsymbol{y}=\boldsymbol{X}\boldsymbol{\lambda}+\boldsymbol{\varepsilon}, $$ where $\boldsymbol{y}$ and the columns of $\boldsymbol{X}$ are standardized. In some ...
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multiple regression model having 2 independent variables [duplicate]

I run a multiple regression model having 2 independent variables. The R-squared value for my regression analysis on two predictor variables is 0.75. How do I interpret this value?
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How regression coefficients change when shifting the scale of the response variable

I am running a regression with y: a 7 point index ranging from -3 to 3, x: binary indicator (0,1) of second wave of data collection. When I fit this regression, I get the following equation: ...
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1answer
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Binary logistic regression coefficients

Consider the following MWE example. A dataset with only one feature (categorical feature with 4 different categories ['cat', 'dog', 'hamster', 'frog']) + target (overall 10% positive class). After ohe ...
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Why is a t statistic used for standardized regression coefficients?

I understand the sampling distribution of unstandardized linear regression coefficients is normal, and therefore a t distribution can be used to determine p values for given coefficient and standard ...
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What is the sampling distribution of the standard error of regression coefficients to get an accurate histogram?

I'm trying to fit the pdf on the variance of regression coefficients. I understand how to plot the regression coefficient estimates, the noncentral t-distribution, but I am always off for when I try ...
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What could be the reasons for regularized logistic regression coefficients are identical?

I found one logistic regression model I built have many identical (but not all) coefficients. I know it is possible to have following problems. Very strong regularization, that all the coefficients ...
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Regression coefficients for (un)known $\sigma_x^2$

I'am currently reading an article A Paradoxical Result in Estimating Regression Coefficients (can be found here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4302277/#S2title) and at the end of the ...
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How to determine the parameters of a linearized model when the line has negative slope and intercept?

I have the following data: Sample $t$ $q_t$ $\ln\left(q_e-q_t\right)$ A 0 0.00 0.31 A 60 0.97 -0.92 A 90 1.30 -2.71 A 120 1.33 -3.40 A 180 1.28 -2.48 A 240 1.35 -4.09 A $q_e=$ 1.37 B 0 0.00 0....
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Different values for intercept estimate in linear regression

I'm reading about linear regression from two sources. In here: https://online.stat.psu.edu/stat415/lesson/7/7.3 the estimate for the intercept is just $\bar y$. However over here: https://www....
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Visualizing time series regression results in a causal framework

Suppose I have a set of independent variables that I believe to, collectively, cause the observed level and changes in the value of the dependent variable, and I have the results of a regression of ...
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Graphing Regression Results with Insignificant Coefficients

Consider investigating an interaction using a linear regression with the specification: Y = β0 + β1X + β2M + β3X*M + e Where: $$ \begin{array}{c} & \text{Coefficients} & \text{Sig.} \\ \...

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