Questions tagged [regression]

Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.

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Proving how scaling of predictor variable in linear regression, affects the fitted coefficient [duplicate]

In linear regression the OLS solution is given by: $$ \hat{\beta} = (X^TX)^{-1}X^TY $$ I want to show that if you scale the $i$th predictor variable by a constant, then the corresponding $i$th ...
Dylan Dijk's user avatar
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Coefficient stability between two different models

I have applied two different models. One OLS model with independent variables X1, X2, X3 and one ridge model with independent variables X1, X2, X3, X4 and X5 through glmnet package in R. So let’s say ...
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Can I violate assumptions of normality for categorical linear regression models?

I'm using packages included in this R/rStudio tutorial to set up some linear regression models comparing a continuous dependent variable (eccentricity) to three categorical variables (year, bird ...
ElizaBeso000's user avatar
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Inverse of a design matrix [closed]

I am a bit confused as to where the 1/3 comes from when we take the inverse. Could someone explain when we take the inverse of a matrix where the constant outside of the matrix comes from?
Harry Lofi's user avatar
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Regression when multiple observations per individual but final result is the same

I'm very new to data analysis. I'm trying to find the causal effect of seating row and laptop use on grades at a specific university. I have data from 15 introductory economics lecture sessions ...
Abdul's user avatar
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How to plot/visualize correlation values from two different methods for comparison?

I am working on a project wherein we are comparing two methods used for modeling gene expression: one method is using elastic net and other is using lasso regression. In one method: we see that ...
Rhea Bedi's user avatar
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Constrained least squares where at least one of two coefficients is zero

I have a linear model with a bunch of variables a number of linear constraints on these variables. I am currently using quadratic programming to solve this constrained least squares problem. However, ...
galpo's user avatar
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How to adjust for double counting data to account for multiple perspectives in logistic regression

I am trying to measure if referees are biased in favor of players from the same geographic region (as themselves) in a sport. I want to see if players from the referee's region are more likely to win. ...
ral's user avatar
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Understanding equatiomatic output

I have fit a lmer model as follows: ...
Rabin KC's user avatar
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Propensity score matching - within subsample analysis

I am trying to understand the impact of a graduate degree in mathematics on the wages of students compared to other degrees. I have been running a probability score matching model using a logarithm ...
Giulio Cavallari's user avatar
2 votes
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How to "see" the covariance matrix and mean vector?

I am working with following model specifications (Regression, Modelle, Methoden und Anwendungen, Springer-Verlag Berlin Heidelberg (2009), p. 147): $$Y \sim MVN(X\beta, \sigma^2I)$$ $$\beta|\sigma^2 \...
BlankerHans's user avatar
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Statistical testing on non-random sample?

I am working with a non-random sample in an observational study but would like to do statistical testing to show certain trends and processes. Statistical tests assume random sampling, which is not ...
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Asymptotic standard errors vs exact standard errors

I am getting confused about the derivation of standard errors for the OLS estimator $\widehat{\beta}$. I have seen two different ways to derive standard errors: (i) from the exact covariance matrix of ...
Residual Claimant 's user avatar
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Panel vs Pooled OLS

My sample comprises of data on accounting performance of companies that had their IPOs between 2009-22. I want to examine if companies which had more foreign investor participation in their IPOs ...
roshnigarg's user avatar
3 votes
1 answer
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How to add interaction and covariates to linear mixed effects model in R

I have some data ($x$ and $y$) collected over multiple days for multiple people. I want to test whether the contemporaneous associations between $x$ and $y$ (measured daily) is stronger depending on ...
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Asymptotic normality implies consistency

I'm trying without success to solve the following exercise in my econometric textbook: Show that $\sqrt{N}\left(\widehat{\beta_1} - \beta_1 \right) \xrightarrow{d} \mathcal{N}(0,a^2)$, where $a^2$ is ...
Residual Claimant 's user avatar
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Check assumptions in generalized linear model binomial family

I have the following dataset ...
GiorgioS's user avatar
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Understanding spline transformation and regression coefficients

