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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Multiple linear regression slopes inconsistent with graph - why?

I am doing a multiple linear regression, with 3 categorical predictor variables (Flow, Drug, Pesticide) each with two levels (0 vs. 1). The response variable is the abundance of invertebrates. I have ...
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How do I choose a spatial unit for fixed effects model

I have a panel dataset of 40,000 observations, that is 8,000 parishes and 5 years. When I run a fixed effects regression, using parish as a spatial unit, it shows negative adjusted R2 and rather ...
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Thesis - asserting good variable selection [closed]

Requesting some input for my thesis; We want to do a quantitive analysis on how consumer satisfaction (Dependant variable) is with Youtube ads. Then run a regression on independent variables like ...
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Fisher r-to-z transformation: comparing correlation coefficient of multiple samples

I am comparing the linearity of a regression model for two independent devices (n=10 each device group). The data is force (newtons) over time (seconds). The regression models show R^2 values of 0.9 ...
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Multiple regression model and correlation between predictors

I am reading the Introduction to Statistical Learning in Python (ISLP) book. I am reading the below paragraph: Now suppose that the multiple regression is correct and newspaper advertising is not ...
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I have a significant change in my outcome with the opposite sign in the lead period. Is this an issue?

Suppose I have a negative significant effect of a variable x on y. Also negative significant effect of the lag ie variable L1.x on y . But I get a positive sign significant effect on y in the future ...
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Can I specify the signs on coefficients of variables in Regression models?

I have a Regression model where the coefficients of each variable need specific signs. For Example, say I have a standard OLS model: Y = β1X1 + β2X2 + … + β7X7. I want coefficients β2 and β5 to be ...
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Multiplicative BIASES in Log-Log regression

When we try to estimate elasticities by regression, we usually estimate the following regression model: $$ln(y) = \beta_0 + \beta_1 ln(x_1) + \dots + \epsilon$$ When we expect to have endogenous ...
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Handling non-significant beta coefficients

In our thesis, we have asked participants (consumers) about how several independent factors/variables (like price) affect the willingness to buy (the dependent factor). We have used the beta ...
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Variable selection based on PLS

What is the logical way to select the variables from PLS? Does choosing the feature from loadings and loading weights make sense? Loadings... Loading weights... Regression coefficients... Variable ...
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Modeling data with continuous and discrete measurements

I am working on a project involving a dataset which includes variable which represents "time spent", but the data is a combination of two measurement sources: one is discrete and one is ...
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How to calculate probability from logistic regression using interaction effect parameter?

I have a logistic regression (logit link) model that I use to estimate probabilities. In the absence of interaction effects this formula is given in a lot of references as $$p_i = \frac{1}{1 + e^{-\...
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Expression for Omitted Variable Bias in Particular Coefficient [duplicate]

Suppose the true model is $y_i=\beta_0+\beta_1x_{1i}+\beta_2x_{2i}+\epsilon_i$, but $x_2$ is not observable. If we run a regression instead on the model $y_i=\beta_0+\beta_1x_{1i}+\eta_{1i}$, what is ...
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Calculate SE of regression coefficients using p-value (for meta-analysis)

I would like to do a meta-analysis of the regression coefficients from a group of 9 studies, but they authors had not reported the SEs. For all of the studies, the tables included in the reports only ...
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Why is the correlation coefficient of these subsections of this dataset indicating a much weaker correlation than the whole dataset?

I have a dataset which includes household income against expenditure. The correlation coefficient of the dataset is 0.7064 which indicates a strong positive correlation. Here's a graph for it: Now I ...
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Testing for a difference in $R^2$ with the same model but two different (equally sized) datasets

I have two datasets of the same size, $\{\vec{Y}_{1},\vec{X}_1\}$ and $\{\vec{Y}_{2},\vec{X}_2\}$. I fit the same regression model to both datasets and calculate the coefficient of determination from ...
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Interpreting Linear model coefficients for either Normalised (i.e. Min/Max Scaling) or Standardised (i.e. zero mean unit standard deviation) inputs? [closed]

I have a Linear Regression model that I have fitted on a set of features X to a predictor variable y. The features and the predictor variable have been normalised using Min/Max scaling. I'm trying to ...
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Detrending and data transformation to logarithm can be done together?

