# Questions tagged [multiple-regression]

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

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### Statistical models with values in non-freely generated R-modules

Setup My general understanding of most statistical models is something like: a type of model for $n$ variables is a vector space $V$ and a function E: \mathcal{P}(\mathbb{R}^n) \times V \to \mathbb{...
1 vote
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### Multiple regression correlated predictors

I am trying to fit a multiple regression model with several predictors. Here you can find a reproducible example. ...
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### Detecting interactions in large logistic regression models

I have a dataset of a few million observations of a binary response with a low "Success"-probability of on average 1% to 2%. The dataset encompasses several categorical (~20 some with up to ...
366 views

### Assumptions of Linear Regression (homoscedasticity and normality of residuals)

I am confused about some assumptions of linear regression: homoscedasticity and residuals are normally distributed. These two require residuals, but to get the residuals, we need to fit the model ...
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### Linear Regression with point data and continuous data [closed]

Question - What type of regression or other statistical technique would be used for continuous data linked with point data? Data - My data is for product that goes through continuous processing lines ...
1 vote
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### Interpretation of (simultaneous) confidence band against fitted values in multiple regression

In a homework question, I am asked to interpret a figure of the confidence band and simultaneous confidence band of 95% confidence level plotted against predicted values. The confidence bands are ...
1 vote
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### What is in-sample vs out-of-sample in a multiple linear regression?

I was just thinking about what would be considered interpolation vs extrapolation for multiple linear regression, and realised I'm not sure exactly how it would be defined, nor could I find an answer ...
1k views

### How to prove an OLS estimator is inconsistent under simultaneity

I have two equations $Y_i = \beta_0 + \beta_1X_i + \epsilon_i$ $X_i = Y_i + Z_i$ and additional information that $cov(\epsilon_i, Z_i) = 0$. And I need to prove that using the OLS estimator in the ...
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### Comparing observed and predicted values across several measurements

I am investigating whether a medical treatment has an effect on cognitive measures (aside from curing the medical problem). I have been looking for a statistically sound method to approach the ...
286 views

### How to "choose" binary variables which have a big impact on a regression?

I am currently facing an issue with analyzing my data for a project. I have a dataset of about 100.000 samples. I have approximate 50 columns which are all binary and my dependent variable is time ...
582 views

### Does it make sense to talk of "multicollinearity" in the context of simple linear regression?

As far as I am concerned, "multicollinearity" referers to the presence of collinearity between two or more variables, even if there is no pair of variables that have a particularly high ...
1 vote
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### Checking linearity assumption in regression with quadratic terms

I have a few questions about checking the assumptions for linear regression: What is the best way to check linearity? Many recommendations I saw said to check scatterplots, but since linearity refers ...
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### Does ceiling effect of outcome variable violate linearity assumption of linear regression

If there is a ceiling effect in the outcome variable, e.g. in my case the outcome variable is limited to a certain value and 25% of data points have that highest possible value, does this mean that ...
1 vote
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### How to visualise the value of one predictor in a multiple linear regression

I'm looking for confirmation on whether the approach I have is statistically correct / straightforward, and if there might be any references supporting this line of thinking on how to visualise ...
1 vote
869 views

### How to choose covariates for synthetic control

Trying to construct a synthetic control and I've chosen a set of covariates that are correlated with my outcome variable and significant for P>|t| using OLS. Is choosing covariates for synthetic ...
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### What is the best architecture for multi-target text regression?

I'm building an AI model using Google's 'Civil-Comments' dataset. It has 7 different labels, each a float than can be anywhere from 0 to 1. Embedding Bags, which I have read about. do not perform well....
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### What I have to do more to improve my regression model in r [closed]

I want to make beverage sales predicting model. I am doing regression analysis. All the column types are integer. The dimensions of the data are 15375 rows x 400 columns. The dependent variable $y$ is ...
251 views

### 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: ...
693 views

### Fitting a decaying exponential curve to a linear regression fixed factor in R

I am looking at how landscape features might impact the presence of bat species using a binomial linear regression model in R. An example of one of my model is: <...
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### I have an insignificant beta weight of a predictor, which the only predictor in a step with significant R-square change and significant F-value

