# Questions tagged [regression]

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

18,206 questions
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### How does bootstrapping (wild) calculate a t-statistic?

I am using the wildbootstrap. Intuitively how do I calculate a t-critical values? Do I use original ones or do I somehow generate them?
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### Calculating MSE for multiple regression

A study was carried out to examine the relationship between cholesterol level in the body (y) and two variables variables 𝑥1:= amount of daily walking (in steps) and 𝑥2:= age. A total number of 63 ...
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### Is it valid to use a difference score as an independent variable in a regression analysis

I would like to see if the difference in the number of BPD symptoms from baseline to follow-up two years later can predict psychosocial functioning at the 2 year follow-up. So I wanted to do a linear ...
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### Is it valid to include a baseline measure as control variable when testing the effect of an independent variable on change scores?

I am attempting to run an OLS regression: DV: Change in weight over a year (initial weight - end weight) IV: Whether or not you exercise. However, it seems reasonable that heavier people will lose ...
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### Categorical control variables PROCESS

At the moment I want to perform a mediated regression analysis using PROCESS. My Independent value (IV), Dependent value (DV) and Mediator (M) are all numerical data. I analyze a simple mediation and ...
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### Multivariate Regression with Uniform Errors

I'd like to know if there is a multivariate regression model with uniform errors. More specifically, I'd like to find the Maximum Likelihood Estimators for $\beta^a$ and $\beta^b$. The model is given ...
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### Solving for regression parameters in closed-form vs gradient descent

In Andrew Ng's machine learning course, he introduces linear regression and logistic regression, and shows how to fit the model parameters using gradient descent and Newton's method. I know gradient ...
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### Correlation between external variables and model coefficients over time

Are there any techniques which can allow me to test for correlations between a set of variables (e.g. population, disposable income) and the time-varying coefficients of a model? I would like to ...
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### How is the correlation matrix in table 3.5 in the book ISLR calculated? What does jt signify?

I was reading the book Introduction to statistical learning by Hastie and Tibshirani and there was this relationship between newspaper, radio & tv ads and their effect on sales in multiple linear ...
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### question about interpretation of results seemingly unrelated estimation (suest) method stata probit model

i use seemingly unrelated estimation (suest) method with probit model in stata but i can't interpret the results i would like to interpret on any group the relation with dependent variables and the ...
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### What is elastic net regularization, and how does it solve the drawbacks of Ridge ($L^2$) and Lasso ($L^1$)?

Is elastic net regularization always preferred to Lasso & Ridge since it seems to solve the drawbacks of these methods? What is the intuition and what is the math behind elastic net?
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### How to prove that X'ε=0 in regression models? [duplicate]

If X is a nxn matrix of some data exogenous to and ε is a 1xn matrix of residuals that sum up to zero, why is X'ε=0? EDIT: It's clear to me why ε sum to zero, but I see no reason why this should ...
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### Covariance matrix and persistence of excitation of input

Assume that a discrete-time system can be described by the following state-space equations $x(k+1)=Ax(k)+Bu(k)+w(k)$ where the input signal $u(k)$ is stationary and ergodic with $\mathbf{E}[u(k)]=0$....
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### Application of oil statics in oil and gas industry [on hold]

How can I determine relationship between number of wells and annual oil production by using statics?
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### Adding a 2nd interaction term makes 1st interaction term and the 2nd interaction term insignificant

I'm running a multiple linear OLS regression (X => Y) on a sample with 125 cases. My regression has two moderator variables (Z and W). Z and W correlate at about .4 but Z and W are two distinct/...
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### How to check for the presence of constant difference within dummy variable?

In econometrics, should two subgroups of the data (for dummy=0 and dummy=1) have some variation, that can be explained also with a constant difference, how would one test for it? And is it a problem (...
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### How do I compare the predictive power of two predictors within a single (logistic) regression?

I've read about how F-tests can be used to compare models and to decide whether an additional variable should be included in the regression. However, I want to test whether A vs. B are better ...
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### logistic regression manipulation [on hold]

hello guys i have a work to do of logistic regression and i'm little bit confused by the way that i must use my data i have about 19 variable and are all factor with labels ofen like yes or no so the ...
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### Is it right of selecting model based on Goodness of fit R2 computed for whole data set

In my regression model building process, I split the data as training and testing set and used all my testing data as external data set and did not use it for training procedure and I have ended up ...
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### Solution of an endogeneity model without instrumental variable, where $E[\varepsilon |x]\neq0$

I know that using Instrumental Variable (IV) solves endogeneity, feedback, unbiased problems and other situations. I was wondering, besides IV, what other method comes to your minds to solve a model ...
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### Logistic regression for complaints on insurance claims

Suppose you have a set of insurance claims and you want to predict the probability that a claim will give rise to a complaint from some features of the claim at a certain point in time such as time ...
364 views

### percent deviation for linear regression

I have 2 sets of experimental data to which I applied a linear fit using Matlab. I can use the slope value to compare between both of them. My question is: can I use the following percent deviation ...
406 views

### Interpreting how much my linear model has improved after Box-Cox transformation

I am working on a linear regression project where I first removed insignificant variables, then looked at a possible transform of the data. I performed the variable selection smoothly, however am ...
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### Covariance of an estimate from optimization

Consider a standard linear regression model, $\boldsymbol y = X \boldsymbol \beta + \boldsymbol \epsilon$. $\boldsymbol y$ is a vector of $m$ responses, $X$ is a design matrix with $m$ rows and $p$ ...
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### Comparing regression/correlation values within-subjects? Repeated Measures ANOVA afters Fishers Transform?

I was interested in the most appropriate way to assess whether there is a difference in the R values from a regression analysis in a repeated measures design. I transformed my R values using a ...
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### Coefficient Interpretation when dependent and independent variables are percentages

I have built a linear mixed regression model with fund returns (measured in percentage ie. 0.01 denotes one percent) as the dependent variable. For the independent variables I have percentage level of ...
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### Computationally verifying the equivalence of ridge regression estimates and Bayesian regression estimates

I'm trying to show that the numerical estimates of ridge regression's parameter estimates are the same as the MAP parameter estimates of a Bayesian regression model with normal prior distributions. So ...
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### Least-angle regression vs. lasso

Least-angle regression and the lasso tend to produce very similar regularization paths (identical except when a coefficient crosses zero.) They both can be efficiently fit by virtually identical ...
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### Developing an appropriate volatility variable to predict stock returns based on past month

I am doing a project about the predictability of stock returns. I am using following regression model: $$r_{t} = \alpha+\beta X_{t-1}+\epsilon_{t},$$ where $r_{t}$ is the ...
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### Nonnegative generalized linear model

Is it possible that all the parameters of a generalized linear model are constrained to be non-negative? If so, when? Any examples?
Typically I use the confidence interval as an indicator of effect size for a negative binomial model, however, I have been told to provide an actual effect size (e.g., pseudo $R^2$). I have looked ...
I have used the cube root $(1/3)$ transformation on both my dependent and one of my independent variables. I would have preferred a log-transformation but my data has both negative values and zeroes. ...