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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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Superimposing regression lines from 2 simple linear regression models into one graph [on hold]

SPSS question, really. Been asked to produce two simple linear regression models, one with an intercept, one without (both for one set of data points). But they have to be on one scatter plot for ...
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Create score for comaparison of algorithms

The following graph gives the results from a test. The y axis shows the MAPE (error) which should be minimum, the x-axis shows the epochs which should also be minimum. As one can see two algos are ...
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1answer
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How to account for incrementation in a log-linear model

I want to perform a mixed regression analysis with random intercept and uncorrelated random slope after multiple imputation. The dependent variable is continuous, namely a duration as number of days ...
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1answer
18 views

How to Interpret p-value for categorical variable in multiple linear regresion? [duplicate]

I have a query on how to interpret the result for multiple regression with categorical variables. I have categorical variable called Stay_In_current_city_years which has 5 levels. After running the ...
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1answer
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What do you call the coefficients other than the intercept in a linear regression

I'm trying to refer to the coefficients other than the intercept. Is there a word/jargon that refers to coefficients other than the intercept? (I'm currently calling them 'other coefficients', which ...
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1answer
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Proof that estimator in overfitted model is still unbiased

Assume that the true population model is given by $y=x'\beta+\epsilon$, where $x$ and $\beta$ are k-dimensional vectors, and suppose that when performing a linear regression, we accidentally overfit ...
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1answer
7 views

Ensemble learning for multiple hypothesis classes

Just to confirm if the following description falls in the category of ensemble learning. Suppose given a training set $D=\{(X,Y)\}$ we are asked to train a regressor. But now the way we do it is to ...
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Specification of a difference-in-differences model in r

I am working through a difference-in-differences model. While I've learned a good deal browsing SE, I'd like to hear from someone more experienced with fixed effects if my model is correctly specified....
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Why high dimensional data is multi-collinear?

As the number of predictors (P) approaches the number of observations (N), the data becomes increasingly collinear. Also, If <...
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0answers
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In the summary of output of the regression analysis in R, is there a way to display categorical variable with just one coefficient

I am doing a linear regression analysis in R with logarithmic dependent variable. One of the control variables is categorical and describes an industry. There are 6 industries and thereby R ...
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1answer
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Model to capture non-linear patterns in data using R

I've fitted a linear model using: m2 <- lm(GPP ~ rainfall + summer.temp + parcel.size + soil.nutrients, data=gpp) As seen from the partial relationship plots ...
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DW critical value for more than 200 sample

does anyone know what is the dU & dL value in DW test for 252 sample? And how to calculate the DW critical value in Ms Excel? In ref., i only found for less than 200 samples. I need your help guys,...
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Why is it okay to suppress constant term in Hubble's law? [on hold]

Although constant term is insignificant in the model, why we can remove the constant term in hubble's law? Some people say it is risky to remove constant term in regression model. What other ...
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Error in drawing normal distribution from Stata [on hold]

I have to draw a normal distribution for an OLS estimator I am using the command drawnorm betaest, n(10000) means(beta_mean) sds(betasq) However, it is giving me the error no; data in memory ...
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1answer
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Need help understanding what a natural log transformation is actually doing and why specific transformations are required for linear regression [duplicate]

I’m taking an online “Intro to AI” course for which I’m doing some azure machine learning labs. This course is largely about how to apply azure ML solutions and, while there is an “essential math for ...
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What statistics can I use?

I have done a research looking at different frequencies of abrasions (ablation, etc.) over time (in hrs) and my data mainly consists of zeros. As I am weak in statistics, I am unsure which statistics, ...
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Cannot get goodnes-of-fit measures from ivprobit output (in ivprobit package)

I am using the ivprobit function from the ivprobit package in R. This ivprobit function is a binary regression with instrumental variables. However, I could not find a way to derive any goodness-of-...
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1answer
7 views

Do you need to correct for a confounding factor if two groups are matched?

I'm looking for group differences in a variable (Power in a frequency band) that depends on age (i.e. increases linearly with age). If the two groups are matched for age, do I still need to include ...
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Interpreting coefficient of a logarithmic coefficient in a logistic regression

I have a regression with a log-transformed independent variable, and I would like to know the proper way to explain its effect on my binary dependent variable. For example, say the equation is: (...
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Large Feature Values for Gradient Descent

Recently, I work on a linear regression model of my project. I have 200 samples, each of which has only one feature, to train my model. When I try to apply ...
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Comparing multiple models across multiple groups or populations

Say I have a series of different regression models (e.g. 8 different models) which I conduct using data collected at a series of multiple locations (same predictor same response variables) and I have ...
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0answers
24 views

Consistency of variance estimator in OLS [duplicate]

Given the model, $$ y_i = x_i'\beta + \epsilon_i \quad \epsilon_i \sim N(0, \sigma^2) \quad iid \quad \forall i = 1, ..,n $$ how can I prove that the estimator of the variance $\hat{\sigma}^2 = \...
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Using Quadratic Programming to solve Lasso and Ridge regression models?

I'm trying to build linear, ridge and lasso regression models for at set of data (40 obs., 4 features, 1 response). I'm building the models using the sklearn package for Python and I can easily find ...
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Interpreting findings of moderation using PROCESS Macro

I have recently conducted a moderation analysis using the PROCESS Macro plug-in for SPSS. I have tested the moderation effect of W (categorical using dummy variables) on the relationship between X (...
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numerically stable sparse gasussian process regression (matrix inversion)

In sparse approximations of GP for large data set $(X,\mathbf{y})$ with $n$ samples, usually $m$ inducing points are chosen such that the true covariance matrix is approximated by $K_{nn}\to K_{nm}K_{...
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How I can sketch the proof of consistency of only one beta in multiple regression?