I want to get the effect of bitcoin price changes on foreign currency price. The third variable is inflation, which is an explanatory variable. Should variables be detrended before regressing? Is it ...
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How to interpret interaction coefficients in a truncated poisson

I'm working with a truncated poisson (also known as positive poisson) and I want to interpret the coefficient interaction between two variables. From this question, we see that the interpretation of ...
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Understanding Mixed Effect Models visually with some questions on P-value calculations

I've been tackling the concept of Mixed Effects Models on and off for the last 9 months. Every time I would give up and come back later to try and understand it again with my basic statistics ...
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$R^2$ but using the average of the linearized data

Suppose you have a set of data $y_i$ and the corresponding linearized data $f_i$ obtained through linear regression. Set: $$(R')^2=\frac{\sum_i (f_i-\bar{f})^2}{\sum_i (y_i-\bar{y})^2},$$ that is a ...
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How do I handle outliers?

I'm calculating the beta coefficients for some stocks using a single-index linear model with the OLS method. I'm computing the betas at different return intervals to assess the interval effect on the ...
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Calculating standardised regression coefficients from GLMER model

I have three separate glmer models investigating the individual and household-level risk factors of malaria infection in three different spatial locations: 1) outside the forest, 2) at the forest ...
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How to estimate the coefficients in OLS (all steps) [duplicate]

I'm a B.S. Math graduate who likes to (attempt) to teach myself statistics on my own time because I can't afford a masters degree. It really bothers me when I can't understand at a fundamental level ...
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Effect on regression coefficients by multiplying a constant to a feature [duplicate]

I was solving one quiz question on Coursera and I found an interesting question. If you double the value of a given feature (i.e. a specific column of the feature matrix), what happens to the least-...
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In a linear model, why do we have $-2X^T \vec{y} + 2X^T X \vec{\beta}=0$? [duplicate]

When we derive the estimates of $\vec{\beta}$ such that they minimize the sum of squared error ($SSE$) we begin with $\sum_{i=1}^{n} (y_i - (\beta_0 + \beta_1x_1 + ... + \beta_kx_k))^2$. This is ...
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Interpret coefficient of categorical variable for group with no observation in fixed effect regression

I have a hard time interpreting a coefficient from a fixed effect logistic regression, especially in the case where no observation has this value in a given group. Consider this model, where we ...
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In a regression, can we find the coefficient error matrix from the covariance matrix?

Suppose a study with dependent variable $y$, and predictors $x_1$, $x_2$, ..., $x_k$. Assume that I have access to the covariance matrix $$\hat\Sigma = \begin{bmatrix}Var(y) & cov(x_1,y) & ... ...
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How to explain correlation between populations of slope and intercept coefficients

According to this post, the expected correlation between the sampling distributions for the slope and intercept in OLS regression is given by E(Corr) = -E(X) / sqrt(E(X^2)). Now, let's consider an ...
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Principal Component Regression with a Generalized Linear MIXED EFFECTS Model

According to the wiki page on Principal Component Regression, it is possible to transform the beta values obtained from doing regression with PCA data into beta values for the original features. This ...
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If you drop the "1-" in the formula of R2 and calculate the adjusted R2, does that metric mean anything?

First off, sorry for the convoluted title, but I didn't manage to come up with a shorter one. Background: I have some 2D particle tracks that I would like to fit with polynomials. The tracks are ...
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Interpretation dummy variables Cox PH model

I'm curious about interpreting the coefficients of dummy variables within a Cox Proportional Hazards (PH) model. Consider a scenario where I have a sample comprising both male and female patients, and ...
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Testing equality of coefficients from regression models with long format dataframes

How can I test the equality of coefficients from multiple regression models? I want to compare multiple measurement methods to see if they capture the dynamic processes of the same construct in ...
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Does anyone recognize this significance test between two regression betas?

I came across the following test for statistical significance between two betas (predictors) from a multiple regression model. Note that $R^2$ is the model coefficient of determination, $r$ is the ...
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Why is the variance smaller for the same coefficient in a reduced regression model vs. full regression model?

