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Questions tagged [regression]

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

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ISLR - Interpretation of Confidence Interval in Linear Regression

I'm reading about Linear Regression in Introduction to Statistical Learning (Chapter 3) I see the confidence interval defined as A 95% confidence interval is defined as range of values such that ...
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How different will that be between the R-squared of linear regression y~x and absolute value of cor(x,y)

Generally, both of them can represent the linear relationship between x and y scale to [0,1]. Are they 99% very similar?
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How to read a multinomial logistic regression output in R

I have already tried google and Youtube but I am still slightly confused on how to read the output. It's difficult to read the output because there are no stars and it's not in a simplified format ...
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homoscedasticity in multilinear regression

I tried to test the assumptions of multilinear regression. For the homoscedasticity, I found the following two graphs: the first graph is for all data and the second graph is for all data after ...
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Should I remove the intercept when regressing against one variable (country income)?

I understand that one should not remove the intercept, unless there is a very special circumstance. (see: When is it ok to remove the intercept in a linear regression model?) However, if I am running ...
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Why does first differencing correct autocorrelation?

If we have an autocorrelated variable in the multiple regression model, why does taking first difference help?
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Calculating standard errors of non-OLS regressions in python and scipy

Scipy provides the ability to get a number of metrics from the output of an OLS regression model, a few examples of which are the following: ...
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When to remove insignificant variables?

I'm working on logistic regression model. I checked the summary of the model which is built on 5 independent variables out which one is not significant with a P-value of 0.74.I wish to know that do we ...
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Interpreting glmer output

I find myself buried deep into a generalised linear mixed effect model, slightly out of my depth, and need help interpreting what its saying and diagnosing the model assumptions. The model: ...
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Using CRLB for proving Gaus-Markov Theorem

Can I use the Cramer-Rao Lower Bound to show that the variance of the least square estimate of the vector of parameters $\beta$ is the same as the the CRLB lower bound, i.e. the first diagonal element ...
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1answer
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Feature Scaling in Regression

I have a dataset in which each sample has only two features. I designed my own gradient descent algorithm, and applied it to my dataset. However, I could not obtain a result. Then, I printed the ...
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3answers
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Details of binary logistic regression, estimating $P(Y=1|X)$

I am trying to understand logistic regression, but most sources I have found tend to leave the actual computational step as sort of a "black box", like using r glm(y~x,...) which obscures the ...
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1answer
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Model selection: Two-Part Mixed Effects Model for Semi-Continuous Data

I have now been studying mixed models for about a month, I am still a pure beginner. I have zero inflated semi continuous dependent variable (yield of trees between two periods). Exploring ...
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Implementation of Hypothesis test on R² for regressions in cross-sectional setup

I am confused by the paper of Kan et al. (2013 - "Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology") which proposes the execution of hypothesis tests on R² of ...
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Optimal NN architecture for regression task that benefits from classification

I am aiming to build a NN that would be optimally combining classification and regression. I have reformulated the task such that it would be less abstract and would like to know if the proposed ...
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1answer
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How do I interpret the random effect in my mixed-effects model?

I have run a linear mixed effects model with individual as a random effect. I have three separate measurements of each individual. The random effect is significant, ...
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Looking for a Regression Method with way to enfornce a reflection/ flip consistency for input [on hold]

I have a set of $N$ dimensional 1D features using which I build a linear a regression model to predict a single scalar value. Say, $\hat{y}(w, x) = w_0 + w_1 x_1 + ... + w_p x_p$ with the regression ...
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Panel regression [on hold]

I am new to this method. The model is a fixed effects model (nor a random effects model or pooled regression). My question is about the assumptions. Does this method assume equal error variance (...
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Equivalence of two optimization problems [duplicate]

Ridge regression problem: $\sum_i^n(y_i-\beta_0-\beta_{1i}-\beta_{2i})^2 \longrightarrow min_{\beta}$ $s.t. \sum_i^p\beta_i^2 \leq c$ $\sum_i^n(y_i-\beta_0-\beta_{1i}-\beta_{2i})^2 + \lambda(\sum_i^...
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How to modify a linear regression model when the variance is not constant?

I have a very basic question. I have a model that has residuals that don't follow a constant variance pattern, but rather it has a clustered pattern (see the figure attached). Any idea of how to deal ...
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1answer
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Why do cubic splines need to be continuous at the first and second derivative, but discontinuous at the third?

I'm working through Introduction to Statistical Learning and came upon this: One can show that adding a term of the form $ \beta_4h(x,\xi)$ to the model (7.8) $$y_i = \beta_0 + \beta_1x_i + \...
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Differences in correlated factors as independent variable changes

My problem is similar to the following: I want to know what factors impact plant growth rates under different temperature conditions. I have data on growth rate, temperature in degrees, and a number ...
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Same model coeffs, different R^2 with statsmodels OLS and sci-kit learn linearregression

I'm getting to know Python regression tools with the intention of benchmarking against ML tools available on a couple of cloud based services. I'm using the boston dataset distributed with scikit-...
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1answer
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Which metric to use to report regression results: RMSE, R2 or Pearsons Corrrelation?

