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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651 views

What do changes in regression coefficients indicate about correlations among predictors?

How do you tell if there is a strong, weak, or no correlation between two predictors if you are only given the regression coefficients from two models. One model contains one predictor and the other ...
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3answers
1k views

Can we visualise regression results through diagram?

I read a journal article, in which the authors made a diagram based on regression results (beta weights). Pretty much looks like a path analysis: I'm very sure that path analysis/SEM was not employed ...
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How to interpret regression coefficients for a variable with takes positive and negative values?

I am running a GEE negative binomial regression to see how predictors affect the onset of violence through time. I have an $X$ variable (vegetation cover) which is calculated as whether an ...
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2answers
63 views

Understanding simplification of constants in derivation of variance of regression coefficient

In looking over TooTone's answer in Derive Variance of regression coefficient in simple linear regression, there's a step in line 3 below where $(\beta_0 + \beta_1x_i + u_i )$ is simplified to $u_i$ ...
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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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1answer
337 views

Interpreting regression coefficients when the outcome variable is an inverse hyperbolic sine function

I just learned that when there are zero or negative values, a good alternative to using a logged function is the inverse hyperbolic sine function. When using log transformation on the dependent ...
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2answers
176 views

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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2answers
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How do I compare 5 simple linear regressions?

I'm trying to compare 5 equations of simple linear regressions. All of them have the same variables: abundance of individuals vs. year. I want to know if the slopes are significantly different from ...
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2answers
233 views

difference between dummy variable categories that weren't omitted

Assume we have a categorical variable (one-hot encoded) with three or more categories. {race1, race2, ..., race-n} To avoid the dummy variable trap, assume we ...
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1answer
2k views

r: coefficients from glmnet and caret are different for the same lambda

I've read a few Q&As about this, but am still not sure I understand, why the coefficients from glmnet and caret models based on the same sample and the same hyper-parameters are slightly different....
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1answer
2k views

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
896 views

Interpretation of coefficient of logistic regression in case of one hot encoding

When we use dummy encoding in logistic regression, then we can interpret coefficients as log of ratio of odds (relative to some base value). I am curious what is interpretation of coefficients when ...
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1answer
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How can I get the variance $\sigma^2$ for Linear Regression under homoscadastic with no serial correlation?

The image is a copied and pasted youtube lecture on Linear Regression. I can sort of understand what the lecturer says during the lecture, but I wonder how I actually calculate the $\sigma^2$ in the ...
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1answer
257 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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1answer
6k views

R: linear regression: very small coefficient and R-squared but significant P values

I've got a very small coefficient (-0.04) and R-squared (0.028) but a significant P value (<0.0001). My question is: Is my result still meaningful? How to interpret it? The result is from a ...
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1answer
726 views

Interpreting the change in two logs in a regression

If I have a log-log regression, like: $\ln(\text {Price}) = b_0 + b_1 \times (\Delta \ln (\text{emp}))$ Where $\Delta(\ln (\text{emp})) = \ln(\text{employment growth_year2}) - \ln(\text{employment ...
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1answer
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Why beta sign is different than correlation sign? [duplicate]

I am trying to interpret the sign of my 5 x-variables against y-variable. The sign of some coefficients in the regression output (command: reg) are different than the signs under correlation matrix (...
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2answers
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High R-squared although many insignificant coefficients

I just did a regression based on the gravity model where I try to identify the most important factors that determine the trade flows. In total I have 18 variables and 363 observations. In fact I would ...
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1answer
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Describing Results from Logistic Regression with Restricted Cubic Splines Using rms in R

Updated I have been developing a logistic regression model based on retrospective data from a national trauma database of head injury in the UK. The key outcome is 30 day mortality (denoted as "...
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1answer
325 views

Does fixing coefficients in a regression make sense, and if so how to do it?

I have a generic question about whether it might sometimes make sense to fix specific regression coefficients to predetermined values. And if this makes sense in particular cases, how do you best go ...
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1answer
810 views

Is a model nested within itself before collapsing categorical variables?

If I have a model with a categorical variable $X_1=\{0,1,2,3\}$ and a continuous variable $X_2$, and I have a regression model that includes an interaction between $X_1$ and $X_2$, then I decide I ...
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1answer
341 views

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 ...
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1answer
93 views

Does dummy code a variable affect the intercept in a linear regression model

My colleague and I were both using R to fit a linear regression with the same dataset and same variables. The outcome variable is test grade while the independent variables are gender, age, and times ...
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2answers
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Including % Race/Ethnicity in Regression Model

I have been examining high school graduation rates, and wanted to include race/ethnicity as a control. The only data available is % of students identifying as one of 7 race/ethnicity categories. My ...
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1answer
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Meaning of $r^2n$ for a large dataset

I have a large astronomical dataset, showing the OLS regression value $r$ between two continuous variables, and the number of observations $n$. My research supervisor has told me to include the value ...
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1answer
70 views

Modelling a percentge as a dependent variable

I have a dataset containing 4 variables: Y - the dependent variable. This is a percentage of students in a school that choose to take an external exam. The values vary from 20% to 70%. X - the ...
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1answer
558 views

Short Run vs Long Run Effect in Dynamic Panel Regressions

This video differentiates between short run and long run effects of an independent variable in dynamic panel regression (from 19:25 to 20:50). Firstly, I would like to know when and why do we ...
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2answers
572 views

Interpret reuslts of PLS regression coefficients

I have performed PLS regression using sklearn library (python 2.7) over three types of soil (PLS model per soil type) and I plotted the regression coefficients, but ...
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1answer
83 views

Comparing coefficients of two different probit models---is this “bad statistics”?