Now assume you additionally obtained data on average parental incomes (PI) and the ethnic composition (EC) of the pupils in school. You regress the score on STR PI EC and a constant. State the ...
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1answer
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Conditions in which the sign of a coefficient will change between a linear probability model and a logistic model

I am estimating a model where the DV is a binary variable and the key independent variable is the interaction between a dummy variable and a continuous variable. I am getting an very odd result where ...
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17 views

How does model accuracy compare across the folds in cross validation

If we have two cross validation from KNN and linear regression like this: KNN: ...
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2answers
174 views

Why does this expression simplify as such?

I'm reading through my professor's lecture notes on the multiple linear regression model and at one point he writes the following: $$E[(b-\beta)e']=E[(X'X)^{-1}\epsilon\epsilon'M_{[X]}]. $$ In the ...
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1answer
22 views

How to estimate confidence intervals for LC50

This is my first question, so I hope the question is properly done (my apologies if it's not...) I am using a binomial GLM model (logit) for some toxicology data investigating the effects of a ...
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Linear Regression and High Dimensional Categorical Data

I've read that mean encoding is useful for classification tasks with high dimensional categorical data. My question: What kinds of encodings are effective for high dimensional categorical data in ...
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Can I do moderated multiple regression with Process by Andrew F. Hayes when my moderator variable has 3 categories?

I have only seen it when the moderator variable has only 2 levels/groups/categories (dichotomous). What if my moderator variable has 3 levels? Should I just use a two-way ANOVA then since it also ...
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0answers
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Dealing with Complete Separation in Logistic Regression when Reporting

I have a question regarding how one would deal with complete separation in logistic regression when reporting the outcome for statistical analysis. For a study, we have group participants into 4 ...
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1answer
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Pairwise comparisons of regression coefficients [duplicate]

I would like to know how to make quickly pairwise comparisons of regressions coefficients across three or more groups in R. Here is a small example: ...
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Books on practical Regression analysis [on hold]

i need you to introduce me some books about regression analysis which have practical examples. to be honest i need some books that teach me how we can work with statistics in industry. and that how ...
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how many knots used in bs() [on hold]

If I fit the following model to some data m_splines <- lm(data$y ~ bs(data$x, df = 6)) how do I know how many knots have been used for the cubic spline?
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how to prove B1 as a consistent estimator in panel data

$Yi=a+ B_1*X_i+ B_2*Z_i+\epsilon_i$, and suppose that $Zi$ is unobservable and not correlated with $X_i$. Is the OLS estimator of $B_1$ consistent by regressing $Y_i$ on a constant a and $X_i$? I ...
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1answer
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Inverted dose-response variables

Context: Often when we carry out dose-response modelling we want to estimate the dose required to elicit a predetermined response (i.e. response ~ dose). Typically this is done with inverse ...
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Regression with dependent data with low dependence

Suppose you have data that is grouped in one way or another and therefore the assumption of independence is suspect. But you look at the intraclass correlation (or autocorrelation) and it is very ...
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1answer
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Why is the product of two gaussian process $f1$ and $f2$ not a gaussian process?

In the book from Rasmussen/Williams on Gaussian Processes we have the following statement without proof (Page 95): "If f1 and f2 are Gaussian processes then the product f will not in general be a ...
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Difference between Partial Residual Regression and Partial Correlation

Trying to understand the difference between a partial correlation (for example, using PROC CORR supplying partial variables used for adjustment) versus a "partial residual regression" which, to my ...
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1answer
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Interpreting ridge coefficients as a function of regularization

Data consists of 40 observations with 4 dimensions and a response-variable. When doing a ridge regression on my data and plotting the coefficients and coefficient errors (MSE of the ridge ...
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0answers
12 views

Elasticity Value for Log-Log and Level-Level Model

For a data if I calculate Elasticity using 1) log-log model with Elasticity = Beta and 2) Calculate elasticity in Level-Level Model with elasticity = beta *(X/Y) should the resultant value of ...
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0answers
24 views

Difference between Wald statistics and effect size in regression models

In some of my regression models (using the rms package), I notice a distinct difference between the result of the Wald statistics (estimated using ...
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0answers
18 views

Goodness of fit test for any regression model?

Is there a general goodness-of-fit test for any kind of regression model? My problem is that I have a deep neural network that tries to predict some real value labels using high-dimensional input. The ...
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0answers
9 views

Regression using previous years results

Is it possible to make a linear model non auto regressive using previous years observation's. For example I have a student score, and I have 3 contributing variables (subject scores e.g. science......
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3answers
44 views

Necessity of standardizing data in regularized regression [duplicate]

It is well known that in Ridge or LASSO regression we add a regularization term to penalize large regression coefficients. What if the true relationship between the response and covariates relies on a ...
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0answers
31 views

Kaggle cereal data set - Rating seems to be a function of other predictors?

I'm doing a project in linear regression and I found the Kaggle cereal data set: https://www.kaggle.com/crawford/80-cereals I did some regressions and, unless I made a big mistake somewhere, it ...
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1answer
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How to “choose” categorical variables which have impact in a regression?

I have a dataset of about 50K samples. I have approximately 90 columns which are all categorical and they're used to predict a price. There's no other continuous value. I'm trying to select "which of ...
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0answers
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Linear regression: right-hand tail of $\sigma$ marginal posterior

Suppose we're doing plain vanilla linear regression for $y$. The likelihood: $y_i \sim {\cal N}(\mu, \sigma^2)$, $i=1:N$. Priors: $\mu \sim {\cal N}(0,1)$, $\sigma \sim {\rm HalfNormal}(1)$. As ...