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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How to convert orthogonal polynomials from MULTIVARIATE regression to basic polynomial equation [duplicate]

I believe the link below converts the coefficients of one x from orthogonal to monomial form, but does someone know an edit to that code that can convert the coefficients of many x's in one regression ...
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Chow test results interpretation

I am analysing time series data right now using gretl, and want to test for a structural break, but I am not quite sure how I have to interpret the results. Let's say I have a wheat price and flour ...
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How to interpret the ratio between a coefficient on a dummy and the coefficient of a log income variable?

I was reading this paper by Kahneman & Deaton: Kahneman, D., & Deaton, A. (2010). High income improves evaluation of life but not emotional well-being. Proceedings of the national academy of ...
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1answer
22 views

Correlation coefficient of x and y

If we have $$ X\sim Poisson(\lambda), Y|X = x\sim Binomial(x+1,p) $$ What is the correlation coefficient of X and Y? So I used $$\rho=\frac{Cov(X,Y)}{\sqrt{Var(x)Var(Y)}} = \frac{E[X[E[Y|X]]-E[X]E[...
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How to interpret my regression results? [on hold]

I am doing a project in which I had to do a regression. The problem is that I don't really understand the results I get from the regression. This are the results of my regression: The question I have ...
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3answers
42 views

Omitted variable bias in regression only containing dummy variables

What is the right way to think of omitted variable bias in a regression that only has dummy variables? Let's say I have the following equation: (1) y=β0+β1x1+β2x2+β3x3+ϵ, where y is the price of ...
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2answers
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How to interpret a negative coefficient in logistic regression?

This is the summary of a fitted model on Titanic dataset in r ...
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2answers
52 views

Coefficient of determination $R^{2}$ for each variable in multiple regression

In multiple linear regression, is the coefficient of determination calculated for each independent variable, or is it only for the model obtained, that is, in relation to all the independent variables?...
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Bootstrapping with repeated measurements

I am trying to estimate a linear relation between body temperature and body mass, and I have a sample of measurements from subjects, with most subjects having one measurement, but several subjects ...
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27 views

Explanatory variable independent of the response, yet has non-zero beta

My intuition was that if an explanatory variable is independent of the response then in a multiple regression it should have a $\beta$ of zero. Consider however the following very simple example: the ...
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Identifying important variables in a PLSDA model using caret in R: are coefficients standardized?

I am doing a PLSDA using the caret package in R. My objective is to predict a status of a cow (0 vs 1) using spectral data. I want to compare the coefficients to know which spectral points contribute ...
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1answer
34 views

Standard error and confidence interval at a point for the fitted value

I have a simple linear regression model $G: Y = \beta_0 + X\beta_1 + \epsilon$. I have found least square estimates for the coefficients, i.e. $\hat\beta_0 = 32.1359$ and $\hat\beta_1=-14.5388$. I ...
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37 views

Interpret GLM log link coefficients

I am currently doing a college assignment in which I have a GLM model in the gaussian family with a log link. I would like to know what the impact per variable is. I know how to calculate the ...
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1answer
31 views

Intuition of second order differencing dependent variable on non-differencing independent regressor regression?

I have two time series sequences. One is $y_t$, which is non-stationary, and the other is $x_t$, which is stationary. Suppose I would like to do a regression of $y_t$ on $x_t$ to forecast $y_t$. The ...
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2answers
41 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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Error variable correlated with explanatory variables

We know that sometimes the error variable in a regression framework may be correlated with explanatory variables; this happens e.g. when we omit an important predictor from our study, getting the well ...
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1answer
23 views

Interpreting coefficients in a regression model for a two-level categorical IV [closed]

I'm running a moderated mediation analysis in SPSS. However, I face some difficulties interpreting the results. I have one independent variable which has two levels (emotional and rational). Since I ...
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Diagnostic test to test for change in regressor

In the previous part of this question, I worked out there is a structural change in the Chow test as 5.04> 2.1 (Fc) hence H0 is rejected and the restriction does not hold. In the next part of the ...
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How to interpret coefficient if the independent variable has negative values?

I have a simple OLS regression: Y=a+B*X+epsilon X is the percentage change in house prices and has negative values (except in the 99th percentile). If the sign of 'B" coefficient is positive, how ...
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1answer
24 views

The interpretation of the economic significance in level-log and log-level models

I have the following two models. The first is a level-log model, and the second is a log-level model. These models are two separate regressions and are estimated independently. Assume that α=0.036 ...
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1answer
44 views

comparison of coefficients (they are not Standardized Beta ones)

I estimated a model with three-stage least squares (3SLS) and have two main explanatory variables (the model also includes a set of control variables but they not important at the moment). I want to ...
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Correlation between external variables and model coefficients over time

Are there any techniques which can allow me to test for correlations between a set of variables (e.g. population, disposable income) and the time-varying coefficients of a model? I would like to ...
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1answer
70 views

Inclusion of standard error in regression equation

$$ \begin{alignat}{14} P = 11&.32 &+ 0&.71 \,\text{PASN} &+ 1&.54 \,\text{DIS} &- 1&.02 \,\text{DIS}^2 &+ 3&.44 \,\text{FUEL} &+ 1&.36 \,\text{FIRST} &...
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1answer
35 views

Coefficient Interpretation when dependent and independent variables are percentages

I have built a linear mixed regression model with fund returns (measured in percentage ie. 0.01 denotes one percent) as the dependent variable. For the independent variables I have percentage level of ...
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What is the effect of balanced class weights on logistic regression coefficients?

