Questions tagged [multiple-regression]

Regression that includes two or more non-constant independent variables. Also known as multivariable regression.

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3 views

Explaining the effect of adding a dummy variable on a restricted model

so I'm learning basic econometrics. I'm looking at a linear regression model on Stata where I have to qualitatively compare a restricted model, where y_i = b_1 + b_2 x_i and y_i = b_1 + b_2.x_i + b_3....
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Interpretation regression coefficient

I have run a regression to estimate the impact of a couple of variables like growth rate, company size or leverage on the profitability of a firm. I know that if e.g. the regression coefficient for ...
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Interaction term when involved variables are colinear

Let's say I want to fit a model that relates a target variable $Y$ to a set of predictors $X_1, ...X_n$. Let's also assume that two of them ($X_1$ and $X_2$ for example) are correlated but allow for ...
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Which variable is independent variable here?

I am confused. Both can be used as the dependent variables. But which will be the appropriate one? The Director of the School of Business is interested to study if there is a relationship between the ...
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60 views

Model specification for a multiple regression

I would like compare the job satisfaction between two industries. I've conducted a t-test and came to the conclusion that they are statistically different at the 5% significance level. Now I would ...
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1answer
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Regression with/without interaction vis a vis CEF

I am interested in improving my understanding of regression and CEF. In particular, I bring two related questions: 1) How to interpret a relationship with two dummy variables without interaction; and ...
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Interpreting p-values of glm with multiple predictor variables

I am looking to test if certain characters change with a predictor variable in significantly different ways for different species. For instance, I want to know if width against height. When I use the ...
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How can one use general linear methods for time series data

I think it is very common to use methods like OLS, ANOVA, Logistic regression etc which do not function well if at all with non-stationarity. And much of the data analyzed will take place over years ...
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What statistical test is appropriate for the following experimental design, apart from mixed two-way ANOVA?

We are planning a study of the effectiveness of two therapies for treating depression. Group A will receive the current therapy and group B will receive a new and improved therapy. Participants are ...
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What do exponential of coefficients (like odds ratio in logistic regression) from linear regression indicate?

The long title says it all. For example, I have performed linear regression (OLS) with commonly used iris dataset using following formula: PL ~ SW + Species ...
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multiple regression for job satisfaction

I would like to know how professional and demographic variables influence job satisfaction. Which method do I have to use? ...
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In regression $y = \beta_0 + \beta_1^2X_1 + \beta_2 X_2$ isn't $\beta_1^2$ just a number multiplied by $X_1$, making it a linear predictor?

Like in the title, in regression $y = \beta_0 + \beta_1^2X_1 + \beta_2 X_2$, is this a linear predictor? Isn't $\beta_1^2$ just a number multiplied by $X_1$, making it linear? I was told this is a ...
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How best to deal with a left-censored predictor (because of detection limits) in a linear model?

Context: I'm new to Bayesian stats and am trying to fit a multiple regression with rstan. All variables are continuous and there is no hierarchical structure. One ...
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multiple regression with continuous and binary regressors

How can I do a multiple regression if I have continuous and ordinal (binary) (eg. male and female) regressors. Can I just add them like this lm(y~x1+x2+x3+x4, data=data)?
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How can I perform a regression analysis for two groups?

I have a problem where I have three groups (responders versus non-responders at baseline, responders versus non-responders at week8, and responders at baseline compared to responders at week8), in ...
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LMM: fixed effect significant in complex model, but not in reduced model

I constructed two models with lme4::lmer: decomposition ~ trait1 + trait2 + trait3 + (1|pair) all trait effects are highly ...
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How to test for overfit in lm() regression?

For a variable x, I find that coefficients of x, x^2, x^3 are all significant in lm(). But I ...
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How do the units of my dependent variable change if I normalize the independent variables before regressing?

If I normalize X the units of y change, so how do I interpret the output?
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How to best summarize Likert data (to use as an independent variable in a regression)?

I want to run a regression where one of the explanatory variables is a "summary" (details below) of a set of questionnaire questions that are answered on a Likert scale (although there are ...
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Can regression coefficients be guaranteed to be normalized?

When solving a multivariate linear regression problem of the form $A\vec{x}=\vec{y}$ where $A$ and $\vec{y}$ are known. Is there any from of preprocessing or scaling that can be done $A$ and or $\vec{...
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Does normalizing the design matrix change predictions? [duplicate]

I'm trying to show that $\hat{y} = X(X^TX)^{-1}X^Ty = \tilde{X}(\tilde{X}^T\tilde{X})^{-1}\tilde{X}^Ty$, where each column in $\tilde{X}$ is normalized by subtracting the mean and dividing by standard ...
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Ridge coefficient estimates do not match OLS estimates when $\lambda$ = 0

I'm trying to understand why ridge regression coefficient estimates (through the glmnet package in R) do not match the ordinary least squares (OLS) estimates in the ...
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About spurious & masked relationship and multicollinearity

I'm reading Statistical Rethinking by Richard Mclreath and I am bit confused about the subjects in chapter 5. The book itself is about bayesian analysis. This chapter specifically point out to ...
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Implication of correlated and non-correlated features and target for machine learning/linear regression

I am new to applying linear regression on datasets. I have experience mostly from Coursera courses and MOOCs. There are certain dilemma i am facing when I look at the feature and their correlation to ...
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Regression prediction with combination of predictors

I have one linear regression model: y ~ x1 + x2 (1) and now let $x_3 = x_1+x_2$, $x_4=x_1-x_2$, to form a new regression y ~ x3 + x4 (2), would the prediction of (1) and (2) be the same? If I add L1 ...
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Statistical comparison of coefficients over multiple models

I have question about statistical significance testing effect accros multiple model. Usually, with panel data we observe multiple cross-section units and account for each individuals fixed effects. ...
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How can a linear regression model give a low root mean square error but have a non well-behaved residuals vs fits plot?

