Questions tagged [multiple-regression]

Regression that includes two or more non-constant independent variables.

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INTERPRETATION OF REGRESSION RESULTS [on hold]

I would like to be able to interpret these results as follows: Result 1: how can I interpret this result? X1 = 0.045 and significant at 10% X2 = -0.036 and significant at 10% Adjusted R-squared = 0....
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Calculate individual squared

My project is in the field of urban design, I have to do a regression analysis, which I did't have any idea what was that. However, I did that and here is the screenshot of my result As you can see ...
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False-discovery-rate correction on a large set of multiple linear regressions with different sample sizes

I have a dataset of brain images in which each pixel value corresponds to a measure of neuron activity. The images were taken in different conditions described by three regressors (two fixed-effects ...
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Difference between estimating parameters for prediction and estimating parameters for their own sake

In a 1989 paper on orthogonal regression, Ammann and Van Ness write: An important caveat should be noted. The errors-variables-model is useful when the primary goal is to estimate the model ...
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Estimating coefficients of a linear model with collinear dependent variables that have errors with known variances

I want to estimate the coefficients $\beta$ of the linear model $Y=\beta X$ from observations of $(Y_i,X_i), i=1\ldots n$, where $X$ is multidimensional. Two problems: All variables have been ...
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Can someone please enlighten me with this restricted econometrics model?

The question is , test the hypothesis: 5% unemployment rate has triple the effect of two extra weekend days a month on total accidents. Test for the corresponding coefficient restriction using eviews ...
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24 views

Linear hypothesis when regressor matrix singular? How do I do F-test?

I have the following model $y_i = \beta_0 + \beta_1 x_{i,1} + \beta_2 x_{i,2}$ I know $\hat{\beta_0} $, $ \hat{\beta_1}$ and $\hat{\beta_2}$, and also the $R_u$ and the covariance matrix of the model. ...
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Formulating Linear regression model [duplicate]

I am trying to make multiple linear regression models for multiple crops where my dependent variable is Yield of crops for ex. Yield of Wheat, Rice, etc. I have data set in which each row represent a ...
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Impact of individual features under multi-collinearity

Assume the following scenario: I have four features: $x_1$, $x_2$, $x_3$, and $x_4$ There are non-negligible multi-collinearity among the features. I want to predict $y$ (response variable) with ...
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Choosing variables in multiple linear regression [duplicate]

I am trying to make multiple linear regression models for multiple crops where my dependent variable is Yield of crops for ex. Yield of Wheat, Rice, etc. I have data set in which each row represent a ...
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How to generate artificial data to have a similar results after doing an OLS estimation?

I am trying to replicate a paper that the data are confidential, however, for the sake of practice in coding and performing similar analysis, I am trying to generate artificial data so that after I ...
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Can I use linear regression for predicting time series? [on hold]

I have the percentage of defaulted clients in porfolio for different periods as target variable and macroeconomic factors as explanatory variables. Can I use simple linear regression? What other steps ...
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Help me interpret this negative linear regression [on hold]

This is the output I have for a multiple linear regression I did in R. ...
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Removing multi-collinearity with PCA for regression analysis

I'm interested in studying the impact or importance of each feature on the response variable. I'm thinking running multiple linear regression with multiple features, and running regression analysis ...
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Choosing the right model: Poisson, Quasi-Poisson and Negative Binomial?

[Edit] I am working in R. I am investigating the effects of weather on restaurant demand. My DV is the number of restaurant visitors per hour, my IVs are five weather variables and all other ...
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Are there constraints on the ratio of dependent variables to independent variables for PLS regression?

I will begin with a disclaimer that while I understand the general underlying principles behind PLS, my linear algebra background is rather limited. I have trouble with the details of constraints on ...
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Multiple Linear Regression using expected values instead of observations

Normally when doing multiple linear regression we use multiple observations of the features to estimate the coefficients, in my case I want to minimize the square error. This formula normally is: $\...
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How to interpret Residuals vs. Fitted Plot

I am investigating the effects of weather on restaurant demand. Currently, I am testing the model assumptions for my multiple linear regression model. My model specification (simplified) is as ...
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simulate data for multiple regression based on standardized coefficients and covariance among predictors

I want to simulate data for multiple regression based on standardized coefficients (denoted $\beta^{'}$) and covariance structure among predictors. My problem is that I don't know how to determine the ...
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What is the difference between “controlling for a variable” and interaction?

I've always believed that multiple regression was to perform what we often call "controlling for a variable". So if I run a multiple regression with height as the dependent variable and weight and ...
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multicollinearity high R squared

I understand that one of the ways to detect multicollinearity would be to observe low t-stats and high r squared. t-stats will will be low because the standard errors of the coefficients will be high, ...
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1answer
61 views

What $A$ would allow $\beta_1=0,\beta_2 = 2$ to be written in the form $A\beta = 0$?

I got this question earlier for a review, but am struggling to find the answer in any texts: Suppose that you have to fit the model $$y=\beta_0+\beta_1x_{i1}+\beta_2x_{i2}+\beta_3x_{i3}+\...
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Role of dummy variable in a multiple regression

If a dummy variable is included in a model, such that $1$ is if the person has retired and $0$ if they are still working, measured over multiple time points, does this mean that the regression ...
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1answer
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Does a Vector Autoregression Model truly avoids circular function issues?