Let's say we have two estimators for $\beta$. $\beta$ denotes all a full set of coefficients, one for each covariate in a dataframe. $\beta$ can be split into $\beta_p$ and $\beta_r$, where $p$ ...
Estimate the estimators's user avatar
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Why do the estimated coefficients in a simple linear regression model have a distribution?

When we do OLS, as I understand it, we do all our derivatives to obtain some $\beta_0$ and $\beta_1$ that minimize the SSE (unexplained error between the observed data and the estimated response $y_i$-...
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Measuring total relative influence of groups in particular coefficients in a multiple linear regression

Suppose I have run a multiple regression model: Y = B0 + x1B1 + x2B2 +..+ xnBn, weighted by w, from a dataset with such covariates and the weight variable of size N. Say there is another column in the ...
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Interpretation coefficients categorical variables

I am working with a large panel dataset studying many companies over a long period of time. Some of these companies receive a negative outlook from an analyst during the sample period. Similarly, some ...
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In APC-Detrended Analysis: Testing for Significant Difference in Cohort Variable Coefficients, Beyond Z-Test

I have conducted an APC-Detrended analysis. Among the results, I want to test whether there is a significant difference in the coefficient values of the Cohort variable especially between the two ...
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Intuition for how individual coefficients change with increasing regularization penalties [duplicate]

I'm trying to build intuition around how individual coefficients change as a regularization penalty is increased (for both ridge and lasso). This is what I understand the curves of the l1 and l2 ...
another_student's user avatar
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Regression coefficient on a triangle using geometry

I am encountering a question as follows: Let $X, Y$ be two independent uniform random variable on $(0,1)$. We consider the regression model $Y = \beta_1 X + \beta_0$, given the restriction that $X + Y ...
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Interpreting Regression coefficients where Y is an index

I am having trouble with the correct interpretation of my regression coefficients. My independent variable is fund allocation which is a continuous variable. I have two output variables on which I ...
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Compare beta of single regression and multiple regression

Given that: $$ \text{Corr}(Y, X_1) > 0 \\ \text{Corr}(Y, X_2) = 0 \\ \text{Corr}(X_1, X_2) > 0 $$ Consider 2 regressions: $$ Y = a X_1 + \epsilon \\ Y = b_1 X_1 + b_2 X_2 + \epsilon $$ Which one ...
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Pros and cons of different methods for comparing betas in regression

In my line of work, we often hypothesize that one continuous predictor will have a stronger relationship with some outcome than another closely related (i.e., collinear) continuous predictor. We fit a ...
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Overfitting if estimating multiple target parameters in dataset (avoiding Table 2 Fallacy)?

For my job I'm sometimes asked to find the driving factors behind a healthcare outcome such as total annual cost or # of inpatient visits. "Driving factors" typically means reporting average ...
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Is there an intuitive explanation for why $R^2 = \hat{\beta_1} * \hat{\alpha_1}$

In simple linear regression with one regressor, if you regress $y$ on $x$, i.e., $\hat{y} = \hat{\beta}_1 x + \hat{\beta}_0$ and $x$ on $y$, i.e., $\hat{x} = \hat{\alpha_1} y + \hat{\alpha_0}$, you ...
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Standardizing OR from logistic regressions with log-transformed variables for meta-analysis?

I´m trying to meta-analyze odds ratios from logistic regressions; some of which log-transformed the independent variable first. (i.e. some studies present an OR per +1 in the independent variable, ...
san festein's user avatar
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Covariance of slope terms in different linear regression models

I have two linear regression models: one with intercept term, and the other is without. I wanted to compare the models based on their parameters. MLE estimator for intercept model is well known to be ...
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Log-Level Model Parameter

Consider we have a population regression function (log-level model) with only one independent variable: $$\log(y) = B_0 + B_1 \times x_1+u$$ In order to find the relationship between the increase of $...
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Using Maximum Likelihood function to find near-optimal solution

For the context, I was writing my BSc thesis on the topic of Linear Regression through the Origin (RTO). My goal is to analyze RTO, and find the appropriate use cases for it. In the case of simple ...
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