# Questions tagged [multiple-regression]

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

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### Why does heteroskedasticity not affect $R^2$ and why does it make estimated regression more statistically significant?

I am studying what the consequences of heteroskedasticity are. And i found that assuming that the model is linear in the parameters (i.e $Y=X\beta+\epsilon$), is identifiable, has no perfect ...
27 views

### Calculating MLE under restriction on coefficients

Consider the following simple linear regression model: $y_i = a + b \cdot x_i + \epsilon_i \space\space\space\space\space\space\space where \space i= 1, 2, 3, \cdots , n$ here $\epsilon_i \space's$ ...
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### Partial effect interpretation and zero conditional mean assumption

Let's say we have the following population equation. $$y = \beta_{0} + \beta_{1}x_{1} + \beta_{2}x_{2} + u$$ Then to explain the interpretation of $\beta_{1}$ or $\beta_{2}$, we can look at the ...
141 views

### Computing the variance explained by a predictor variable in logistic regression

I'm keen to know how to compute the variance explained by a particular predictor variable in the model (say component specific R squared). I went through Calculate variance explained by each predictor ...
6 views

### How can I calculate the proportion of influence 2 factors have on a continuous variable?

I have a dependent continuos, but not normal variable y and want to know how much of the variance of y is explained by x_1 and x_2. Both x variables are nominal. The Levene test y~x_1+x_2 led to the ...
1 vote
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### sample size calculation for generalized least squares regression

I want to calculate the sample size for a multiple linear regression with correlated residuals, specifically using generalized least squares. For OLS, it appears that there a various different rules ...
48 views

### Difference between multivariate regression and running multiple linear regression models for every dependent variable

This post is to understand differences between multivariate linear regression models (i.e multiple independent variables predicting multiple dependent variables) and running multiple linear ...
38 views

### interpretation of loglog regression

It is common in marketing and other econometric disciplines to model an baseline + incremental quantity due to treatment. E.g baseline sales + incremental sales(due to marketing). It is common to ...
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### Can you use linear regression to predict individua or group player performance from team performance in a Public Good Game?

I am doing an analysis of the experimental data I have collected. In particular, I should do a panel regression. I have collected data from my experiment on public goods. My variable of interest is ...
636 views

### Can I use multiple linear regression with binary output?

I have a dataset with $10$ inputs containing real numbers and an output which is binary ($0$ or $1$), and I need to make predictions. So, I thought of using multiple linear regression to predict an ...
1 vote
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### How to do a pairwise test of each regression model coefficient over groups?

Given a regression model $F(X) = y$, where $F(X) = \beta_0 + \beta_1:groupX + ...$ I want to test a null hypothesis that there is no difference in the coefficients between groups for each coefficient ...
24 views

### Interactions in Moderated Regressions with multiple IVs

I have multiple IVs in my moderated regression model, but I want to look at the specific interactions with each of the IVs. Is this possible? I did run the regressions separately but because I have so ...
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### How to tell if I'm pseudoreplicating in a mixed model by taking slices of the same measurement

Here is my data setup. The dependent variable is mean resultant length (MRL), i.e., in context, the degree to which a firing unit is firing in phase with a particular frequency of the local field ...
23 views

### ANOVA is significant but also demonstrates non-inferiority

I have data that is looking at comparing a cheap (T) to expensive (V) ultrasound device with the hopes that the cheap is the same as expensive. There was 4 different examiners that used 4 different ...
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### Linear Trend across Sessions and Timepoints: Which Matlab function?

I would like to test for linear a increase in performance in my training study using MATLAB. In this study each participant went through 6 training sessions, each session containing 4 time points of a ...
89 views

### Obtaining Residual Sum of Squares from a large OLS problem using a naive sequential approach - why doesn't it work?

Suppose we have an OLS problem with a large number of predictors: $Y = X_1 + X_2 + \cdots + X_p$. I want to obtain its RSS. I don't need to know the regression coefficients or individual residuals, ...
1 vote
32 views

### Distinguishing between $\epsilon$ and $e$ in interaction with residual maker matrix $M$

I've hit a small snag in working out some of the implications of the residual maker matrix $M$. Through previous posts I've been able to understand the difference between the use of $e$ and $\epsilon$,...
40 views

### Non-significant predictor variable becomes significant when two control variables are introduced into model

I want to investigate the correlation of $A$ and $B$ on $X$, so i do a multiple linear Regression. On their own $A$ and $B$ are significant predictors of $X$ in a simple linear regression. When i test ...
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### Is adding variables to a multiple regression Model always "Hierachical Regression"?

