# 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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### Math behind the standardized effects from Minitab

I would like to understand the mathematics behind the Standardized effects (SE) as found in, e.g., Minitab. I'm far from an expert in statistics, but I found this page which treats the same question. ...
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### Interpretation of logistic regression coefficient

Within logistic regression framework, odds are defined as: $$\frac{p(X)}{1-p(X)}=e^{\beta_0+\beta_{1}X}.$$ In the textbook "An introduction to Statistical Learning" (Gareth James, et al., ...
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### Comparing coefficients and confidence intervals when some categories have very few observations (logistic regression)

I'm fitting a logistic regression model (with multiple predictors) to data where the outcome is a success or failure. My data points are in the range of 100,000. Most of my variables are categorical, ...
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### The distribution followed by the number obtained by dividing coefficient a1 by the other coefficients a2 in multiple regression

Given the following multiple regression model. $$y\sim N(a_0+a_1x_1+a_2x_2,\sigma)$$ where $y$ is the response variable, $N(\mu,\sigma)$ is the normal distribution following the mean as $\mu$ and ...
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### Variance ratio when including irrelevant variables in a regression model

I am interested to know if there is a general formula for the ratio of the variance of regression coefficient for a predictor in a correctly specified model and a misspecified model. Specifically, let'...
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### Equality arising from coinciding of $R^2$ with slope of regression of predicted vs observed values

If I am able to interpret this correctly, then in the accepted answer to Does the slope of a regression between observed and predicted values always equal the $R^2$ of the original model? it is proven ...
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### Handling the situation: (x ~ y) == (y ~ x)

If fitting the following two models, using linear regression, produces coefficients that are essentially the same, what is the appropriate modelling technique to use? ...
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### What is the best model for this case?

I have the following problem: A data set, which is about the soft drink consumption of people, that covers 300 subjects are available to us. Using Excel tabulations and graphing capabilities only: ...
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### What is the likelihood of a regression? [duplicate]

I understand linear regressions themselves have likelihoods. Is this simply the likelihood of the error? I thought it was the likelihood of the data for Y given X. In other words, $Lik(Y$~\$X)=Lik(Y|...
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### logistic regression coefficient interpretation - with / without interaction [duplicate]

In this model: ...
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### Interpreting log transformed variables in a regression [duplicate]

I am very confused about the interpretation of log transformed variables in a regression. For example, I have a log-level model with a B0=4.95 and B1=-1.07. So my model would be log(y)=4.95 - 1.07X. ...
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### Can Multiple Regression Output (coefficients, ratios, etc.) Be Given a Predictive Interpretation?

Generally speaking, regression output can be given a causal interpretation for typically one variable in the model (that is under the assumption of no unobserved confounding and this is not to speak ...
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### Binary logistic regression: why do these two coefficients have opposing signs when they are indicators of the same outcome?

I hope someone can help me understand why this is happening. Reproducible example in R: ...
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### what are the consequences of re-encoding with 0 or -1?

I have a dataset of information about students and the last column is the target variable which is the final note. My goal is to make logistic regression and ordinal regression models to see whether ...
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### Understanding linear regression output for ordinal independent variable

I'm running a linear regression on JASP with an ordinal independent variable (education level with levels 1, 2, 3) and I am wondering what is meant when the coefficient table includes different ...
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### Coefficient in Regression Analysis

I am running regression on two variables (independent and dependent). If the results show p-value > 0.05, it is not statistically significant. Does this mean we reject the coefficient as well? If ...
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### Event study regression specification: interacting covariates with leads and lags

I want to create an event study regression specification for the following: $$\ln(y_{ijt}) = \gamma \ln (x_{jt}) + \tau \ln(p_{t}) + \lambda \ln(x_{jt}) * \ln(\mbox{p}_{t}) + \epsilon_{ijt}.$$ I am ...
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### Several regressions with different dependent variables

I'm working on a project where I want to compare two groups of participants based on several different metrics. Right now, I'm estimating separate regressions with different dependent variables (i.e. ...
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### Working out/Derivation of Standard Error of Coefficient in Logistic Regression

Let's keep it simple and just go with Simple Logistic Regression where there is only 1 continuous independent variable. I.e. Log(P/1-P)=B0 + B1X1 What is the working out to derive the standard error ...
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### Mathematical formula for interaction term in multiple regression with two predictors [duplicate]

I am trying to understand the math behind the coefficients in a multiple regression with two predictors and their interaction. I know that this can be done in matrix notation OR directly in any ...
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### Manual specification of knots vs bs() for Piecewise regression

I am learning how to specify and plot piecewise regressions and have encountered a confusing situation. Namely, I have specified the knot for a piecewise regression using 2 methods: (1) manual and (2) ...
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### Is an interaction term essentially interpreted as just another independent variable?

I'm trying to understand if the linear regression model interprets an interaction term as just another independent variable? This is the formula for linear regression with 2 independent variables ...
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### Cohen's d or Cohen's d-like effect size estimate for regression slope?

Can Cohen's d be calculated for the linear regression coefficient associated with a continuous predictor? If so, what is the formula? I found one question asking this already, with an answer ...
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### Simple Regression Coefficient Formula for Categorical Variable?

For an indepdent numerical variable X the B1 coefficient is COV(X,Y)/Var(X). Since Categorical Variables don't have things like Means(from which things like COV and VAR are derived) how would it work ...
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### Comparing regression coefficients across non-nested SEM models (Lavaan)

I had question about SEM in Lavaan which I cannot seem to get a grip on through any google forums or my old lecture slides... I wish to explain cognition using several variables (CR1/CR2, which stand ...
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