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Questions tagged [multiple-regression]

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

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412 votes
7 answers
419k views

When conducting multiple regression, when should you center your predictor variables & when should you standardize them?

In some literature, I have read that a regression with multiple explanatory variables, if in different units, needed to be standardized. (Standardizing consists in subtracting the mean and dividing ...
mathieu_r's user avatar
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117 votes
12 answers
68k views

When should linear regression be called "machine learning"?

In a recent colloquium, the speaker's abstract claimed they were using machine learning. During the talk, the only thing related to machine learning was that they perform linear regression on their ...
jvriesem's user avatar
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96 votes
7 answers
190k views

Explain the difference between multiple regression and multivariate regression, with minimal use of symbols/math

Are multiple and multivariate regression really different? What is a variate anyways?
Neil McGuigan's user avatar
81 votes
5 answers
40k views

How can adding a 2nd IV make the 1st IV significant?

I have what is probably a simple question, but it is baffling me right now, so I am hoping you can help me out. I have a least squares regression model, with one independent variable and one ...
EvKohl's user avatar
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81 votes
2 answers
79k views

Multivariate multiple regression in R

I have 2 dependent variables (DVs) each of whose score may be influenced by the set of 7 independent variables (IVs). DVs are continuous, while the set of IVs consists of a mix of continuous and ...
Andrej's user avatar
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81 votes
0 answers
64k views

How can a regression be significant yet all predictors be non-significant? [duplicate]

My multiple regression analysis model has a statistically significant F value however all beta values are statistically non-significant. All the regression assumptions are met. No multicollinearity ...
Serene's user avatar
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75 votes
12 answers
6k views

What are some of the most common misconceptions about linear regression?

I'm curious, for those of you who have extensive experience collaborating with other researchers, what are some of the most common misconceptions about linear regression that you encounter? I think ...
73 votes
2 answers
27k views

Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression?

The coefficient of an explanatory variable in a multiple regression tells us the relationship of that explanatory variable with the dependent variable. All this, while 'controlling' for the other ...
Siddharth Gopi's user avatar
68 votes
3 answers
134k views

What is the effect of having correlated predictors in a multiple regression model?

I learned in my linear models class that if two predictors are correlated and both are included in a model, one will be insignificant. For example, assume the size of a house and the number of ...
Vivek Subramanian's user avatar
67 votes
5 answers
50k views

Is adjusting p-values in a multiple regression for multiple comparisons a good idea?

Lets assume you are a social science researcher/econometrician trying to find relevant predictors of demand for a service. You have 2 outcome/dependent variables describing the demand (using the ...
Mikael M's user avatar
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60 votes
9 answers
3k views

Are we exaggerating importance of model assumption and evaluation in an era when analyses are often carried out by laymen

Bottom line, the more I learn about statistics, the less I trust published papers in my field; I simply believe that researchers are not doing their statistics well enough. I'm a layman, so to speak. ...
Adam Robinsson's user avatar
58 votes
4 answers
125k views

How to visualize a fitted multiple regression model?

I am currently writing a paper with several multiple regression analyses. While visualizing univariate linear regression is easy via scatter plots, I was wondering whether there is any good way to ...
Shawn Wang's user avatar
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56 votes
3 answers
38k views

Why is polynomial regression considered a special case of multiple linear regression?

If polynomial regression models nonlinear relationships, how can it be considered a special case of multiple linear regression? Wikipedia notes that "Although polynomial regression fits a nonlinear ...
gavinmh's user avatar
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56 votes
3 answers
42k views

Multivariate linear regression vs neural network?

It seems that it is possible to get similar results to a neural network with a multivariate linear regression in some cases, and multivariate linear regression is super fast and easy. Under what ...
Hugh Perkins's user avatar
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54 votes
3 answers
93k views

Suppression effect in regression: definition and visual explanation/depiction

What is a suppressor variable in multiple regression and what might be the ways to display suppression effect visually (its mechanics or its evidence in results)? I'd like to invite everybody who has ...
ttnphns's user avatar
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53 votes
2 answers
73k views

Multiple regression or partial correlation coefficient? And relations between the two

I don't even know if this question makes sense, but what is the difference between multiple regression and partial correlation (apart from the obvious differences between correlation and regression, ...
user avatar
51 votes
6 answers
161k views

Choosing variables to include in a multiple linear regression model

I am currently working to build a model using a multiple linear regression. After fiddling around with my model, I am unsure how to best determine which variables to keep and which to remove. My ...
cryptic_star's user avatar
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51 votes
5 answers
31k views

Why do we need multivariate regression (as opposed to a bunch of univariate regressions)?