I'm specifically using sklearn's LogisticRegression on my unbalanced dataset, which has around 97% negative responses and 3% ...
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1answer
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How to test whether individual fits to regression line or not

I have a defined regression model for the healthy control (HC) group, with corresponding CIs of coefficients and of E(Y). I would like to test whether individuals belonging to another population (...
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1answer
41 views

Interpretation of removed continuous variables in regression due to linear dependence

I have created a standard OLS regression model to estimate the House Price and one group of variables describe the age group percentage of population in a particular neighborhood (ranging 0 to 100). ...
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Obtaining Mean Differences from DESeq2 Output

I have conducted some analyses using DESeq2 and obtained the output. However, instead of interpreting the effect sizes as log2FoldChanges, we would prefer to obtain a model-based mean difference. I ...
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Is the Coefficient of Variation valid for data which does not follow a normal distribution?

I am trying to compare the dispersion of several data vectors. As an example I have that via two methods produces one vector of data that fits a normal distribution and other one that follows an ...
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1answer
59 views

How to calculate the coefficient of a dummy variable reference category?

I am currently building a regression model with numerous continuous, categorical (employing dummies) and interaction variables. I understand we must use k-1 dummies with one variable becoming the ...
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23 views

interpretation of coefficients of independent variables in fractions

I am a bachelor student finishing my thesis and desperately need some help with the interpretation of regression coefficients. I am currently quite confused and my deadline is three days away. I have ...
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1answer
79 views

Interpretation of standardized (z-score rescaled) linear model coefficients

I have analyzed some data on vegetation change as a function of change in soil parameters. I compared a dataset from 2001 with a dataset from 2018 (fully balanced). To investigate the change in ...
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1answer
51 views

ANOVA is significant but coefficients aren't

My master thesis investigates the relation between stock raw returns and sentiment scores. To make a conclusion there is a multiple linear regression with the mean sentiment, the variance of the ...
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Multiple regression and multiple comparisons 3 groups

I'm trying to compare the effect of an IV on my DV, where my data are separated into 3 groups. Specifically, in one group there is a significant correlation between IV and DV, but in the other two ...
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1answer
20 views

regression with very low R2, metric coefficient interpretation

my regression model give extremely low R2. In this case can i still interpret my X variables with significant p-value in the way that x goes up by 1 unit, y goes up by coefficient unit (with others ...
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1answer
54 views

Log-linear difference-in-differences

I am estimating several linear models using a difference-in-differences (DiD) framework. The model interacts a treatment indicator (i.e., 1 for the treatment group, 0 for the control group) and a "...
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Elastic Net - number of non-zero variables

I have a question regarding the interpretation of the trace of coefficients when running Elastic net with the package glmnet in R. This is the plot I obtain with alpha = 0.5 My understanding is that ...
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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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how to report paired comparisons in linear basis function model?

I am struggling with correctly reporting the results of a linear (mixed) basis function model I ran. The model is specified in R as ...
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1answer
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Ceteris Paribus interpretation if it isn't possible in reality

Does it make sense to include both respondent's age (in years) and respondent's partner's age (in years) in a simple linear regression with cross-sectional data? The outcome variable, for example, ...
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1answer
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OLS loss function 3-d surface plot

I was trying to plot the OLS loss function as a function of coefficients $\beta_0$, $\beta_1$. As far as I know it should be a convex function with one local minimum which is also a global minimum. I'...
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Will LASSO choose variables that are highly correlated with the outcome variable?

Suppose we have access to an outcome variable $Y_i$ and a $p$-dimensional vector $X_i$ for $i=1,\ldots,N$. We run a LASSO regression of $Y$ on $X$ for every penalty/shrinkage parameter $\lambda$ in an ...
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Error estimates for coefficients of a non-negative quantile regression

I am looking for a way to provide an error estimate for coefficients obtained from a non-negative quantile regression. The complicated part aside from positivity constraints is that my observations ...
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1answer
15 views

Corroborating a differnce in differences identification strategy

I read in Mostly harmless econometrics that a good way of testing whether a difference in differences is a good identification strategy is running this equation: where the first sums are post-...
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2answers
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Validity assessment of multiple regression marketing mix model

My employer has engaged a consultancy firm to carry out marketing mix modeling in order to quantify the impact of various marketing activities and promotional campaigns on overall sales and also for ...
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1answer
65 views

Intercept in demeaned and rescaled regression model

Suppose I have a linear model; $Y=X\beta+\epsilon$ Where $X$ is $(n \times p)$, with the first column of $X$ being an intercept column (consisting only of ones). Now suppose I construct $\tilde{X}$ ...
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Coefficient of variation and residual standard deviation

From my knowledge, coefficient of variation and residual standard deviation are highly correlated. Such that if we find a significant change in one, we will find a significant change in the other. In ...
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Interpretation of regression coefficients: second-order differencing

Main Question: How are the coefficients of the second-order differenced explanatory variables to be interpreted? (See the attached screenshot of my result.) Analysis framework: I examine the ...
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2answers
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Estimating effect of linear regression coefficients with multicollinearity

As I didn't find a satisfying for that questions I try it here: I have a multivariate Lineare Regression model with some correlated predictor variables. The "simple" question I want to answer is: "If ...
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How to determine predictor importance at each level of an HLM model

I am working with a Hierarchical Linear Model (HLM). I want to determine which predictors are important at each level of the data. Across different hierarchical levels the fixed effects along with the ...