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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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Dealing with oversized effects in Linear Regression

I'm learning about GLMs and interpreting regression coefficients and so I'm experimenting with simulated data and pymc3. I've synthesised a dataset where X is an array of 5 normally distributed ...
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Interpreting Median Absolute Deviation score [on hold]

I am Playing around with walmart recruitment dataset. I am getting Median Absolute Deviation score as 9457 and the random model score as 12456. I know that the model is a pathetic model just wanted to ...
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In linear regression, are the regressors correlated with coefficient estimates?

Consider a gaussian linear model with random regressors $X_i \sim N(\mu_X,\sigma_X^2), 1 \leq i \leq n$, i.i.d. $Y_i | X_i \sim N(\beta_0+\beta_1 X_i,\sigma_\varepsilon^2)$ Are either of the ...
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Is it appropriate to use 3 linear regressions to assess the impact of one common independent variable?

I need to assess the impact of cultures on urban economies. The hypothesis is that more entrepreneurship oriented culture will better facilitate the local economy, controlling for other factors (that ...
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28 views

Interpretation of higher coefficient for group with smaller mean

I am running a fixed effects poisson model with robust standard errors in STATA (xtpqml). The model I run it on has my count data as dependent variable and then as my independent variable I have a ...
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2answers
6k views

Testing a regression coefficient against 1 rather than 0

Brief caveat- I haven't dusted off my stats knowledge since some university courses a few years ago, and I'm struggling with cobwebs. I have a model where a linear 1 to 1 relationship has been ...
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1answer
131 views

Heteroskedasticity Question

I have a model that's affected by Heteroskedasticity: bptest(m1) studentized Breusch-Pagan test data: m1 BP = 65.055, ...
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1answer
82 views

Coefficient marginal to interactions in linear regression

Consider this model: $$y = \beta_0 +\beta_1x_1 + \beta_2x_2 + \beta_3x_1x_2 + \varepsilon$$ Somebody told me today that the coefficient for the main effect of $x_1$ (i.e., $\beta_1$) will be '...
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In linear regression, any intuitive explanation why duplicating samples will reduce coefficients' std-dev? [duplicate]

I read the explanation by Ocram here about how to calculate the stddev of coefficients in linear regression. I also run experiment with my sample data. I have test1 which contains 1000 samples; I ...
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Interpreting Logistic Regression Categorical Coefficients

So I have this question: If we fit a logistic regression with categorical predictor X with categories A, B and C, and have the estimated coefficients β0=−2.5 and βB=0.5 and βA=−0.2. (a) Interprete ...
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1answer
48 views

how to interpret/report estimated spatial lag coefficients

I estimated a spatial lag model with pysal. I want to know how to correctly interpret and report the resulting parameter estimates (given that spatial spillover exists). R's ...
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812 views

Why may results from model with interaction term and stratified model be different?

Suppose I wanted to explore the relationship between smoking (X; yes/no) and an disease outcome (Y; eg. visual analogue scale of depression from 0 to 10). But, I know that irrespective of X, Y is ...
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166 views

Does the high coefficient of determination in this graph predict a huge spike in global warming? [closed]

I have had three semesters of college statistics as part of my BSBA degree. From what I recall from regression analysis the graph seems to show a very high coefficient of determination between CO2 ...
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1answer
145 views

Why doesn't standardization work in the linear regression?

I have a matrix containing the attributes of the item and their corresponding rating. All of the attributes are in the range of (0,1) and the rating is in [1,5]. I transform the range of rating to (0,...
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Why is the intercept in multiple regression changing when including/excluding regressors?

I have a seemingly naive question regarding the interpretation of the intercept in multiple regression. What I found several times is something like this: The constant/intercept is defined as the ...
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1answer
204 views

F-statistics and coefficient p-value of model with only one variable

F-test tests the null hypothesis that all coefficient of variables in the model equal to zero. P-value in a hypothesis test shows the probability of having observed results if null hypothesis is ...
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Converting coefficient of slope to autoregressive factor

I realize this is very fundamental. I apologize. Is there any way to convert the coefficients from a linear model into the decay factor if i want to express it as an autoregressive model? For a ...
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Interpretation of a quadratic term on a log transformed target variable

I've done some searching and found several posts related to this, e.g.: In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values? Suppose I ...
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Interpreting statistical significance

Suppose I repeatedly run the same regression model for a set of individuals and I am interested in determining whether a given independent variable has a statistically significant impact on the ...
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1answer
32 views

Get odds ratios with confidence intervals from a lasso regression model

I try to understand lasso regression. So far, I do understand that it can be used to shrink regression coefficients in case of few events. The coefficients of some covariates are even shrunk to zero. ...
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Interaction term and main effect multicollinearity [duplicate]

If I have the predictors $X$, $Y$, and $XY$ to fit a linear regression model. Won't I be increasing the standard error of the regression coefficients? This is because $XY$ is collinear with $X$ and $...
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In Simple Linear Regression $\hat \beta_1$ and $\bar Y$ are independent [duplicate]

I want to show that, in simple linear regression $\hat\beta_1 $ and $\bar Y$ are independent. My attempt: I have calculated the $\mathcal Cov(\hat \beta_1,\bar Y)$ and it turns out to be $0$.I also ...
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56 views

Quantile regression and linear regression coefficient comparison

I am trying to understand the concept of quantile regression by modelling the monthly expenditure on insurance on several variables. The R package ...
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1answer
145 views

Provide a precise and concise statement on what a simple linear model is

I have recently commenced a 2nd-year course on linear models and have been a little overwhelmed by either the abuse of notation or the lack of clarity behind what a linear model is. I've read multiple ...
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137 views

Attempting to interpret both Beta Regression and transformed DV model results

After reading a good amount of the answered questions on interpreting Beta Regression results (Best explanation here) and reading through the Betareg vignette, I still feel a lack of confidence ...
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How to perform a multiple non linear regression without knowing the functions for each variable and the constraints for their coeffcients?