Apologies for any stupid mistakes, or if the answer to this question is trivial: I have no formal statistical training. Long story short: can we meaningfully compare coefficients of two different ...
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1answer
331 views

How to test Heteroskedasticity for regression model with 5 independent binary variables

I have 5 independent variables at 3 levels : 0, -1, +1 and dependent variable y at Likert scale (1 to 5) The residual vs Fitted value plot doesn't look okay. Please throw some light.
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2answers
183 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
341 views

Negative intercept in negative binomial regression , what is wrong with my model/data?

I am running a negative binomial regression using statsmodels on Python. My DV is count data and zero-inflated. The one IV in my model is categorical and I have no constant term, and my understanding ...
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1answer
208 views

Can I apply ARIMA(p, d, q) model to testing dataset and make forecast with the testing dataset? Just like the scenario of regression model?

After I fit a sarima model with some historical sales data (for example A dataset), I get coefficients of sma1 and ar1. And I'd like to apply this model to current sales data (for example B dataset) ...
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1answer
64 views

What explains a sudden change in the magnitude of logistic regression coefficients when increasing the sample size

Last week my team and I discovered a strange phenomenon with the coefficients of a logistic regression (LR). As we included more samples from a static dataset, the magnitude of the coefficients of the ...
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1answer
29 views

How can I look for correlations between variables with large deviations?

I'm researching the correlation between the magnitude (a measure of brightness) and redshift ($z$ - a measure of distance) for a variety of galaxies called quasars. Plotting the magnitude against $log(...
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1answer
30 views

Relationship between correlations and model coefficients

I have done a machine learning regression task. I am confused by the correlations and regression coefficient. The correlations of the datasets are depicted using seaborn library heatmap: ...
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1answer
441 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
454 views

Variance of $\hat{\beta}_0$ in heteroskedastic case

Stock and Watson say nothing about that, so I ask you if you know how to derive the variance of the estimator of the intercept in a simple regression, $\beta_0$, i.e. $$\sigma^2_{\hat{\beta}_0}=\frac{...
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1answer
1k views

Back transform mixed-effects model's regression coefficients for fixed-effects from log to original scale

I am running a mixed-effects model with the lme4 package. The model specifications are: ...
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1answer
58 views

Excluding predictors with small effect sizes: not worth it to obtain data?

Suppose I have the following completely-made-up logistic regression model: ...
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1answer
568 views

Coefficient equality test for multinomial logit (preferably in R)

If I want to test the equality of the coefficients of two IVs in the same regression (same DV) I can do a Wald test. If I want to test the equality of the coefficients of the same IV in two different ...
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1answer
170 views

Diagnosing coefficient estimates through Ridge Regression

I want to use Ridge Regression to find out whether my estimated coefficients in a linear regression are stable (as the variance inflation factors tell me that there is multicollinearity). But I'm not ...
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1answer
161 views

How does case-resampling bootstrap work for positive-value estimators?

I've looked at some other questions on bootstrap significance testing: Non-parametric bootstrap p-values vs confidence intervals Computing p-value using bootstrap with R p-value vs. confidence ...
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3answers
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Is logistic regression a valid way of analyzing A/B testing results?

I'm very new to the idea of A/B testing and I want to see if my train of thought here makes sense. Suppose that I run an experiment with two designs. I get two sets of resulting data, one for each ...
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1answer
564 views

Coefficients linear and log-linear regression model

I performed both a linear and log-linear regression to predict the price of a smartphone based on its characteristics. Now I have a question concerning the coefficients between the two models. In the ...
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1answer
168 views

What is the relationship between regression analysis, LASSO, and coordinate descent?

I'm a complete newbie and trying to understand what exactly LASSO is, how coordinate descent is used with LASSO, and how all of that factors into regression analysis. I'm totally confused about the ...
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1answer
45 views

Finding the Coefficients of regressors

I understand how to find the coefficients of a bivariate regression and univariate regression w/o an intercept, i.e: Univariate: Y = BX + e ...
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1answer
143 views

How can my regression coefficients be so far from the underlying model? [duplicate]

I'm performing regression on data derived from a known underlying model with normally distributed errors, and I don't understand how the fitted regression coefficients can be as far as they are from ...
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1answer
813 views

Standard error of the intercept in orthogonal regression

I want to perform a univariate regression but with substantial measurement error in both $x$ and $y$. I therefore want to try orthogonal regression with R. The best answer to my question so far have ...
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1answer
203 views

How are the results of multivariable quantile regression interpreted?

Is multivariable quantile regression interpreted the same way as a multivariable linear regression would be interpreted? For example, would I say something like "the coefficient represents the ...