I do not understand properly what a spline does even in a simple situation of a piecewise regression, and I need some help. Consider the following basic example: ...
denis's user avatar
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Predictive capacities of Generalized Linear Models and significance

I have the following data ...
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Linear regression estimator with unknown noise variance

I have a noisy linear regression model, $Y = X \beta + \epsilon$ with noise $\epsilon$ sampled from a normal distribution $N(O, \sigma)$, where $\sigma$ is unknown and in turn sampled from a uniform ...
Max Vladimirov's user avatar
2 votes
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How is the weight vector calculated when using kernel trick for ridge regression

Im trying to understand how kernelized ridge regression works, and how we manage to first transform, and subsequently learn on higher-dimensional features without explicitly having to calculate them. ...
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Stepwise Regression - when will bi-direction give different results?

There is forward selection and backward elimination, and in both cases we can not only add or subtract variables, but also do both. My question is under which circumstances would the ...
Maverick Meerkat's user avatar
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Predicted circular regression curve from a bpnr regression

I'm trying to understant how to interpretresults from the bpnreg package to do glm on a circular response variable (flight directions). I understood from the paper that the interpretation can be done ...
Tanuki's user avatar
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Cubist Model Tree Overlapping Rules

Can someone help me understand the output of a cubist model created by the R Cubist package? The documentation package manual for objects of class "cubist" seems to be nonexistent. Looking ...
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How does correlation give better model predictability?

Does correlation give better model predictability. In case of using regression models, typically OLS, how does it help with the model predictability and what are its limitations. Any articles or other ...
user402101's user avatar
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Log-log regression model vs. that in levels

Assume that we have a log-log regression model of the form: $$ \log\left(Y\right)=\alpha+\beta\log\left(X\right)+u $$ Here, the elasticity is defined as $$ \epsilon=\frac{\text{d}\log Y}{\text{d}\log ...
Kwame Brown's user avatar
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Do I have to use the exact same variables in each step, if I have a two-step propensity score match followed by a regression?

I am using the propensity score match to grow my sample based on a smaller dataset of existing units that received the treatment. The match will find more likely units from its large population that ...
LifelongLearner2's user avatar
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Is it okay to report zero eigen values for some PC components if the first few components are greater than one?

I have a dataset which collected household responses over 3 years. It is unbalanced since not all households participated during the three surveys. I run multilevel PCA in stata to account for within ...
Zainab Hassan's user avatar
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Can I specify the signs on coefficients of variables in Regression models?

I have a Regression model where the coefficients of each variable need specific signs. For Example, say I have a standard OLS model: Y = β1X1 + β2X2 + … + β7X7. I want coefficients β2 and β5 to be ...
user402101's user avatar
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Autocorrelation and heteroskedasticity in time series regression

I'm running time series regressions with a small dataset (about 50 obs and < 10 variables) and wondering about correcting for auto correlation and heteroskedasticity in the same regression model. I ...
brian's user avatar
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How to handle multicollinearity with varying length and type of conjoint treatments?

We ran a complicated experiment and are struggling to build a linear model that estimates everything we're interested in. We showed each person a description of a product (for illustration, let's say ...
Tia's user avatar
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Full conditional posteriors

so up to now I dealt with posteriors in the form of: $$p(\theta|x) \propto p(x|\theta) p(\theta)$$ No we started to model a linear regression with the bayesian approach: $$Y \sim MVN(X\beta, \sigma^2I)...
BlankerHans's user avatar
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In R, why are the results of summary(lm(y~-1))$sigma^2 and mean(y^2) same?

Consider the following data and the model: y <- c(9,3,-2,7,6,12) lm(y~-1) summary(lm(y~-1))$sigma^2 [1] 53.83333 I expected ...
user232597's user avatar
1 vote
1 answer
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Mixed effect models where one fixed effect leads to very different outcomes [closed]

I am running a pilot experiment that is testing whether a modified form of music notation results in fewer errors in performance than conventional music notation. Our experiment involves participants ...
David's user avatar
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Multiplicative BIASES in Log-Log regression

When we try to estimate elasticities by regression, we usually estimate the following regression model: $$ln(y) = \beta_0 + \beta_1 ln(x_1) + \dots + \epsilon$$ When we expect to have endogenous ...
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What metric should I use for a Regression model with a gamma distributed target?

