# Questions tagged [multiple-regression]

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

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### Partial derivative of a linear regression with correlated predictors

Let's set up the situation of having some $Y$ that I think depends on a linear combination of $X_1$ and $X_2$. I could fit a regression model:
$$y_i = \beta_0 + \beta_1x_{i1} + \beta_2x_{i2}$$
We ...

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### Logistic regression model for the probability of a don’t know response and a separate ordinal model for the ordered categories

Questions:
A response scale has the categories (strongly agree, mildly agree, mildly disagree, strongly disagree, do not know). A two-part model uses a logistic regression model for the probability ...

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### Gaussian Process Regression for High Dimensional Data: Vanishing predicted y values

I am working on a dataset with roughly 196 dimensions. I have been trying to fit Gaussian Process Regression into this dataset but it does not perform well.
Mathematically speaking, I found out that ...

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### Is it valid to use company/year combinations for (financial) data analysis?

I want do to a multiple regression analysis on some financial data. Sadly I only have 30 observations (the 30 different companies) and I would like to have more. My friend asked me why I don't add the ...

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### Statistical illusion? What's statistically happening, when regression analysis results get significant only with all predictors and interaction term?

I got a research question, where the hypothesis (derived from theory) postulates, that the relationship between predictor X and outcome Y is moderated by W (X+W+X*W -> Y). All variables are sums of ...

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### Drivers that should be positively correlated to Y have a negative correlation with the residuals?

In my data set it's clear that X,Y, and Z are positively correlated with A, since they have a strong correlation (close to 1) when I test the correlation in Excel. However, I took the regression of ...

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### Lagged (in)dependent variables: 2 time periods

Summary
I have a dataset with observations regarding an industrial process in two time periods. My goal is to find predictors of future performance, and I am wondering whether panel data regressions ...

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### Comparing two logistic regressions

I am working on creating a predictive model using logistic regressions. I am hoping to compare two different populations, using the same set of variables but different data sets with different sample ...

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### IHME Model Chris Murray [closed]

For Coronavirus death projections, does anyone know of any documentation on how Chris Murray produced the model?

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### Liklihood ratio test and linear mixed effects regression

I have a data set which includes sex, age, and 5 polygenic scores as independent variables, with 16 dependent variables. I have constructed univariate linear mixed effects regression models and ...

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### Superiority of two competing subset of predictors in terms of predictive information: Degrees of freedom?

Let's say we have four potential predictors in a linear regression model: $x_1, x_2, x_3, x_4$. Based on expert knowledge, we will always include $x_1$ and $x_2$. It is further decided that either $...

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### Extremely high MSE values for Lasso regression in R

So I've used the Lasso method to fit a 15 predictor multiple linear regression model on the College dataset (ISLR package) with Outstate as the response variable. The problem is that the MSE value ...

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### Can I use time as a predictor variable in a panel regression?

Is it possible to generate a new variable "phase" that is based on the time the participants were questioned? I generated this new variable by dividing the time into three phases (beginning, middle, ...

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### Multiple Regression Coefficient output

I am a University student running an analysis of data collected during a field trip.
The goal of this analysis is to determine whether the length and species of a limpet are good predictors of where ...

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### Can a predictor variable from one regression be the outcome variable in a multivariate-like regression?

I was hoping to get advice on what I believe might qualify as a multivariate regression analysis. The first equation is a rather simple linear multiple regression. However, one of the independent ...

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### Multiple Regression Analysis Beginner

Background: I am using an instrument that measures two physical properties, X1~Temperture and X2~ Velocity. When gathering the data to make the curve a set of predetermined concentrations are chosen ...

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### build and evaluate prediction model with the same data

I have a dataset with a sample size of n=30, one dependent variable and 31 possible predictors.
Now I want to build a regression model as part of a regression kriging model to predict my dependent ...

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### Mutliple Regression Calibration Curve

Background:
I am using an instrument that measures two physical properties, X1~Temperture and X2~ Velocity. When gathering the data to make the curve a set of predetermined concentrations are chosen ...

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### lm() coefficients -> vector with commas [closed]

Question:
I want to put the coefficients from a call to lm() into a vector with commas such as
vec=c(325.4361167,0.0675257,2.5519813,3.8001944,-22.9494678,2.4174843 )
How to do?
My Code
...

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### Software for multiple logistic regression analysis

Which free and easy to use statistical software can I use to perform a multiple logistic regression analysis?

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### Multiple regression or separate linear regressions

I have 2 predictor variables (x and y) and I want to find if they can predict scores on a z scale (response). All variables are moderately correlated with each other (in different directions).
My ...

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### Why is my A.T*A (A transpose A) matrix singular?

I'm running into an wall on my intuition when using least squares. I'm trying to simulate some data, for fun, and I'm getting a result that says my (A.T * A) matrix is singular.
In order to condense ...

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### What conclusion to make when multiple regression gives a relationship yet a linear regression doesn't

I had this exercise in my class, and as it will be not corrected, I have no clue which conclusion to get.
Assume we perform a multiple linear regression, for the sake of illustration, assume we do ...

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### Is a multivariate Beta Regression appropriate for modelling multiple dependent variables where each variable is a percentage?

I have a dataset with multiple predictors, some discrete and some percentages. My response variable is essentially 3 categories: percentage of high, medium and low life satisfaction, or maybe they are ...

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### Linear predictive model: how to attribute performance to individual features?

Here is my use case:
I am running some data analysis for a large retail chain who has thousands of outlets across the country. I am using a linear predictive model to predict whether we should start ...

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### Regression with two independent variables - optimize for linear error instead of quadratic error

I am trying to solve a set of linear equations in the form of ax1 + bx2 = c, where I know the values for a, ...

