Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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.

Given the following models, as examples, built from regression techniques: \begin{align} Y &= \beta_0 + \beta_1X + \varepsilon \\ Y &= \beta_0 X^{\beta_1} + \varepsilon \end{align} $\beta_0$ and $\beta_1$ are regression-coefficients (or parameters) on above equations (regression models).

2097 questions
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How to convert standardized coefficients to unstandardized coefficients?

My goal is to use the coefficients derived by previous research on the subject to predict actual outcomes given a set of independent variables. However, the research paper lists the Beta coefficients and t-value, only. I would like to know if it is…
user12127
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Population parameters of a regression

So this has really been bothering me and I was hoping for a (simple!) explanation if possible. Suppose I've specified a linear regression model: $$ Y = \beta_0 + \beta_1 X + \epsilon $$ And an alternative: $$ Y = \beta_0 + \beta_1 X + \beta_2 X^2 +…
Sue Doh Nimh
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Adjusting regression coefficient for predictor error

I saw a famous review paper about intelligence, and the authors introduced a way to adjust the regression coefficient for predictor error. As many of you might know, if the predictor has a measurement error or if it has reliability less than 1, the…
KH Kim
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How to interpret two observations that are otherwise identical in a regression model

I am confused trying to interpret how two observations are otherwise identical but differ by a dummy variable. For example if we have the following model with a factor variable race being White race the reference category: Call: lm(formula = Score ~…
Ronnie
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Using Lin Reg parameters without Original Dataset

suppose I have a linear regression model that was trained on a dataset of size $n$. Unfortunately, I no longer have access to the original dataset; the only thing stored is the model parameters $B_0, B_1$. Suppose I come across another dataset (from…
Bepop
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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 &= \beta_0 + \beta_1 X^7_t + \epsilon_t, \end{align*} where the…
Andrew
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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 = 1. The final model has 8 predictors. My question is regarding the interpretation of…
Courtney
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Interpreting a simple linear regression coefficient scaled by the mean of y?

I have come across an industry example of a simple linear regression ($y=a+bx+\epsilon$) where the slope coefficient has been adjusted by the mean of $y$ ($b/\text{mean}(y)$) and described as a "slope impact". The exact interpretation that they use…
barryq
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Equivalence of a slope coefficient in a regression using individual and aggregate data

I want to compare the coefficients of the two linear regressions: $$ \begin{array}{c} y_{ij} &=& \beta_0 + \beta_1 X_{j} + u_{ij} \\ y_{j} &=& \alpha_0 + \alpha_1 X_{j} + u_{j} \\ y_{j} &=& \frac{1}{N_j} \sum_{i=1} ^ {N_j} y_{ij} \end{array} $$ so…
Florian Oswald
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coefficient magnitude interpretation

I have a question regarding the interpretation of coefficient magnitude (not coefficient) in linear regression when the dependent variable is log-transformed. When the y is not log-transformed the interpretation is like the following an increase of…
Roxanna
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coefficient magnitude

"An interpretation based on coefficient magnitude also suggests that an increase of x (independent variable) by one standard deviation is associated with the increase of y (dependent variable by 2.63% of its standard deviation." Could somebody…
Roxanna
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How to tell the importance of regression coefficients when both continuous and binary features exist

Let's say I have 3 features for a regression model: if_smoking, if_drinking, and body_height. The first 2 are binary, while the 3rd is continuous. I have coefficients like: bias/y_intercept: 1.2 coefficient for if_smoking: 0.8 coefficient for…
Fred Chang
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determine the growth rate given a time series data

I have a data sets like this: structure(list(Month = structure(c(14975, 15006, 15034, 15065, 15095, 15126, 15156, 15187, 15218, 15248, 15279, 15309, 15340, 15371, 15400, 15431, 15461, 15492, 15522, 15553, 15584, 15614, 15645, 15675, 15706, 15737,…
user1471980
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Multiplying regression coefficients by a constant

Lots on this on CV already but most tend to be about multiplying predictors by constants before performing the regression. I feel like I should know this already but I'm wondering if it's kosher to multiply the regression coefficients by a constant…
llewmills
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Interpreting coefficient for regression with log dependent variable

Say I estimate $$ \ln y_i = \alpha + \beta x_i $$ I understand that my estimate , say it comes out, $\hat{\beta} = 0.01$ is approximately the percentage variation in $y_i$ since $$ \ln y'_i - \ln y_i = \ln (\frac{y'_i - y_i}{y_i} + 1)\approx…
Three Diag
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