Background I'm building a regression model on insurance data to predict the losses associated with a policy. I'm running an Optuna optimisation function to help me with this, but I'm struggling with ...
Connor's user avatar
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How to fix signs of variable coefficients apriori in a linear regression model? [duplicate]

I want to restrict the signs of variable coefficients in a linear regression model. For example, if I am using the mtcars dataset from R to build a linear regression model I will get these ...
T_S's user avatar
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How to prove the square of the t-statistic is the F-statistic in a linear regression without Lagrange multipliers?

My question is essentially identical to this In linear regression, how to prove the equivalence of F-test and t-test? - it was (I believe humbly) erroneously marked as a duplicate of this Prove F test ...
NovicePatience's user avatar
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What happens to the parallel trends assumption when we estimate unit fixed effects at the micro level in TWFE?

I am a bit confused about the recent difference-in-differences/ two-way fixed effects literature. For example, in this paper the authors analyse a policy effect that happened at a state level on ...
Izzy's user avatar
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1 answer
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Three-way interaction terms

One question about three-way interaction terms. Let's label each variable: $A$: main variable $B$: 1st moderator $C$: 2nd moderator I'm interested in hypothesizing the relationships $A$-$B$ and $A$-$...
Sangcheol Song's user avatar
3 votes
1 answer
224 views

Multicollinearity and control variables dilemma

I had some superficial understanding of multicollinearity, that two highly correlated variables in the regression model are not what we want, as the estimated coefficient would be biased. Control ...
LJNG's user avatar
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5 votes
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Modelling a proportion/percentage which is left censored

I am looking at component wear type problem, where the dependent variable is a percentage of the original wall thickness. I had read on these forums that the use of a beta regression would make sense ...
Meep's user avatar
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8 votes
1 answer
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How did Auguste Bravais come up with the regression line?

I am new to statistics and linear regression and I came across the face that auguste bravais discovered regression line but didn't realize it. Auguste Bravais (1811-1863), professor of astronomy and ...
Alexander's user avatar
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How to derive OLS estimates of beta by minimizing the error sum of squares?

For the model: $Y_i=\beta_0+\beta_1X_i+\epsilon_i, \epsilon_i \sim^{iid} N(0,\sigma^2)$ for $i=1,...,n.$ Let $X_i >0$ and $\sigma^2_i=\sigma^2X_i$. $\tilde{Q}(\beta)=\sum^{n}_{i=1}\sigma_{i}^{-2}\{...
Harry Lofi's user avatar
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Regression model with 3 outputs and different dataset to train each of them

In general I want to predict 3 parameters ISO, aperture and exposure from photo. I was thinking about using cnn with regression. Despite of fact that this is hard task, my minor problem is with ...
swaxkidrauh's user avatar
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19 views

How to fit a dataset like this, and what's the recommended evaluate metrics for it

the dataset seems like non-linear, is there any recommended way to fit the datatset? since it's a non-linear regression problem, what's the correct way to evaluate the model's prediction? is the MSE ...
Wuuu's user avatar
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2 votes
2 answers
237 views

Is it okay to use different data preparation procedures for different models?

I'm currently learning some basics of building models, and I was wondering whether it's okay to use different data preparation procedures for different models. Specifically, I was considering an ...
mrepic1123's user avatar
4 votes
1 answer
369 views

Regression model not significant, but the predictor significant

I'm testing the hypothesis that variable $x$ predicts the variable $y$ AND that it predicts it when adjusted for other variables that have been shown to predict $y$ in the literature ($z_1$ to $z_5$). ...
user216960's user avatar
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0 answers
18 views

Test of association and Logistic regression

Hi I have 9 predictor variables and 1 binary dependent variable. After running chi-square test of association, 8 out of 9 are significantly associated to the dependent variable. My question is, should ...
Raven Mark S. Eduardo's user avatar
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Log transformation uses

I am trying to understand how the migration of a male member affects the number of hours spent by left-behind women in various agricultural and non-agricultural activities. I used a simple OLS model ...
Sapna's user avatar
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