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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Difference between two coefficients

I have an unbalanced panel dataset for a list of firms for the period extending from 2000-2015. Set of standards issued in 2003, and the adoption is voluntary. Firms started to adopt in different ...
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How to recover estimates on original scale in log-linear model?

If fitting a linear model to a untransformed and log-transformed y variable, can anyone explain why the coefficients are different from the log-transformed model even after exponentiating the ...
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Estimates from MCMCglmm multivariate regression

I'm running a multivariate regression on two response variables (X and Y) using MCMCglmm in R. X is a continuous variable (family = Guassian) while Y is a binary response variable (family = threshold)....
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Simulating slope coefficient for linear regression

I'm currently reading an article: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4302277/#S5title And in Section 5 I've come across a simulation for a few estimators of the slope $\beta_1$. I wanted to ...
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Interpreting mixed effects model results. Why are my coefficients for mixed effects model are so large?

I am an economics grad student and I am in the process of writing a paper disproving using the Gini coefficient as a solitary measure of income inequality in migration determinants analysis. I have ...
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Calculating the effect of trustworthiness on obtaining bank loan and on loan rate (interpretation question)

I am reading a paper that discusses how people's perception of borrower's trustworthiness affects his/her probability of loan approval, and also loan rate. This is from a RFS paper on page 2474 (2.1) (...
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MLE of regression coefficients depends only on correlation matrix and single-predictor z-scores

Assume a standard linear model $$ \boldsymbol{y}=\boldsymbol{X}\boldsymbol{\lambda}+\boldsymbol{\varepsilon}, $$ where $\boldsymbol{y}$ and the columns of $\boldsymbol{X}$ are standardized. In some ...
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multiple regression model having 2 independent variables [duplicate]

I run a multiple regression model having 2 independent variables. The R-squared value for my regression analysis on two predictor variables is 0.75. How do I interpret this value?
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How regression coefficients change when shifting the scale of the response variable

I am running a regression with y: a 7 point index ranging from -3 to 3, x: binary indicator (0,1) of second wave of data collection. When I fit this regression, I get the following equation: ...
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Binary logistic regression coefficients

Consider the following MWE example. A dataset with only one feature (categorical feature with 4 different categories ['cat', 'dog', 'hamster', 'frog']) + target (overall 10% positive class). After ohe ...
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Why is a t statistic used for standardized regression coefficients?

I understand the sampling distribution of unstandardized linear regression coefficients is normal, and therefore a t distribution can be used to determine p values for given coefficient and standard ...
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What is the sampling distribution of the standard error of regression coefficients to get an accurate histogram?

I'm trying to fit the pdf on the variance of regression coefficients. I understand how to plot the regression coefficient estimates, the noncentral t-distribution, but I am always off for when I try ...
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What could be the reasons for regularized logistic regression coefficients are identical?

I found one logistic regression model I built have many identical (but not all) coefficients. I know it is possible to have following problems. Very strong regularization, that all the coefficients ...
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Regression coefficients for (un)known $\sigma_x^2$

I'am currently reading an article A Paradoxical Result in Estimating Regression Coefficients (can be found here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4302277/#S2title) and at the end of the ...
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How to determine the parameters of a linearized model when the line has negative slope and intercept?

I have the following data: Sample $t$ $q_t$ $\ln\left(q_e-q_t\right)$ A 0 0.00 0.31 A 60 0.97 -0.92 A 90 1.30 -2.71 A 120 1.33 -3.40 A 180 1.28 -2.48 A 240 1.35 -4.09 A $q_e=$ 1.37 B 0 0.00 0....
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Different values for intercept estimate in linear regression

I'm reading about linear regression from two sources. In here: https://online.stat.psu.edu/stat415/lesson/7/7.3 the estimate for the intercept is just $\bar y$. However over here: https://www....
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Visualizing time series regression results in a causal framework

Suppose I have a set of independent variables that I believe to, collectively, cause the observed level and changes in the value of the dependent variable, and I have the results of a regression of ...
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Graphing Regression Results with Insignificant Coefficients

Consider investigating an interaction using a linear regression with the specification: Y = β0 + β1X + β2M + β3X*M + e Where: $$ \begin{array}{c} & \text{Coefficients} & \text{Sig.} \\ \...
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Interpretation difference between log link and log transformation

I have a question about the interpretation difference between log link of GLM and log transformation of LM. I know that log transformation is for target variable but log link is for mean .But related ...
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Differentiating expected prediction error (EPE)

From Hastie-Tibshirani-Friedman p.18-19 $$ EPE(f)=E(Y-f(x))^{2} = \int[y-f(x)]^{2}Pr(dx,dy) $$ If $f(x)\approx x^{T}\beta$ shows that by plugging in $f(x)$ in $EPE$ and differentiating w.r.t. $\beta$ ...
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Bootstrap to increase robustness of longitudinal models?

I'm evaluating repeated measures longitudinal data with mixed effects lme4::lmer(). Due to all discussion in favor of bootstrapping as a strategy to perform ...
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Multiple linear regresion in R

I am creating a multiple linear regression model $M_1$ with aggression as response and parenting_style and ...
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Interpretation of coefficients in a regression with a lagged dependent variable [migrated]

I have estimated the following dynamic panel data model using GMM:           $\ln Y_{it}=\beta_0+\beta_1\ln Y_{it-1}+\beta_2\ln X_{it}+\epsilon_{it} $ where $Y$ is employment and $X$ is productivity. ...
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Calculate residence time from double exponential fit

I did a tracer addition experiment. I added a tracer in Mass 1 (see figure), the tracer moves from Mass1 to Mass2 and then to Mass3 and so on. The flow of the tracer between the mass happens over days....
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How to prove the Standard error of fitted value given the standard error of each coefficients [duplicate]

I know those Equations but I cannot show the standard error of fitted value, please help me out, much appreciated. $$ SE(\hat{\beta_1})=\hat{\sigma}\sqrt{\frac{1}{(n-1)s_x^2}}\\ SE(\hat{\beta_0})=\...
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How to show that linear regression coefficient estimators are mutually independent?

