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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Linear regression without intercept - sampling variance of coefficient

I am comparing linear regression with and without intercept for the general sampling case. For this, I have $n$ samples of two correlated random variables $X \sim N\left(0,\sigma_X^2\right)$ and $Y \...
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Converting the beta coefficient from matrix to scalar notation in OLS regression

I've found for my econometrics exams that if I forget the scalar notation, I can often save myself by remembering the matrix notation and working backwards. However, the following confused me. Given ...
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1answer
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How can I interpret coefficients of categorical predictors in the negative binomial regression model?

I used some categorical variables as predictors to a negative binomial model. The dependent variable is numerical. I used glm.nb in R and the results show relative coefficients of one category ...
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How to read the Interaction effect in multiple linear regression with continuous regressors?

If the interaction happens between a continuous and a discrete variable it is (if I'm not mistaken) relatively straightforward. ...
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1answer
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Will larger correlation coefficient values result in greater slopes between x and y?

For example, if there are two data sets, and the first has a larger correlation between x and y than the second, does this mean the first data set has a greater slope than the second?
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Comparing coefficients in logistic regression

I have some problems I need help with. I am running a binary logistic regression. ...
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3answers
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Interpretation of coefficients in polynomial regression for predictive modeling

I am building a predictive model (binary target variable) in the financial services industry. One of the (many) potential predictors I am adding to the model is related to the customers checking ...
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4answers
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How to interpret regression equations with logarithms, based on log difference being approximate to percentage change?

$y = 4 + 2.5\,x + u$ For an increase of 1 unit of $X$ (that is, $X$ to $X+1$), we expect an increase $2.5$ units of $Y$ (that is, $Y$ to $Y+2.5$). Is that right? What if there's a/an $\ln$? $\ln(y)...
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In R, test whether coefficients in lm are different each to a given value (other than zero)

In R, is there a way to use the lm function to test for the hypothesis that the coefficients are different from a value other than zero? For instance, if the model ...
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1answer
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Standard error for the sum of regression coefficients when the covariance is negative

I have a question about appropriately calculation the standard error for the sum of two coefficients in a linear regression model. My question is similar to this and this, but I can't seem to solve ...
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1answer
720 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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If all components of a hierarchical model have not converged, can we say that any parameters have truly converged?

I'm working with a hierarchical regression model of the following form similar to that presented in Peter D. Hoff's book, A First Course in Bayesian Statistical Methods: $\boldsymbol{Y}_j \sim \text{...
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1answer
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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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Is it valid to solve an equation for multiple coefficients, then average them to obtain overall effect?

I have a regression model, the setup for which is as follows: I am using manyglm, a multivariate general linear model approach to determine the difference in several invertebrate species between two ...
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1answer
237 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
230 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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2answers
483 views

Coefficient Significance in Regression with Arima Errors

In the R package forecast, when you run dynamic regression (regression with arima errors), the coefficients and their standard error are output, but there is no significance test available for the ...
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1answer
44 views

Coefficient of multiple correlation for multiple linear regression with degree > 2 and interaction terms

I want to calculate the Coefficient of Multiple Correlation $R^2$ for a multiple linear regression with polynomial features of degree >= 2 (with interaction terms). Let's say I want to obtain the ...
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Test statistic for regression slope in terms of correlation

Consider two data series, $X = (x_1, x_2, ..., x_n)$ and $Y = (y_1, y_2, ..., y_n)$, both with mean zero. We use linear regression (ordinary least squares) to regress $Y$ against $X$ (without fitting ...
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1answer
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How do I interpret interaction effects in a log-log regression model?

I have the following model: $\log(y)=\beta_0 + \beta_1 x_1 + \beta_2 \log(x_2) + \beta_3 x_1 \log(x_2) $ In interpreting the % change of $y$ that corresponds with a 1% increase in $x_2$ at a ...
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Interactions - using ratio of variables

I have 3 variables, colony size, colony age and growth rate (colony size/age). I am interested to predict various other properties ($y$) of a colony using these 3 variables; $y = a_1 \text{ size} + ...
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Regression coefficients significance

What are theoretical reasons to keep variables which coefficients are not significant? I have several coefficients with p > 0.05. What's causing large p values?
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What is the formula for the beta coefficients in logistic regression?

I am doing a study about logistic regression. I have to write a program for the admission process of the school. The result is passed or failed. ...
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How to do permutation test on model coefficients when including an interaction term?

Given the following model as an example: $$Y=\beta_0+\beta_A\cdot A+\beta_B\cdot B+\beta_{AB}\cdot A \cdot B+\epsilon$$ In alternative notation: $$Y\sim A + B + A: B$$ The main question: When ...
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1answer
399 views

Comparing coefficients of time series models

How do I test if two time series' coefficients differ significantly from one another? I feel like this should be pretty simple... should I just use the estimates/standard errors and calculate a Z-...
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1answer
763 views

Time varying coefficient in Cox model

I have a model for survival after an injury that is borderline passing the Schoenfeld test for the proportional hazards assumption (cox.zph() in R). However, ...
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Can I calculate Cohen's $d$ from multiple regression coefficient?

