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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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lmer: standardized regression coefficients

I have analyzed some data (the exact nature of which, I assume, is irrelevant for this question) using linear mixed effects models with the lmer() function from lme4. There has been at least one ...
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Are t tests of coefficients in multiple regression post hoc tests?

In multiple regression, if a global F test is significant, then are t tests (or Wald tests) for the coefficients considered to be multiple comparisons and post hoc tests and should they be adjusted?
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Linear regression without intercept - sampling variance of coefficient

I am comparing linear regression with and without intercept for the general sampling case. For this, I have $n$ samples of two correlated random variables $X \sim N\left(0,\sigma_X^2\right)$ and $Y \...
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How can I interpret coefficients of categorical predictors in the negative binomial regression model?

I used some categorical variables as predictors to a negative binomial model. The dependent variable is numerical. I used glm.nb in R and the results show relative coefficients of one category ...
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Will larger correlation coefficient values result in greater slopes between x and y?

For example, if there are two data sets, and the first has a larger correlation between x and y than the second, does this mean the first data set has a greater slope than the second?
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Interpretation of coefficients in polynomial regression for predictive modeling

I am building a predictive model (binary target variable) in the financial services industry. One of the (many) potential predictors I am adding to the model is related to the customers checking ...
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4k views

Comparing coefficients in logistic regression

I have some problems I need help with. I am running a binary logistic regression. ...
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3answers
3k views

How to read the Interaction effect in multiple linear regression with continuous regressors?

If the interaction happens between a continuous and a discrete variable it is (if I'm not mistaken) relatively straightforward. ...
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In R, test whether coefficients in lm are different each to a given value (other than zero)

In R, is there a way to use the lm function to test for the hypothesis that the coefficients are different from a value other than zero? For instance, if the model ...
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How to interpret regression equations with logarithms, based on log difference being approximate to percentage change?

$y = 4 + 2.5\,x + u$ For an increase of 1 unit of $X$ (that is, $X$ to $X+1$), we expect an increase $2.5$ units of $Y$ (that is, $Y$ to $Y+2.5$). Is that right? What if there's a/an $\ln$? $\ln(y)...
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1answer
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Standard error for the sum of regression coefficients when the covariance is negative

I have a question about appropriately calculation the standard error for the sum of two coefficients in a linear regression model. My question is similar to this and this, but I can't seem to solve ...
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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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366 views

Model stability and variability

I am using polynomial regression to predict mean occupancy in a hospital unit using average length of stay (LOS) and arrival rate to the unit. I am using different percentages of training sets to ...
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1answer
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If the f-test is insignificant but coefficients are significant, can I use it?

If the linear regression's f-test is insignificant but its coefficients are significant in t-test, can I use this regression and its coefficients? In academic journals, I find people use linear ...
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1answer
240 views

Interpreting ordinal GEE coefficients

I have a dataset with an ordinal dependent variable (iws_w) with a range of -3 to +1. I placed it, with two independent variables in an Ordinal Generalized ...
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Is it valid to solve an equation for multiple coefficients, then average them to obtain overall effect?

I have a regression model, the setup for which is as follows: I am using manyglm, a multivariate general linear model approach to determine the difference in several invertebrate species between two ...
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If all components of a hierarchical model have not converged, can we say that any parameters have truly converged?

I'm working with a hierarchical regression model of the following form similar to that presented in Peter D. Hoff's book, A First Course in Bayesian Statistical Methods: $\boldsymbol{Y}_j \sim \text{...
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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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Test statistic for regression slope in terms of correlation

Consider two data series, $X = (x_1, x_2, ..., x_n)$ and $Y = (y_1, y_2, ..., y_n)$, both with mean zero. We use linear regression (ordinary least squares) to regress $Y$ against $X$ (without fitting ...
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Interactions - using ratio of variables

I have 3 variables, colony size, colony age and growth rate (colony size/age). I am interested to predict various other properties ($y$) of a colony using these 3 variables; $y = a_1 \text{ size} + ...
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Coefficient Significance in Regression with Arima Errors

In the R package forecast, when you run dynamic regression (regression with arima errors), the coefficients and their standard error are output, but there is no significance test available for the ...
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1answer
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How do I interpret interaction effects in a log-log regression model?

I have the following model: $\log(y)=\beta_0 + \beta_1 x_1 + \beta_2 \log(x_2) + \beta_3 x_1 \log(x_2) $ In interpreting the % change of $y$ that corresponds with a 1% increase in $x_2$ at a ...
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Coefficient of multiple correlation for multiple linear regression with degree > 2 and interaction terms

I want to calculate the Coefficient of Multiple Correlation $R^2$ for a multiple linear regression with polynomial features of degree >= 2 (with interaction terms). Let's say I want to obtain the ...
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Regression coefficients significance

What are theoretical reasons to keep variables which coefficients are not significant? I have several coefficients with p > 0.05. What's causing large p values?
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What is the formula for the beta coefficients in logistic regression?

I am doing a study about logistic regression. I have to write a program for the admission process of the school. The result is passed or failed. ...
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Converting the beta coefficient from matrix to scalar notation in OLS regression

I've found for my econometrics exams that if I forget the scalar notation, I can often save myself by remembering the matrix notation and working backwards. However, the following confused me. Given ...
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1answer
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Time varying coefficient in Cox model

I have a model for survival after an injury that is borderline passing the Schoenfeld test for the proportional hazards assumption (cox.zph() in R). However, ...
6
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1answer
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How to do permutation test on model coefficients when including an interaction term?