Let's say you have a VAR model that estimates GDP and Unemployment among many other variables using a certain number of lags. This VAR model can estimate or regress GDP using Unemployment. And, it ...
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I want to understand how to interpret variance inflating factors

If I have a multivariate model with one outcome and two exposures of interest and the variance inflating factors are equal to each other...what does that imply? I am trying to understand if I should ...
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Finding the Case with the Highest Influence

I'm new to regression and diagnostics so if this seems a bit basic/unnecessarily long-winded that's why. I perform a multiple regression of a response variable on four predictor variables. There are ...
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Can collinear variables be justified because both “matter”?

Slightly related to previous questions by others, but more theoretical/hypothetical. Is there an accepted phrase, or perhaps a decent argument to which you can kindly refer me, for including two ...
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How to detect influential points in multiple regression?

I have a multiple linear regression model with two exposures and four covariates. Can anyone please clarify my understanding on how to detect influential points? Run a multiple regression model and ...
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Sample Size Estimation for Multiple Linear Regression

I am constructing a multiple linear regression model to estimate a population mean from a population of unknown size. My data currently has 100 observations and 5 variables. 2 of these variables are ...
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How to measure the difference between two random forest models?

Suppose that I have training data defined as a set of N records (or samples) defined by its attributes (or descriptors, features, as you prefer), and I trained two random forest models with two parts ...
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Fitting many curves with many parameters : an error-matrix based strategy

I have multiple curves : $\tilde{f}_i(t_j)$ with $i\in \{1,...,n\},n\in\mathbb{N}$ and $j\in\{1,...,N\},N\in\mathbb{N}$. I want to fit them with functions $f_i(t)$. Those functions depend on $K$ ...
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Taking the square root of my DV solved problems with scewness in residuals. What does this mean?

As you could probably guess, I am -very- new to both statistics and R. SO the obvious answer would be that I have to get home and study more, but I would also appreciate some pointers here. I have ...
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Multiple regression and confounding

I have a multiple regression where I have been asked to consider two exposure measures (say X1 and X2) and outcome Y. The overall aim of the analysis is to examine the evidence for an association ...
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Fit a linear function to multiple measurements

I have the data of a measurement of the same value that was repeated multiple times to decrease random noise. There are multiple values per input-value (time), an example could look like this: ...
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Least squares estimates

Problem: Suppose we have $Y_{1j}=\beta_1 +\epsilon _{ij}$, $j=1,...,n_1$, $Y_{2j}=\beta_1 +\beta_2 +\epsilon _{ij}$, $j=1,...,n_1$,and $Y_{3j}=\beta_1 -2\beta_2 +\epsilon _{ij}$, $j=1,...,n_2$., where ...
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Nested quasi-experimental multi-group time series modeling

I'm trying to figure out how to model a research design. I'm conducting a study in two classrooms, one is a control and the other is a treatment. Therefore, it's quasi-experimental as there is no ...
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Is this plot of residuals and fitted values homoskedastic?

If not, why not? The first plot shows residuals against fitted values, the second plot shows standardized residuals against fitted values. Overall my aim is to determine if a multiple linear ...
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Identifying most significant variables in multiple regression

Imagine that the total cost for 100 patients undergoing the same procedure in a hospital, is further broken down into 10 cost categories (such as the surgery fees, room charges, consumables cost etc). ...
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How to interpret these residual plots in regression analysis?

I did multiple regression analysis. There are 2 independence variables and one dependence variable. Because there are heteroscedasticity problem, I did log transport about dependence variable. All ...
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1answer
23 views

Doesn't adding a quadratic term in Linear Reg Model violate independence of predictors (Multicollinearity)?

I was going through an example of Polynomial regression and could not understand why adding quadratic term doesn't violate Linear Model assumption of multi-collinearity as we are just squaring the ...
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1answer
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Recoding Categorical Variable for multiple regression

My independent variables include continuous (Age, weight), binary (Smokes or not) and count data (number of visits to doctors 0-5), while the dependent variable is continuous. Should I use dummy ...
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Is it appropriate to use 3 linear regressions to assess the impact of one common independent variable?

I need to assess the impact of cultures on urban economies. The hypothesis is that more entrepreneurship oriented culture will better facilitate the local economy, controlling for other factors (that ...
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Equivalence Testing in multivariate regression models

This questions seems to have been asked, but never answered before. The question I have is: is it possible to implement the idea of equivalence testing in multivariate regression models? For example, ...
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38 views

is “multivariable linear regression” the same as logistic regression?

I am new to machine learning and I am simultaneously studying linear and logistic regression. Logistic regression is when there is one dependent variable and there may be more than one independent ...
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How do I choose the order of a hierarchical model with 3 predictors when 2 have a high correlation

I have 3 predictors (x,y,z) for a multiple linear regression and two of them (y,z) have a high correlation (>0.95). I know I shouldn't include both of those predictors in the model because it can ...
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17 views

Using the sum of the absolute residuals divided by the sample sum as a normalized goodness-of-fit estimator

I am trying to make an automatic method to do a peak fitting to some spectra, using multiple least squares. I would like to be able to compare the quality of the fit between several different cases. ...
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Multiple Linear Regression with Mediator in SPSS

My variables (all continuous): IVs: Secondary Traumatic Stress and Vicarious Traumatization DV: PTSD Mediator: Social Support I checked the correlations between the variables and they are all ...
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How to incorporate a non-linear relationship in a multiple regression model?

Suppose the beta coefficients of a weighted multiple regression model is given by the matrix formulation: ${\boldsymbol \beta} = ({\bf X}^T{\bf W}{\bf X})^{-1}{\bf X}^T{\bf Wy}$ Suppose that the ...
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35 views

What kind of multiple regression should I use?

I have a lognormally distributed continuous dependent variable that I would like to predict using multiple regression. I am using a forward selection process and have selected three predictor ...