Question: Is it appropriate to calculate Cohen's $d$ (effect size) from the regression coefficient of an independent categorical variable? Background: My regression coefficient represents ...
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1answer
453 views

Averaging LASSO coefficients for repeated random partitioning of data

Is it reasonable to average LASSO coefficients from repeated reshuffling of training/test sets? Suppose I randomly divide my data into testing & training sets, then within the training set use 10-...
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1answer
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Zero regression coefficient when correlations are not zero

I don't really have a motivation for this - but I was thinking about this and couldn't work it out. Suppose I have a random variables $X$ and $Y$ which are correlated. Is it possible that the ...
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1answer
6k views

Testing a regression coefficient against 1 rather than 0

Brief caveat- I haven't dusted off my stats knowledge since some university courses a few years ago, and I'm struggling with cobwebs. I have a model where a linear 1 to 1 relationship has been ...
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1answer
225 views

How can I get information about coefficient std. error, t value and p value for Regularized Linear Model

In R we can get a lot of information from summary model. ...
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2answers
514 views

How to interpret logistic regression coefficient

How do I interpret a regression coefficient in a logistic regression with two predictors? $\hat{L} = -14.27+3.32(3)+0.88(7)$ My understanding is to take the anti-log of the coefficient, like $e^{3....
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1answer
478 views

Is there something called “mean coding” (like dummy coding & effect coding) in regression models?

When we perform a regression analysis with categorical predictors, we can use (1, 0), called "dummy coding". The coefficients in this case represent the deviation of the groups' means from the mean of ...
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1answer
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Interpretation of coefficients in logistic regression output

I am doing logistic regression in R on a binary dependent variable with only one independent variable. I found the odd ratio as 0.99 for an outcomes. This can be shown in following. Odds ratio is ...
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1answer
121 views

Why do descriptive statistics contradict with regression coefficents?

I am estimating a binary logistic regression with L1 norm. According to the regression coefficients, the sign of x1's ...
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1answer
201 views

Uniqueness of $x'\beta$ even when $\mathbb{E}(x^Tx)$ is not invertible

As discussed in user25658's answer to this question, when one wants to compute $$ \beta = \mathbb{E}(x^Tx)^{-1} \mathbb{E}(x^TY) $$ but $\mathbb{E}(x^Tx)$ is not invertible, $\beta$ is not uniquely ...
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1answer
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Compare coefficients from two separate panel regressions in Stata

I am trying to compare the coefficients of two panel data regressions with the same dependent variable. What I am aiming at is the following: ...
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1answer
97 views

Linear regression with error dispersion dependent on the independent variable

Suppose $y=ax+z$ where $x, y, z$ are random variables with range in $\mathbf R$, $\mathbf E[x]=0$, the probability distribution $p(z|x)$ is 1) normal distribution $N(0,\sigma(x)^2)$ with mean $0$ ...
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1answer
479 views

Co-variance of beta coefficients for Dummy Variable regression with intercept

If I have a dummy variable regression output with intercept included (base category as omitted category), and I have to do a hypothesis test for difference of means between two categories other than ...
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1answer
153 views

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 =...
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1answer
301 views

Backtransforming the vertex of a quadratic function

I have created a model for which it was necessary to scale my predictor values by subtracting by the mean and dividing by the standard deviation of the X values. This resulted in variables centered ...
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1answer
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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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2answers
121 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
695 views

Why may results from model with interaction term and stratified model be different?

Suppose I wanted to explore the relationship between smoking (X; yes/no) and an disease outcome (Y; eg. visual analogue scale of depression from 0 to 10). But, I know that irrespective of X, Y is ...
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1answer
63 views

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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2answers
117 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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1answer
73 views

Interpretation of regression coefficients with different subsets of independent variables

I have a multiple regression problem. Let's say there is a physical system with a true model: $$ y = b_0x_0 + b_1x_1 + b_2x_2 \;\;\;\;\;\;\;\;\;\; (1) $$ Now, imagine I only have access to a ...
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0answers
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Coefficient of determination of a orthogonal regression

Context I must find the general form of a linear equation. The $X$ and $Y$ values are the location coordinates of touches on a screen. I want to find the best fit line, described by equation $mX + nY ...
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2answers
661 views

Prove Estimated Regression Coefficients are the same with or without an intercept term

I am mostly having trouble with this question in that I don't think I know where to start and I am not confident in my answer that I have at the moment. The answer I have currently is mostly just ...