Given the following model as an example: $$Y=\beta_0+\beta_A\cdot A+\beta_B\cdot B+\beta_{AB}\cdot A \cdot B+\epsilon$$ In alternative notation: $$Y\sim A + B + A: B$$ The main question: When ...
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Comparing coefficients of time series models

How do I test if two time series' coefficients differ significantly from one another? I feel like this should be pretty simple... should I just use the estimates/standard errors and calculate a Z-...
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Can I calculate Cohen's $d$ from multiple regression coefficient?

Question: Is it appropriate to calculate Cohen's $d$ (effect size) from the regression coefficient of an independent categorical variable? Background: My regression coefficient represents ...
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1answer
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Interpretation of coefficients in logistic regression output

I am doing logistic regression in R on a binary dependent variable with only one independent variable. I found the odd ratio as 0.99 for an outcomes. This can be shown in following. Odds ratio is ...
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0answers
256 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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1answer
482 views

Averaging LASSO coefficients for repeated random partitioning of data

Is it reasonable to average LASSO coefficients from repeated reshuffling of training/test sets? Suppose I randomly divide my data into testing & training sets, then within the training set use 10-...
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1answer
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Zero regression coefficient when correlations are not zero

I don't really have a motivation for this - but I was thinking about this and couldn't work it out. Suppose I have a random variables $X$ and $Y$ which are correlated. Is it possible that the ...
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2answers
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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
213 views

Uniqueness of $x'\beta$ even when $\mathbb{E}(x^Tx)$ is not invertible

As discussed in user25658's answer to this question, when one wants to compute $$ \beta = \mathbb{E}(x^Tx)^{-1} \mathbb{E}(x^TY) $$ but $\mathbb{E}(x^Tx)$ is not invertible, $\beta$ is not uniquely ...
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540 views

How to interpret logistic regression coefficient

How do I interpret a regression coefficient in a logistic regression with two predictors? $\hat{L} = -14.27+3.32(3)+0.88(7)$ My understanding is to take the anti-log of the coefficient, like $e^{3....
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How can I get information about coefficient std. error, t value and p value for Regularized Linear Model

In R we can get a lot of information from summary model. ...
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1answer
487 views

Is there something called “mean coding” (like dummy coding & effect coding) in regression models?

When we perform a regression analysis with categorical predictors, we can use (1, 0), called "dummy coding". The coefficients in this case represent the deviation of the groups' means from the mean of ...
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1answer
135 views

Why do descriptive statistics contradict with regression coefficents?

I am estimating a binary logistic regression with L1 norm. According to the regression coefficients, the sign of x1's ...
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1answer
122 views

Linear regression with error dispersion dependent on the independent variable

Suppose $y=ax+z$ where $x, y, z$ are random variables with range in $\mathbf R$, $\mathbf E[x]=0$, the probability distribution $p(z|x)$ is 1) normal distribution $N(0,\sigma(x)^2)$ with mean $0$ ...
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1answer
510 views

Co-variance of beta coefficients for Dummy Variable regression with intercept

If I have a dummy variable regression output with intercept included (base category as omitted category), and I have to do a hypothesis test for difference of means between two categories other than ...
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1answer
315 views

Backtransforming the vertex of a quadratic function

I have created a model for which it was necessary to scale my predictor values by subtracting by the mean and dividing by the standard deviation of the X values. This resulted in variables centered ...
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1answer
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Binary logistic regression: interpretation of explanatory variables

I have performed a binary logistic regression in R using the glm command and family=binomial. The dependent variable (DV) is not re-contracted = 0 or re-contracted =...
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2answers
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continuous vs categorical logistic regression for marks and admission

I have a list of marks scored by students in Science (X, between 0 to 100%) and whether they went to college to or not (Y). High marks in science showed a higher concentration of college admits and ...
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2answers
152 views

Regression with log transformation of dependent variable that has negative values

I am working with a dataset that contains: a dependent variable (DV) taking both positive and negative values a binary independent variable (IV). And I'm interested in the following specification: ...
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1answer
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Updating regression solutions for a new regressor without the original dependent variable

Note: This question is analagous to the question I asked here except instead of a removing column, I am adding it. I am interested in a linear regression on the model; $Y= X\beta + \epsilon$ And I ...
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2answers
787 views

Interpreting main effect coefficient in different models

My interest lies in finding the "right" correlation between a continuous IV ($x$) and a continuous DV ($y$). At first I ran a simple linear regression: $$ y=a+b_1 x $$ However, lots of other factors ...
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2answers
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Interpretation of β in case of log-lin model for relationship between X and Y

In many papers, the dependent variable is transformed by taking natural log. For instance, consider the following model: $$\newcommand{\Cov}{{\rm Cov}} \ln(\text{Y}) = \alpha + \beta\, X_1 + \epsilon ...
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1answer
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Should I report the standardised or unstandardised coefficient in a regression?

When I run a multiple OLS regression, SPSS will give me a thing called a 'standardized coefficient' and another called an 'unstandardized coefficient'. I understand that, essentially, the ...