I just browsed through this wonderful book: Applied multivariate statistical analysis by Johnson and Wichern. The irony is, I am still not able to understand the motivation for using multivariate (...
KarthikS's user avatar
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47 votes
2 answers
4k views

How well can multiple regression really "control for" covariates?

We’re all familiar with observational studies that attempt to establish a causal link between a nonrandomized predictor X and an outcome by including every imaginable potential confounder in a ...
half-pass's user avatar
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46 votes
4 answers
45k views

Significance contradiction in linear regression: significant t-test for a coefficient vs non-significant overall F-statistic

I'm fitting a multiple linear regression model between 4 categorical variables (with 4 levels each) and a numerical output. My dataset has 43 observations. Regression gives me the following $p$-...
Leo's user avatar
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45 votes
5 answers
143k views

How to derive the least square estimator for multiple linear regression?

In the simple linear regression case $y=\beta_0+\beta_1x$, you can derive the least square estimator $\hat\beta_1=\frac{\sum(x_i-\bar x)(y_i-\bar y)}{\sum(x_i-\bar x)^2}$ such that you don't have to ...
Saber CN's user avatar
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41 votes
3 answers
34k views

How to present results of a Lasso using glmnet?

I would like to find predictors for a continuous dependent variable out of a set of 30 independent variables. I am using Lasso regression as implemented in the glmnet package in R. Here is some dummy ...
jokel's user avatar
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39 votes
1 answer
9k views

Why do we do matching for causal inference vs regressing on confounders?

I'm new to the area of causal inference. From what I understand, one of the main concerns that causal inference tries to address is the effect of confounders! For the sake of reference, let's denote ...
Ehsan Sh's user avatar
  • 555
38 votes
3 answers
27k views

How to tell the difference between linear and non-linear regression models?

I was reading the following link on non linear regression SAS Non Linear. My understanding from reading the first section "Nonlinear Regression vs. Linear Regression" was that the equation below is ...
mHelpMe's user avatar
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35 votes
2 answers
52k views

What does an Added Variable Plot (Partial Regression Plot) explain in a multiple regression?

I have a model of Movies dataset and I used the regression: ...
Abhishek Choudhary's user avatar
34 votes
1 answer
15k views

Geometric interpretation of multiple correlation coefficient $R$ and coefficient of determination $R^2$

I am interested in the geometric meaning of the multiple correlation $R$ and coefficient of determination $R^2$ in the regression $y_i = \beta_1 + \beta_2 x_{2,i} + \dots + \beta_k x_{k,i} + \...
Silverfish's user avatar
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34 votes
4 answers
27k views

Importance of predictors in multiple regression: Partial $R^2$ vs. standardized coefficients

I am wondering what the exact relationship between partial $R^2$ and coefficients in a linear model is and whether I should use only one or both to illustrate the importance and influence of factors. ...
robert's user avatar
  • 746
33 votes
1 answer
20k views

How to calculate the prediction interval for an OLS multiple regression?

What is the algebraic notation to calculate the prediction interval for multiple regression? It sounds silly, but I am having trouble finding a clear algebraic notation of this.
Michael's user avatar
  • 693
33 votes
4 answers
7k views

What are variable importance rankings useful for?

I have become somewhat of a nihilist when it comes to variable importance rankings (in the context of multivariate models of all kinds). Often in the course of my work, I am asked to either assist ...
Matthew Drury's user avatar
33 votes
1 answer
21k views

Sandwich estimator intuition

Wikipedia and the R sandwich package vignette give good information about the assumptions supporting OLS coefficient standard errors and the mathematical background of the sandwich estimators. I'm ...
Robert Kubrick's user avatar
33 votes
1 answer
1k views

Bound for Arithmetic Harmonic mean inequality for matrices?

NOTE: This question has originally been posted in MSE, but it did not generate any interest. It was first posted there, because the question itself is a pure matrix-algebra question. Nevertheless, ...
Alecos Papadopoulos's user avatar
32 votes
2 answers
10k views

Why are p-values misleading after performing a stepwise selection?

Let's consider for example a linear regression model. I heard that, in data mining, after performing a stepwise selection based on the AIC criterion, it is misleading to look at the p-values to test ...
John M's user avatar
  • 2,147
32 votes
1 answer
18k views

The proof of shrinking coefficients using ridge regression through "spectral decomposition"

I have understood how ridge regression shrinks coefficients towards zero geometrically. Moreover I know how to prove that in the special "Orthonormal Case," but I am confused how that works in the ...
jeza's user avatar
  • 2,109
32 votes
4 answers
62k views

ANOVA vs multiple linear regression? Why is ANOVA so commonly used in experimental studies?