I'm a bit confused about when to use RMSE, R2 or Pearsons Correlation Coefficient (Rp). I've read some papers that reported RMSE and Rp and didn't even mention R2, but I also found papers reporting ...
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Finding slope of regression line [on hold]

Consider the following econometric model : $q_{i} (quantity demanded)= a_{0} +b_{0}p_{i}+ u _{i}$ $q_{i} (quantity supplied)=a_{1} +b_{1}p_{i}+ v_{i}$ Where $b_{1} > 0$ and $b_{0} < 0 $. ...
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How is the bayesian update (least-squares) derived? [on hold]

I would like to know how the Bayesian update function using least squares is derived
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How to account for repeated measures in a logistic ordinal regression on longitudinal data?

I have longitudinal data on soccer players' performance. All 235 players have been tested several times over the years on a cognitive test, ideally once a year. Hence, there are repeated measures (...
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Example usage of maximum modulus method t-intervals method

I'm looking for an example of maximum modulus t-intervals method for simultaneous confidence region of the regression coefficients. I've read through the theory, but my book doesn't seem to provide ...
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2answers
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Correlation with a highly significant P value and a low Pearson (r) value

I am working on patients data (168614). I examined the correlation between blood test (HbA1c) and average weekly max temperature. I found a highly significant correlation but low Pearson (r) value (as ...
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1answer
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Significance of a variable - Regression Model alternatives

I am looking at cross-sectional data. I have a dependent variable and a set of independent variables. Specifically, I want to assess whether a binary variable has a significant influence on the ...
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Creating multivariate regression model out of multiple univariate models

A bunch of ML regression models are defined only for predicting the value of a single variable. Or have standard implementation that are only for the univariate case. For example support vector ...
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1answer
23 views

How to run regression in a within subjects design? [on hold]

I would like to conduct regressions to test for a hypothesized relationship between personal motivation and sharing news stories on social media. I used a survey to ask respondents about the ...
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Hausman test problem

I am doing a gravity model analysis using panel data. I got nice results from RE but a Hausman test suggests that FE is the appropriate model. But the FE model has omitted one of my most important ...
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Meaning of centred and uncentered r square [on hold]

I'm not sure I understand fully the meaning of centred/uncentered r2. Is uncentered r2 is same as adjusted r2? and if not, how can I know the adjusted r2? That result estimated by IV analysis. the ...
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2answers
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How can I compare regression coefficients across multiple groups in SPSS? [on hold]

For my thesis research I want to compare regression coefficients across multiple groups in SPSS. I have classified each participant in my sample into one out of 10 groups. Now I want to run a simple ...
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What are the weakest assumptions about the errors needed to derive the ordinary least squares estimator? [duplicate]

This is a question from a past paper. The answer given in the mark scheme is that the minimal assumption is just $\textrm{Var}(\epsilon)=\sigma^2I_n$. I'm struggling to understand why this is the case,...
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Code incorrectly determines that a poor fit is a good fit

I'm trying to find the best polynomial fit for a set of data. It calculates the AIC for each polynomial fit of a certain degree, and then chooses the one with the lowest AIC. To my knowledge (which I ...
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How to create a reliable regression model with a large number of variables and a few observations in R

I am newbie with R and I am trying to create a model that explains sales value. In particular i want explain how this series of variable (downloaded from http://data.un.org/ and merged with Excel) ...
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Bootstrap Non Parametric Regression standard error comparisons

Suppose that we use a Non parametric bootstrap regression.If I'm not wrong ,that means that we have to sample with replacment from the residuals, for an amount of times. Lets assume that we have $i=1,...
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Why we do not use least squares in logit model? [duplicate]

I am very wondering why we do not use least squares instead of maximum likelihood? for example we have 3 choices k= 1, 2 ,3 $minimizing: (e^{\beta_{i} X}/(1+\sum e^{\beta_{i} X})- Y)^{2} $ for i=1,...
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1answer
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Which regression type should i use?

I want to use logistic regression on spss to examine the factors associated with bottled water use. A survey was distributed with these questions: 1.enter your gender (m, f), faculty (8 faculties to ...
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Regression when dependent and independent variables come from different datasets

I am trying to figure our the most robust way to combine two different sets and run a regression. The first dataset gives me an outcome value for each of several categorical treatment variables, each ...
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Effect on SSE of adding a variable in regression [on hold]

What happens to the SSE in an OLS regression when we add an additional non-zero coefficient variable?
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1answer
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Best activation and loss function for regression problem where outputs are from 0 to 1

I'm currently working on a regression problem, where the targets are from 0 to 1. Which would be the best pair of activation and loss function for these kinds of problems? The ones that I have ...
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2answers
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Linear model with binary variable VS create two linear models

Let's say, there is a variable sex in the data set. I could either: Build one model on the whole data and encode the sex into <...
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0answers
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Censored regression but dependent variable is sum of two censored variables

Suppose we have two censored variables: $$y_1 = \begin{cases} 0, & y_1^*\leq 0\\ y_1^*, & 0< y_1^* < 1000 \\ 1000, & 1000<y_1^* \end{cases}. $$ $$y_2 = \...
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1answer
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Problems from having too many interactions in a regression?

Excluding the 'dummy variable trap', are the problems from including too many interaction terms in a regression any different from the problems of including too many continuous or binary variables in ...
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Question About Preprocessing And Regression Models

My first question is weather or not the head of data below needs to be further processed, or if the format is good the way it is. ...
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1answer
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Why is Pearson correlation is not an effective metric?

I found this statement in some documentation but I could not make sense of it. "Correlation is not a good metric for regression because it is scale and offset invariant". I understand that ...