I'm looking at linear regression with $y=\alpha+x\beta+e$. About half-way down the page, https://online.stat.psu.edu/stat415/lesson/7/7.5 states that "a=$\hat \alpha$, $b=\hat \beta$, and $\hat \...
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Three-way interaction interpretation

Suppose that I am interested in the effect of income on consumption by gender: $$consumption_i = \alpha_i + \beta_1income_i + \beta_2 male_i + \beta_3 (income * male)_i + \varepsilon_i$$ In this two-...
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Converting the beta coefficients of a lognormal regression back in to unit scale after modeling the scaled and centered variables

I have fit a lognormal regression model, after scaling and centering the independent variables only. I did this using the brms package in R using the family = lognormal() argument, which fits a model ...
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Time-varying coefficients in coxph

I'm trying to understand time-varying coefficients in survival::coxph and the tt notation. I found this paper, which clarified ...
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Why use least squared solution of linear regression when we can use X inverse? [duplicate]

I know linear regression gets the estimate of beta by minimizing the squared errors. I'm curious why can't I use inverse of X to get the estimate of beta. I know there is errors and etc. but if X ...
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Why orthogonal polynomials lead to diagonal matrix $X^{T}X$ when estimating regression estimates?

We believe that the response variable $Y$ can be modeled in a following way: $$Y_i = \beta_0 + \beta_1 x_i + \beta_2 x_i^2 + \beta_3 x_i^3 + \epsilon_i $$ where $\epsilon_i$ is independently ...
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OLS- relation between R-squared an t-stat

I read here and in a comment by "Jeff" to the first answer here that $R^2= \frac{t^2}{t^2+df} $ I presume this is valid for simple linear regression only (with only one x variable, so not ...
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Distribution in simple regressions without intercept

how can I find the distribution of Yi = β1Xi + εi, when we know Xi is normally distributed and mean and standard deviation are unknown and εi is normally distributed with (0,1)? Can we assume it is ...
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How to interpret marginal effects on a dependent variable that is a ratio?

I have run a basic OLS regression in Stata using a basketball data set I created. My dependent variable is a points ratio that divides the home teams final score by the away teams, which means if the ...
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Predict on a log growth model, adjust starting value from r generated model

For a project that I'm working on we consider a cohort a set of people who installed our app on any given day. The cumulative revenue from a cohort is logarithmic in shape and I'd like to use this ...
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Timeseries OLS Coefficient Interpretation - Log Sum Transformation

This should be straightforward and I apologize in advance but for some reason, a colleague and I are in disagreement over the interpretation of some regression coefficients. Suppose we have a time-...
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1answer
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Effect size derived from LME longitudinal model: the statistical findings projected back down onto a group of people

I have been studying the change in a metric X with a linear mixed effect model. I have built this model in a multivariate setting, so I can see how each of my covariates (Time, sex, age) affect X. ...
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How can I use this Regression Plot on new data?

I'm trying to use this regression plot, but I haven't looked at one in ages. I read it that for every 15.23 (x axis) increase in Population Density, there is a $0.95 (y axis) increase in Weekly ...
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Interpreting $R^2$ when using a single categorical variable

My understanding of $R^2$ is that it represents three things: The linear relationship between variables in a regression. The amount of variability explained by a regression. A proxy for the efficacy ...
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Using outliers in independent variable for inference

I am interested in studying the main and interaction effects of the treatment D, i.e., Y = aX + bD + cXD. I only have observational data, very noisy. D, X and Y are continuous. I noticed that there ...
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Comparing the size effect of regressor coefficients

I am dealing with multiple regression and I would like to understand when I can make comparisons about the magnitude of the beta coefficients. In particular, I have this kind of model: Y = ...
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Comparing regression coefficients between models with dependent predictors and dependent criterions

I would like to compare regression coefficients between two models as part of a within-subject study setup. The problem is that both the predictors and criterions are likely to be correlated and that ...
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When I interpret the output of n-way ANOVA or regression, should I adjust the p-values per each main and interaction effect or coefficient?

Statistical packages report regression and ANOVA/ANCOVA models consistently in the same manner - a list of model coefficients, standard error, test statistics (Wald, F) and the p-value. Let's assume I ...
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r package pglm outputs coefficient sigma?

I'm running a logit regression on panel data, (first time with this combination), and am running this piece of code from the pglm package in r. ...
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Interpreting interaction effects in regression

Suppose we are regressing Y = aX + bD + cXD. a and b are main effects of variables X and D, and c is the interaction effect. Assume both X and D are continuous variables. How to interpret the effect ...
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How to interpret the value of an interaction coefficient between two effects coded binary predictors?

Let's imagine an experiment where people look at pictures and then rate their mood after each one from 1 (sad) to 7 (happy). The pictures can either be happy or sad (IV1), and participants are either ...
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Rolling Regression Coefficient Analysis

I have been creating a rolling regression where the dependent variable is the return of an asset and the independent variable is a Market Factor / CAPM. I have been creating the rolling regression for ...
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Interpret the slope coefficient of a variable (%)

I'm fairly new. I'm trying to interpret the slope coefficient. My regression is as follows : Y - GDP Growth (annual %) (i.e 6% it appears as 6 in my dataset) X - Ethnic fractionalisation (entered as ...
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How to simulate standard error of regression coefficient?

I was conducting this exercise for my own understanding of standard error of regression coefficient. It is explained as 'an estimate of the standard deviation of the coefficient, the amount it varies ...

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