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### How to determine statistical significance in hierarchical regression analysis?

I have the following results:
My first hypotheses (H1a and H1b) are that X positively affects Y for two groups; G1 and G2 respectively.
Now I can see that H1a is supported, but how about H1b?
Before ...

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### Which assumptions do I need to test?

I am currently doing an OLS regression where my dependent variable is a Likert scale going from 0 to 10 and my independent variables are factor variables such as gender, ethnicity etc. Now, I know ...

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### Multivariate regression: independent categorical variable with 5+ non-mutually exclusive levels

My data set consists of around 461 acquisitions of firms, each with different motivations, that is acquisition_reason.
I want to predict a count variable using acquisition_reason as my main ...

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### how to determine the contribution (%) of predictors in multiple regression on distance matrices (MRM)?

Here i am trying to perform MRM with ecodist package, and i want to determine the relative importance of predictors in MRM model but i don't know how to do it.
For example
...

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### importance of regression MSE & variance of residuals

I have some code to create an OLS regression model, and the data is electrical demand interval data recorded on 1 hour increments along with outside air temperature. All other variables are dummy ...

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### Minimizing the expectation value of least-squares loss when data and model are randomly distributed with known normal distribution

How do you minimize the stochastic robust least-squares problem
$$
\min_x \mathbb{E}\left\{||A x - b||^2\right\}
$$
in which both the parameters $b$ and the model $A$ are normally distributed with ...

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### Significance test for mean predicted probabilities between two groups

I have survey weighted predicted probabilities from a multivariate Poisson regression, and calculated the adjusted prevalence difference of my outcome between two groups using the predictions. While ...

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### Multivariate regression - multiple regressions

Objective: To formulate (regress) x in terms of y and z, where
Data set 1
$x = a_1 x_1 + a_2 x_2 + a_3 x_3 + a_4 x_4 + c_1$ (linearly regressed; $R^2 = 0.70$)
Data set 2
$y = b_1 y_1 + b_2 y_2 + b_3 ...

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### Why should $n$ be greater than $k$ for multiple linear regression?

For multiple linear regression we have $n$ observations of the $k+1$ variables,
$$y_i = \beta_0 + \beta_1x_{i1}+ ... + \beta_kx_{ik} + \epsilon_i \text{ for i in 1,...n }$$
$n$ should be ...

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### ANCOVA, Covariates, & Variable Selection

I just want to preface this question by saying: I've searched extensively for answer elsewhere without luck. If, however, you think this question has been answered elsewhere please point me in the ...

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### Model specification through machine learning (neural network)

Assumptions:
I observe the entire population N, so in my setting there is no overfitting, a model that fits perfectly with my data is a "perfect" model
I know that the variables at play are the only ...

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### How to fix heteroscedasticity (funnel shape)?

I am running a mlr in python on a dataset with 2D feature vectors, X1 and X2 on a single response, Y. The data ends up being funnel-shaped, as below:
X1 v Y, with the colors being X2.
It was ...

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### In a linear regression, how can I test whether a given variable is driving the regression's predictive power?

Let's say I have at linear regression of income per capita (PPP) and other variables on food-prices
I suspect that the variable that is driving most, if not all, the prediction power of the ...

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### Maximum likelihood estimation using R [closed]

I have a multiple linear regression, that I want to estimate using a MLE approach. I would like to make the fit using a Beta distribution, with parameters u and v. How can I do this using R?

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### Comparing highly correlated predictors in log-binomial regression

I'm trying to figure out the best way to assess which of my highly correlated independent variables best predicts my dependent variable (y), a binary variable coded ...

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### R utility for pulling out parameters for individual variable in lm when there are effect modifiers (interactions with categorical variables)

NOTE: I think the emmeans package may be what I'm looking for. Still welcome any input!
Suppose I have a regression model $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_1 x_2$, where $x_1$ is ...

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### Determining the distribution of fitted values and residuals [duplicate]

For exam prep, we're supposed to answer this question (which we are supposed to be able to find the answer to in the course literature)
For the model specified in a) and proper normality ...

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### Multiple linear Autoregression

i'm new at statistics and can't be sure with my equation, which model it is.
I have a dependent variable Y (from 1.Jan. 2020 to 20.March., every 10 seconds.) and
independent variables in the same ...

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### Can someone provide the intuition as to why least squares and MLE lead to the same coefficient estimates for linear regression?

In books, I am seeing that the estimates for a linear regression are the same whether you do least squares estimation or maximum likelihood estimation (with certain assumptions).
I am not ...

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### Multiple Regression - How to find the case that worsens my model the most?

The big picture problem
I am missing participants for a Multiple Regression (MR) (as judged by a-priori power analysis). I want to be able to say: "Not enough participants, but even in the worst-case ...

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### Longitudinal data modeling with lmer

In a longitudinal dataset, each subject is tested every x period of time. I need to find the correlation coefficients between the score, age, and experience in years.
The age and experience increase ...

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### Interpreting regression with log transformed outcome + 1 control variable

I have checked the numerous posts on interpreting regressions with log-transformed outcome variables, but none that describe if this interpretation is impacted at all by the inclusion of a log-...

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### Why is it that $M_{X_2} M_X = M_X$ for two different residual makers?

I can't seem to figure this out algebraically, or intuitively.
Same with a result like $M_X M_X = M_X$ which I know is the idempotent property for a residual maker.
If I think of $M_X X = 0$, this ...

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### Regression Standard Error of $\beta_0$ and $\beta_1$ without inversion of $\mathbf{X}^\top \mathbf{X}$

I was working on a statistics homework and this is one of the questions:
]1
One of the parts asks to calculate a 95% confidence interval for the slope of each predictor. We are given that the ...