I want to test the connection between N,G and the Interaction of NxG to Y for an assignment. My task is to first do an multiple Regression with N+G and then integrate the interaction of both in a ...
429 views

### How can I interpret it when correlation between two variables is significant, but not in a multiple regression?

I want to investigate the correlation of $N$ and $G$ with $X$. In a correlation matrix, $N$ and $G$ are both positively correlated with $X$. $N$ and $G$ are correlated, too, by the way. In a multiple ...
11 views

Typically in genetic studies, sensitivity analyses are used to quantify how estimates of genetic effects are affected by adjusting for additional covariates $Z$. So we have separate regressions for a ...
27 views

### Understanding the results of the GLM in R

I have data on the abundance of beetles I have collected (I have also done this for biomass of beetles and proportion of abundance represented by a particular functional group of beetles, but only ...
16 views

### Time Series Modeling Question

I am trying to model the effect of volume traded on implied volatility of weekly options. I have the data for 52 weekly expiries at 5 minute intervals. However the key insight is that each weekly run ...
32 views

### Multivariate analysis for non-normal variables

Edit: I am trying to produce a model in R in order to analyze the relationship between several variables. I am looking at the relationship between behaviour and dispersal of a population. Each ...
9 views

### Creating a scoring system in binary logistic regression

I have used forwards binary logistic regression to determine which predictors are significant in classifying patients into two clinical categories. Three significant predictors were identified. Could ...
1 vote
16 views

### Quantifying the impact of multiple time series on another time series

I have a few time series that correspond to the popularity of various documentaries about food, and other time series that correspond to outcomes of interest (various dimensions of food consumption). ...
38 views

### Algebraically, how to calculate coefficients for multiple regression with 3 input variables?

I need to run a multiple regression in some limited software that cannot preform any matrix calculations. I am not so good at deriving these on my own and would love some assistance. I need something ...
1 vote
25 views

### Categorical variables & their co-occurence as an explanatory variable?

A colleague of mine has performed experimental evolution of some bacteria populations in the presence of several antimicrobial agents. The experiment has been replicated twice (2 blocks containing ...
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### Hierarchical Regression analysis: predictor sig, block non sig

I ran hierarchical regression. Block 1 and Block 2. add block 2 does not significantly improve model fit (p>0.05). However, one predictor in block 2 is sig. (p<0.05) In this case, can I report ...
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### Practical examples of multiplicative regression model

Majority of the examples of multiple regression in practice is written as additive model. Can you give me some practical examples of a multiplicative regression model (i.e. a model that can be fitted ...
28 views

### Do you need control variables in multi level regressions?

I am working with multilevel regressions. Do these need control variables? I ask as I am wondering if the independent variables grouping of multi level regressions is enough? In this case, the groups ...
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### Analytical form of Linear Mixed Model Regression With Interacting Random Effects?

I have been reading up on Linear Mixed Models with random slopes, and I have a question that I could not find addressed anywhere. I have seen a lot of R model formulae (example) where random slopes ...
426 views

### Any way to test if the association between X and Y could be causal, reverse-causal or non-causal (just correlation)?

I'm doing a regression between Institutional Investment and Total Debt for 500 companies over 2000-2022. Basically, it's panel data. I get the results of the regression and I see that the two are ...
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### Interpreting linear and quadratic terms with same sign

I am running a second order model with betweenness centrality and closeness centrality as independent variables and cognitive demand as dependent variable. The results shows that betweenness ...
20 views

### are these repeated measures?

I have a set of 30 patients. Each patient has a variable number of observations over a variable length of time(ranging from 4 to 10 data points per patient). My outcome variable is whether they have ...
32 views

### Is it possible to generate a linear regression from another linear regression?

To provide context with the data, I have several variables $X_1, X_2, \cdots, X_K$ that represent $K$ individuals. When using all of these variables in a multiple regression (with ridge restriction) I ...
39 views

### When adding control variables to a regression, are we actually literally changing the comparisons being made in the data?

If I am regressing wages on years of schooling, I can think of this as I am comparing the wages of people with different years of education. But now if I were to add the age of the individual as a ...
1 vote
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### The reason of different regression results between "enter" and "stepwise" methods

I and one of my colleagues conducted regression analysis in SPSS. There is a significant difference in our regression results obtained using the "enter" and "stepwise" methods. All ...
1 vote
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### Comparing the PCA modes from two different covariances

Suppose I have a set of $n$ vectors $x_i$ arranged as columns of a matrix $X$ and I want to perform PCA to reduce the number of dimensions needed to explain some set of observations. I have developed ...
268 views

### Help with the normality of the residuals of my regression model

I am doing a regression in R on the effects of EU and UN economic sanctions on GDP. My model looks like this: ...
1 vote
79 views

### Heteroscedasticity still present after Box-Cox transformation

I just started to learn regression and I'm trying to fit a linear regression model to some data with one continuous independent variable x1, one categorical variable x2, and the dependent variable y. ...
1 vote
50 views

### Multicollinearity in Multiple Regression with SPSS

I want to run a multiple regression in SPSS with 7 independent variables but 3 of them are showing high correlation coefficients in the correlation matrix. How do I diagnose multicollinearity?
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### Log Transforming variables already in percentage [duplicate]

I'm running a regression analysis and I'd like to know if log transforming a percentage value is ok. My y-values are already in percentages and my x-values in absolute numbers. But I'd like to know by ...
361 views

### Proper analysis for vernal pool study data

I am trying to analyze a dataset consisting of counts of amphibian egg masses (3 different species) in nine vernal pools over a four-year period (consecutive years, 2014 to 2017). During each count (...
103 views

### Is it possible to use smooth functions as part of a nonlinear regression?

Background I am fitting nonlinear regressions with a single response and two predictors. I know the relationship between the response and each of the predictors, but I do not know how they interact. I ...
1 vote
I'm trying to work out a linear regression model where both inputs and outputs are multidimensional. Suppose we have $n$ input variables, $m$ output variables and $k$ observations. Each observation ...