Questions tagged [regression]

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

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21 views

Regression with sigmoid link for diminishing returns?

I am working with some researchers who would like to see how a dozen or so "life inputs" can affect a measure of happiness. My feeling is that treating these as additive, as in a regular ...
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19 views

Insignificant likelihood ratio but significant parameter estimate?

So I am running multinomial logistic regression and the likelihood ratio (chi aquare) is insignificant, but the predictor is significant in the parameter estimates. I don't know if I should interpret ...
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ANOVA 1-way - How to calculate SSF

I'm studying and I can't find an answer to make the ANOVA table for this. I have 4 groups, with mean and variance group. My N=60, n=15 for each group. To find Sum Square Errors I did Sum( ni * ...
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cross entropy logistic test set

In logistic regression, the binary cross-entropy (logistic loss function) is defined as $$\ell (\boldsymbol{y}, \boldsymbol{\hat{y}}) = - \sum_{i=1}^n y_i \log \hat{y}_i + (1-y_i) \log (1-\hat{y}_i).$...
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How to do Maximum Likelihood Estimation (MLE) of a Poisson Regression using numpy

I am currently trying to learn how MLE in a poisson regression context works. As such I am trying to compute a poisson regression from scratch using numpy. Furthermore, I try to solve the MLE using ...
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Goodness and prediction measures for conditional logistic regression models

As mentioned in this comment and answer How to get fitted values from clogit model, it is not clear that predicting from a conditional logistic regression model is meaningful. It seems to me that it's ...
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Using residuals from regression as new dependent variable in another regression

My code is below. I first open and read in data from a file and compute a least squares regression model and a regression model using a Copula method to account for endogeneity of one of the ...
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20 views

the conditional expectation of the error term in linear regressions (OLS assumption)

I have some questions regarding the least square assumptions for causal and prediction models. I know that in linear regressions, for the coefficient on the regressors to have causal interpretation, ...
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Help with needed with Fractional outcomes Logit Regression?

For my master thesis I am studying the effect of certain individual characteristics, such as financial literacy, on the probability of using a fintech. My dependent variable is a continuous variable ...
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38 views

What statistical test should I use to compare two slopes of dependent data?

I have some data on mean kinship values of a single population for a number of consecutive years. After plotting this data, I saw that the kinship coefficient is decreases a bit until 1994/1995, after ...
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When do we require to calculate the confidence Interval?

I am using various machine learning algorithms for last 7 years. To validate the model in classification algorithm we use precision, recall, f1 score. For regression methods we use R^2,RMSE kind of ...
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What is the consequence of misspecification in logistic regression

In linear regression, the Ramsey RESET test can be used to test if the model is misspecified. The Gauss-Markov theorem allows us to understand the consequences of misspecification in linear regression....
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Why can we mix standard errors with raw covariances when calculating standard error of sum of regression coefficients?

Let's have a look at this post: Standard error for the sum of regression coefficients when the covariance is negative We have: $SE_{b_{2+3}} = \sqrt{SE_2^2 + SE_3^2+2Cov(\beta_2,\beta_3)}$ But why do ...
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How to interpret variance explained and r-squared outcome from a multiple regression model in R?

I am running a regression model in R and I want to interpret the variance explained percentage, as well as, R-squared value. ...
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245 views

Do random forests work better than multinomial logistic regression for prediction of categorical non-binary variables? Why?

I posted another question that was well received. I am posting this new question because it was suggested by other members of Cross Validated. Here is the link of the original question that I posted: ...
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In R, how can I test if B1 = B2? [duplicate]

I have the following model : Y = B1X + B2X + e. I want to test if B1 = B2, and also if B1 = B2 = 0. Any suggestions to which test that would be appropiate? Thanks in advance.
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Good reference book for linear statistical models? [duplicate]

My Ph.D. training is mostly in applied mathematics. I'm interested in learning materials of linear statistical models, especially their applications in data science or statistical machine learning. Is ...
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44 views

In R Linear Regression , a categorical variable is changed to numeric to build a model. Would that trick work to predict a categorical variable?

In R Linear Regression , a categorical variable is changed to numeric to build a model. Would that trick work to predict a categorical variable? Are these results valid? I have seen some R code that ...
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Binary predictive model in R

I want to develop a predictive model based on a binary dependent variable (1 if default, 0 otherwise). Based on methods like logistic regression, decision trees, and random forest in R. My independent ...
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How to recover estimates on original scale in log-linear model?

If fitting a linear model to a untransformed and log-transformed y variable, can anyone explain why the coefficients are different from the log-transformed model even after exponentiating the ...
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Problem understanding why a variable of interest becomes significant when adding another variable

Now this is a thoroughly discussed topic but unfortunately I've never come across an explanation that is intuitive, also there may be several reasons, none of which are intuitive. I have a study in ...
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28 views

Expected value of given x for simple linear regression?

I understand statisticians call the predicted y in a simple linear regression the “mean of y.” Let’s assume we only have 3 pairs of x and y values: (1,1), (2,3), (3,1). Whatever the regression line ...
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Which model is the most appropriate for my data?