According to this criteria, a good residuals vs fits plot should look like this: A plot like this: would not be considered a good linear model. Why would the model still give a low root mean square ...
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Which of two predictors reliably correlates with the DV changes, depending on the analysis. Evidence that it's their shared variance that correlates?

I'm working on a manuscript addressing hypothesized links between each of two empathic tendencies (measured with newly created, reliable self-report scales)—to share pleasures [Resonant Pleasure], and ...
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Least Square Estimator in terms of residuals

Given the following problem: Suppose the data vector $Y$ satisfied the model $$Y=X\beta+\epsilon.$$ Here $X=(X_1 ,X_2) $ is an $n\times k$ matrix, where $X_1$ and $X_2$ are $n \times k_1$ and $ n \...
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What are the best practices approaches for forecasting responses with multiple regression Timeseries models?

I am building a multiple regression time series model, in the response(y) depends on the relative amounts of two independent variables (x1,x2). However, both of the independent variables (x1,x2) are ...
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Does it change anything in a multilevel model when the predictor is a higher-level variable?

I am working on a project where I have to study the link between hospital competition and mortality (but also the duration of hospital stays). More precisely I want to determine whether the more a ...
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What is the meaning of the regressor characteristic root?

As described by Greene's Econometric Analysis (7th Edition), the regressor matrix's condition number measures how singular the matrix is. Therefore, the condition number is a measure of ...
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What is the difference between SUR and OLS?

How is the output different in the SUR (Seemingly Unrelated Regressions) equation from the OLS? Is it still the same as Bo + B1x = y?
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Johnson Relative Weights Analysis - Predictor variables

For Johnson Relative Weights analysis, can I have a mix of binary variables and continuous variables as predictor variables? I am doing relative weights analysis on a survey data which has rating ...
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1answer
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Using different multiple regression models that each change the available data

So I'm trying to analyse the difference in taxes paid between listed and unlisted companies. However, the sample consists of around 6000 unlisted and only 70 listed companies (there are only 210 in ...
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26 views

Should you standardize when using a Log link?

If I use a model with a log link function should I still standardize independent variables (since they differ in the scales range) or the log transformation is enough?
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Dealing with groups of high dimensional data

I've got a dataset that follows patients who underwent different treatment options for aneurysms. They can have more than one aneurysm and each may be treated differently. So I have variables like: <...
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Interpreting the coefficients of indicator variables in regression equation without indicator term

Suppose we were trying to estimate the impact of $Size$ of a house on its price while controlling for whether or not the house is located by the water. Suppose we constructed a dummy variable for ...
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Determining whether logistic regression with robust variance for repeated measures is appropriate for my data, or which other model type to use

I am doing an analysis to identify independent predictors of a positive drug test result for patients who self-report being on medication in a cohort study (i.e., I am assessing recent medication ...
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1answer
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quantile regression (cross validation in R) [closed]

How can I do a cross validation for quantile regression in R or any other methods to compare between multiple regression and quantile regression?
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Box-Cox data transformation to enable linear regression

I am performing multiple linear regression to predict a score (dependent variable) from multiple categorical variables. My dependent variable has skewed distribution with a large number of zero values ...
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Presenting crosstabs in addition to multinominal logistic regression results (SPSS)

I'm using multinominal logistic regression (MLR) in SPSS to build a predictive model to identify which variables have an independent effect on an outcome, all things being equal. I then want to use ...
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Is it useful or even necessary to standardize independent variables for linear regression?

When performing a linear multiple regression $ Y = X_1 + X_2 $ is it necessary that $ X_1 $ and $ X_2 $ provide the same scale? When I think of the variables being represented by an orthogonal axis, ...
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Can we compare the effects of continuous covariate and categorical covariate on response variable in generalized linear regression?

I want to construct a linear model among several variables. The model is $y = \beta_0 + \beta_1 x + \beta_2 z + \varepsilon$, in which $x$ is a continuous variable, and $z$ is a dummy variable, i.e. $...
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1answer
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Why the regression coefficient for normalized continuous variable is unexpected when there is dummy variable in the model?

I am doing a numerical experiment about linear regression modeling with presence of both continuous and categorical variables. As done in classical regression modeling practice, the categorical ...
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1answer
25 views

Checking the constant variance assumption for residuals vs fitted plots: What about for the same fitted values?

For a residuals vs fitted plot, we use the fitted values $\hat{Y} = \beta_0 + \beta_1 + \cdots + \beta_p x_p$ on the horizontal axis and the residuals on the vertical axis, and then compare the ...
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reporting results of a multivariate logistic regression using the glm function in R

I would like to use the glm() function in R to run a multivariate logistic regression. I have also run bi-variate statistics for each variable but want a test that controls for all variables at once (...
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1answer
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Logistic regression model predicts only one outcome, producing a high specificity but very low sensitivity. How do I improve the model?

I'm designing a logistic regression model to predict hospital mortality. Why? To identify 'adjusted' odds ratios for a variable of interest on mortality. Methods: - set up using a training dataset (75%...
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53 views

Linear regression is a estimation of conditional expectation?

I am studying the topic of regression for the first time and some questions arise. First, linear regression is a estimation of conditional expectation? And also the conditional expectation estimate is ...
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Normalizing zero inflated predictors for multiple regression

Hope I got it right, as this is my first active post :-) I was trying to find a solution the whole day for my problem. I am trying to predict a continuos variable based on 20 different predictors. The ...

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