ANOVA vs multiple linear regression? I understand that both of these methods seem to use the same statistical model. However under what circumstances should I use which method? What are the ...
florian's user avatar
  • 561
32 votes
3 answers
51k views

How to deal with multicollinearity when performing variable selection?

I have a dataset with 9 continuous independent variables. I'm trying to select amongst these variables to fit a model to a single percentage (dependent) variable, ...
Julie's user avatar
  • 811
32 votes
1 answer
9k views

How incorrect is a regression model when assumptions are not met?

When fitting a regression model, what happens if the assumptions of the outputs are not met, specifically: What happens if the residuals are not homoscedastic? If the residuals show an increasing or ...
SpeedBirdNine's user avatar
31 votes
2 answers
96k views

Transforming variables for multiple regression in R

I am trying to perform a multiple regression in R. However, my dependent variable has the following plot: Here is a scatterplot matrix with all my variables (...
zgall1's user avatar
  • 869
31 votes
3 answers
12k views

Does the order of explanatory variables matter when calculating their regression coefficients?

At first I thought the order didn’t matter, but then I read about the gram-schmidt orthogonalization process for calculating multiple regression coefficients, and now I’m having second thoughts. ...
Ryan Zotti's user avatar
  • 6,707
30 votes
3 answers
19k views

What does "all else equal" mean in multiple regression?

When we do multiple regressions and say we are looking at the average change in the $y$ variable for a change in an $x$ variable, holding all other variables constant, what values are we holding the ...
EconStats's user avatar
  • 865
30 votes
2 answers
42k views

Interpretation of betas when there are multiple categorical variables

I understand the concept that $\hat\beta_0$ is the mean for when the categorical variable is equal to 0 (or is the reference group), giving the end interpretation that the regression coefficient is ...
Renee's user avatar
  • 435
30 votes
4 answers
57k views

How to describe or visualize a multiple linear regression model

I'm trying to fit a multiple linear regression model to my data with couple of input parameters, say 3. \begin{align} F(x) &= Ax_1 + Bx_2 + Cx_3 + d \tag{i} \\ &\text{or} \\ F(x) &= (A\...
kris's user avatar
  • 433
29 votes
2 answers
5k views

In what order should you do linear regression diagnostics?

In linear regression analysis, we analyze outliers, investigate multicollinearity, test heteroscedasticty. The question is: Is there any order to apply these? I mean, do we have to analyze outliers ...
halil's user avatar
  • 295
28 votes
3 answers
8k views

Can (should?) regularization techniques be used in a random effects model?

By regularization techniques I'm referring to lasso, ridge regression, elastic net and the like. Consider a predictive model on health care data containing demographic and diagnosis data where length ...
RobertF's user avatar
  • 6,144
27 votes
3 answers
7k views

How to model this odd-shaped distribution (almost a reverse-J)

My dependent variable shown below doesn't fit any stock distribution that I know of. Linear regression produces somewhat non-normal, right-skewed residuals that relate to predicted Y in an odd way (...
rolando2's user avatar
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27 votes
2 answers
75k views

What is the correct way to test for significant differences between coefficients?

I'm hoping someone can help straighten out a point of confusion for me. Say I want to test whether 2 sets of regression coefficients are significantly different from each other, with the following set ...
cashoes's user avatar
  • 543
27 votes
1 answer
48k views

How to calculate p-value for multivariate linear regression

Software packages that calculate regressions sometimes also return p-values. I want to understand how to calculate this p-value by hand. Here's what I think I understand: I want to calculate the ...
Mars's user avatar
  • 1,108
26 votes
1 answer
47k 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.
1190's user avatar
  • 1,140
26 votes
1 answer
61k views

How to deal with high correlation among predictors in multiple regression?

I found a reference in an article that goes like: According to Tabachnick & Fidell (1996) the independent variables with a bivariate correlation more than .70 should not be included in ...
Ander's user avatar
  • 301
25 votes
2 answers
162k views

What happens when I include a squared variable in my regression?

I start with my OLS regression: $$ y = \beta _0 + \beta_1x_1+\beta_2 D + \varepsilon $$ where D is a dummy variable, the estimates become different from zero with a low p-value. I then preform a ...
seini's user avatar
  • 381
24 votes
5 answers
54k views

What is simply meant by reduced form?

In econometrics, what is meant by reduced form? Also, what are people looking for when they say "I would like to see the reduced form estimates." This has been thrown around at work and individual ...
LF12's user avatar
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