I am running a hierarchichal multiple linear regression with 4 steps containing theoretically justifyable variables: Outcome: pain rating Step 1: demographic variables (age, gender) Step 2: Pain ...
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### Use of multiple comparison correction and composite DV

I am investigating the effect of a single X on a composite DV, Y. I want to also investigate the effect of X on the 36 sub-components of Y. Thus, I would have to run 37 multiple regression models, ...
352 views

### How to include dummy variables in multiple regression equation

I have run a multiple regression analysis and have three explanatory variables (two quantitative and one categorical). The categorical variable has 4 levels; therefore I have 3 dummy variables in my ...
1 vote
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### Why estimates of data via residuals has 50/50 effect on significance compared to original data?

I am generating data according to the following model In the real dataset, variable I is unknown and the goal is to study the relationship between I and D, B11, to see if it is significantly non-zero....
1 vote
661 views

### Determining independent vs dependent variables for multiple regression models

I am trying to create a multiple regression model in Python that takes hours slept, minutes of exercise, and my average daily mood to fit a 3D surface of $1^{st}$ (plane) to $5^{th}$ order polynomials....
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### Measuring Standard Error of two or more coefficients combined

A silly example. ...
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### Standardized regression coefficient

I was wondering the following: Does the standardized coefficient on X1 in a regression of Y on X1, X2, ...,XN go to one, as the bivariate correlation of Y and X1 goes to one. If so, why? Or is it ...
1 vote
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### Residual plot has pattern when all predictors included, less of a pattern when only weak predictor included

I saw something unexpected in the residual plots of my regression analysis: when I plot the residuals vs. the fitted values for the full model with multiple predictors (R squared = 0.24), I get a plot ...
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### Selection of confounding variables in multiple linear regression with AIC, BIC, or both? [duplicate]

I am using multiple linear regression to control for confounding variables. I have analyzed my data using Bayesian Information Criterion. Is there an advantage to also using Akaike Information ...
892 views

### OLS - Why coefficient Beta has Normal Distribution but not t-Distribution?

I have a little trouble understanding the solution to the following problem. To my understanding, coefficients in OLS should follow t-distribution. However, the solution says it follows Normal. Please ...
15 views

### zero values in dependent variable , correct structure of the data , zero-inflated model

I want to understand the relationship between macroeconomic variables and the fundraising volume for specific funds (secondary funds). I got the following dataset (assume a table: 1. Fundname: Abbott ...
1 vote
695 views

### Cross-level correlations in a Multilevel Model

I'm currently running a daily diary study, where participants first complete a baseline survey and then complete the same survey each day for 10 days. My data has a nested structure (days nested ...
1 vote
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### Can I run a regression model if I don't have the same years of data across all variables?

I am still identifying co-variables for my regression model. I now have a dataset across 10 years. But one variable (self-rated physical health) does not appear in all the 10 years. According to the ...
659 views

### Transforming a natural log of a variable into the original variable

I am using a replication dataset for a research, and one variable (GDP per capita) is included in the dataset only as a natural logarithm. Is it possible to transform the ln(GDP per capita) back into ...
1 vote
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### Assumptions of linear regression, when its results are input for a ranking based algorithm

I ran a linear expression with gene expression being the explained variable. Two characteristics of the cell in which it is expressed (the data is single-cell data) are predictors. There are about 300 ...
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### How to verify linear functional form in a MLRM?

I'm performing a Linear regression but I don't know how to verify that the coefficients are linear (Performing with Gretl software) could you guys help me to find a way to verify this?
1 vote
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### Multivariate logistic regression not returning expected significant p-values in R

I am very new to R and statistics in general and have been stuck on this for a couple of weeks so any input would be greatly appreciated. I have a binary outcome variable ...
48k views

### Hat matrix and leverages in classical multiple regression

What is Hat matrix and leverages in classical multiple regression? What are their roles? And Why do use them? Please explain them or give satisfactory book/ article references to understand them.