I have a data for number of cars and its causal variables are identified as GDP, population, urban fraction and fuel price but they have non-linear positive correlation but I don't know what that is. ...
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compare coefficients from different regression

I estimate the following models using the Hausman-Taylor estimator: $$y_{i,t} = a_{0} + B_1 controls_{i,t} + \beta_1x_{i,t=2000} + B_2 Year_t + B_3 x_{i,t=2000}*Year_t + e_{i,t}, (1) $$ $$y_{i,...
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Log level model - do I exponentiate all coefficients for interpretation?

I'm working with a regression model where I have a log transformed target variable due to the distribution of the log transformation being more normal. I have some numeric variables and also some ...
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1answer
40 views

Does High Information Value (IV) for a variable implies high coefficient in logistic regression?

I'm performing a Logistic regression for a binary classification task. As a preprocessing technique I use a transformation with WOE and Information value(IV), but I found something counterintuitive ...
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1answer
162 views

Multiple Linear Regression Output Interpretation for Categorical Variables

I'm a bit confused on interpreting the coefficient estimates for a multiple linear regression model with categorical variables and their interaction. The dependent variable is pesticide levels (DDE ng/...
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1answer
61 views

Test significance of weighted average of multiple regression coefficients from different models

I have 3000 independent time series samples (customers) where I fit a dynamic regression model with ARIMA errors to each sample and estimate regression coefficient of interest (intervention), $B_1{_i}$...
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21 views

Linear Regression with Changes

Consider two variables with levels over two time periods $\{y^i_t,x^i_t\},\{y^i_{t+1},x^i_{t+1}\}$. For example, it could be profit and cost data of various firms over two quarters. Suppose I take ...
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What is the difference between using random intercepts and slopes instead of separate regressions per subject?

I have recorded a DV and IV of 20 participants. The IV is a repeated measure, and my goal is to see how variation in the IV can explain variations in the DV. More specifically, I want a beta ...
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1answer
228 views

Decomposing $R^2$ into independent variables

Consider a linear regression model: $$y = β_0 + β_1X_1 + β_2X_2 + ... + β_kX_k + ε$$ where $R^2 = 1 - (SSR/SST)$. I would like to determine the contribution of a factor $i$ (call it $R^2_i$) into ...
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1answer
221 views

CUSUM test for regression model

I guess my question is rather basis. Unfortunately, I still did not manage solve it, although searching for hours. I have a linear regression model and need to do a CUSUM test for parameter stability....
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Spatial Lag or spatial Error Model? Deciding by using the Lagrange multiplier diagnostics

Honestly, my knowledge of geostatistics is limited. My assumptions are as follows: If I want to choose between a Spatial Lag Model (SLM) and a Spatial Error Model (SEM), I can use the Lagrange ...
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Intuition for nonmonotonicity of coefficient paths in ridge regression

Intuitively, why may some of the slope coefficients in ridge regression increase in magnitude when the penalty parameter $\lambda$ is increased? Or in other words, why are the coefficient paths ...
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1answer
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Selected variables varies depending on whether or not standardization is in lasso regression (glmnet)

The paper often suggests both standardized and unstandardized coefficients in the lasso model (glmnet in R). However, when I run glmnet, the selected variable is different depending on standardized =...
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1answer
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Capturing effects / Controlling for variables [duplicate]

I understand the idea behind regressions and know how to interpret them, however, when I hear the term "capturing the effect of.." or "controlling for.." so far I've just accepted it without ...
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1answer
57 views

Regression with related coefficients

I've worked out that some physical process has the form $y = ax_1 + (1-a)x_2$, and would like to perform regression to find $a$. I thought about multiple regression of $y$ on $x_1$ and $x_2$ and ...
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223 views

Testing the equality of Beta Estimates from Multiple (>2) Quantiles in Quantile Regression

I'm trying to determine whether Beta estimates at different quantiles obtained using quantile regression (quantreg package in R) are statistically different from ...
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257 views

Cross model comparison of quantile regression coefficients

I am looking for a way to compare coefficients obtained from quantile regression. The two surveyed models are nested, estimated on the same sample and for the same quantile. $$ Y = \beta_1X+\epsilon_2\...
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13 views

SVM as linear equations

I'm using SVM for a regression problem (sklearn.svm.SVR). After I train my model I use these 2 attributes svr.coef_ and ...
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29 views

How to compare LME regression coefficients across models with same variables but different sample sizes/trial numbers?

I have a quite specific situation that does not seem to be covered by other, similar posts: I ran a study where a task (Task A) was periodically interrupted by a probe that asked participants what ...
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14 views

Using a subset of parameters in joint confidence region of a linear model

For a standard linear model of the form $y = X\beta + \epsilon$, where $\beta$ is a vector of parameters. we can calculate an individual confidence interval for each parameter (of 1-$\alpha$ quartile)....
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How to interpret the resulting negative regression coefficient? [duplicate]

How to interpret the resulting negative Poisson's regression coefficient? I am investigating the effects of environmental factors on mortality. A negative regression coefficient means feedback (proves ...
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1answer
25 views

How can I compute the standard error and confidence intervals for the base level on a variable?

I'm running a GLM with a tweedie, log-link function. That said, I have a categorical variable that transformed to dummy variables leaving off one of those variables when I modeled. Now that I'm ...
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452 views

Standard Error of simple linear regression coefficients

dear members, I have been troubling myself with this question for the past few days but have not found any answers on the Internet: For a simple linear regression, you get the estimates ...