I've been searching for the right model for several months, but i ended up with nothing untill now. That's why i'm here asking for help. My research purpose is to analyse the impact of rural programs ...
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Multiple regression - covariance matrix, law of large numbers

I'm currently reading an article: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4302277/#S6title And in Section 6 there is a least squre estimator of $\beta$ given of course as $\hat \beta = (X_c'X_c)^{...
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35 views

Adjusted R-squared formula

I am studying linear regression lately and I notice this adjusted r-squared formula in a youtube video: $$adj. R^2 = \frac{\frac{SSE}{n-k}}{\frac{SSTO}{n-1}}$$ While the formula that I know is this: $$...
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Weighting logistic regression in R

I'm doing a simple logistic regression in R where I'm trying predict the outcome of sales calls. I have data/observations from the past 12 months but I would want that the most recent observations ...
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11 views

Adjusted R squared formula [duplicate]

I am studying linear regression lately and I notice this adjusted r-squared formula in a youtube video: $$adj. R^2 = \frac{\frac{SSE}{n-k}}{\frac{SSTO}{n-1}}$$ While the formula that I know is this: $$...
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What arguments can be used for/against clustering standard errors and/or estimating coefficients using the fixed effects model?

I'm writing a thesis based by using the following papers as a starting point: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3051151 https://www.sciencedirect.com/science/article/abs/pii/...
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I am doing a simple Moderation regression: there is multicolinearity in my model when I add the interaction term. I want to check if this is ok

The first step of my regressionmodel with both predictor variables and the outcome variable meet all assumptions. However when I add the second term there is multicolinearity. This seems obvious since ...
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Kernel trick to logistic regression

Why can't I apply the kernel trick in logistic regression? My reasoning is: in SVM the logit is: $z = \sum_i \alpha_i K(x_i, x) + b$ Where K is the kernel function. In logistic regression you have ...
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41 views

$H_0$ vs $H_1$ in diagnostic testing

Consider diagnostic testing of a fitted model, e.g. testing whether regression residuals are autocorrelated (a violation of an assumption) or not (no violation). I have a feeling that the null ...
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How can I predict a new x using coefficient of B-spline basis functions?

I have a nonparametric regression problem using B-spline basis functions. The range of x is a vector as (350,370,390,410,430). I`ve obtained coefficients. How can I predict the value of response for x=...
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41 views

Change in mean of y given change in mean of x?

I am a bit confused about interpreting simple linear regression coefficients. My understanding is that for a linear regression equation, increasing x by one unit corresponds to a change in the mean of ...
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46 views

Show that $\pmb y = \pmb X \pmb \beta + \pmb e = \pmb X_1 \pmb \beta_1+ \pmb X_2 \pmb \beta_2 + \pmb e$

Say we take $\pmb X \pmb \beta$ and partition the columns of $\pmb X$ so that we have $\pmb X \pmb \beta_1$ and $\pmb X_2 \pmb \beta_2$. Why does: $\pmb y = \pmb X \pmb \beta + \pmb e = \pmb X_1 \pmb ...
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Should I aggregate explanatory variable?

The dataset I have is an aggregated outcome, e.g., the quarterly revenue of each firm (that manages a number of plants), revenue is measured by the end of each quarter a focal explanatory variable, e....
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Correlation coefficient between a stochastic and non-stochastic variable or, what is the difference between a non-stochastic variable and a constant?

I am asking in the context of simple linear regression. If my regressor $X_i$ is non-stochastic, should $\mathbb E(X_i) = \overline X$ or $X_i$ i.e., treat it like a constant? I presume the latter ...
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Simple Linear Regression Anova statistics

I am running a regression test for which I overall have two variables (x and y) and I would like to test if any of them is dependent on the other. ...
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Why does a non-proportional odds model produce the Hauck-Donner effect while a proportional odds model does not?

I'm working with the pneumo dataset from the VGAM package. Here is the data: glimpse(pneumo) ...
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Is it possible to specify different quantile regression models for each quantile?

As the title says. I have never seen it, but I see no point that would prohibit me to do it. For example, a different set of variables might bear predictive value for the 25th-percentile of the ...
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23 views

Simulating slope coefficient for linear regression

I'm currently reading an article: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4302277/#S5title And in Section 5 I've come across a simulation for a few estimators of the slope $\beta_1$. I wanted to ...
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Why won't my xgBoost regressor predict above a certain value, even though it sees higher in training?

I have created my first xgboost regressor. I input some self collected data, which I scale using sklearn's standardScaler. The model is trained on approximately 25,000 samples, and then tested on ...
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multivarte prediction task for ordinary tabular data

I have an ordinary tabular data with varibales x0,x1,x2,x3,x4.....xn. They affect each others. The things I want to know is once I set x0 a specifiic value (say 200) , how would x1,x2.....xn's value ...
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Logistic Regression with Newton's method

Consider the prediction of a binary value $G$ on the basis of a quantitative predictor $X_1$. I use a linear logistic regression (without intercept) for predictions. I want to know if I have formed ...
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How to interpret the coefficient when both Y and X are expressed in %?

I have an issue: my dependent variable is expressed in % (it's the % of people that think they will lose their job) , my regressor is expressed in % (it's the share of foreign residents on total ...
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1answer
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How to build a saturated model

I am struggling with the understanding of a saturated model. As far as I know, the saturated model is the model that have as many parameter as the data points. But I don't know how to build it or what ...
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Regression for Completely Randomized Experiments

I'm reading Guido W. Imbens and Donald B. Rubin's book on Causal Inference. In chapter 7 they try to justify using a regression model to estimate the mean casual effect in a completely random ...
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Fixed effects in DAGs

Let's imagine I'm interested in studying the causal effect of beliefs in some ideas and behavior related to these ideas (say, if I believe sunscreen is good for my health, I use more sunscreen etc.). ...
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Robust linear regression for group differences

I am trying to understand what it means when a p value for a grouping variable is < 0.05 after running robust linear regression. Does this mean that the 2 groups significantly differ with respect ...
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calculate adjusted p and t value after Bonferroni Correction

I am using linear mixed effect models to analyse my data. I am looking at how 4 independent variables might affect 5 dependent variables. I read an article by von der Malsburg and Angele (2017) which ...