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

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How to read the summary for weighted least squares?

How do I interpret the summary for weighted least squares when I am trying to find the standard deviation function?
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Product term as interaction only in 'special circumstances'

In an online post, T. Therneau (author of R survival package) writes "For continuous variables the use of "*" in a formula adds the product of the two terms, which is not an interaction except in very ...
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type 3 analysis of effects

I have different logistic models and I want to analyse each one and compare them, and I'm not sure how For exemple, I have this for one model ...
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9 views

How do I set a prior on regression coefficients given partial information over them?

Let's say I have a dataset about student performance in mathematics: together with the scores (response variable, I can approximate continuity) I have a set of covariates regarding each student. For ...
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10 views

Changing Significance Level in R [on hold]

I am running a logistics regression analysis in R. I know by default, the output is based on 95% significance level. I want to know how to change the significance level in R from 95% to maybe 90% or ...
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1answer
22 views

Proof of the distribution of the residual standard error

In my notes from university I have written down that the residual standard error (from normal linear regression) has the following distribution $\frac{\hat{\sigma}^2}{\sigma^2}\sim ...
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1answer
23 views

What does multiplicativity and additivity mean in the context of regression?

I frequently read that multiplicativity and additivity applies to this and that in various forms of regression. However, in the textbooks I've read, no authors seems to declare what that actually ...
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Modeling rare events

I am looking to model fraudulent cases using logistic regression. However there are tow different datasets which are available. I used to build my model on; it had 4% of fraud cases. My model on ...
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16 views

Estimating $a + bX + cY + bcZ$

How can I estimate functions of the form: $f(X,Y,Z) = a + bX + cY + bcZ$ I know through expert knowledge that the population coefficient of $Z$ is equal to $bc$ but am not sure how to estimate the ...
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how to run a hierarchical Bayse using runiregGibbs [on hold]

I want to run a hierarchical Bayes regression model using this runiregGibbs function. My data is like the following: ...
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Relation between cost ratio and cut off probabiltyy

I was solving an assignment related to logistic regression where in, the cost ratio was given as 4:1 and was asked to take the cut-off probability to be 1/(4+1). I couldn't understand the logic behind ...
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In R package caret, how is linear regression model trained by using resampling?

Resampling is usually used to find the best tuning parameters for a model. However, for some models, such as linear regression model, there is no tuning parameters. In this case, what can we get from ...
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35 views

When I center data, should I take the absolute value or keep the sign?

When I center data, is it the absolute value that you use or do you keep the sign? For example: you have data (4,5,6) and the mean is 5. After centering, is the data (-1,0,1) or (1,0,1)?
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Test linearity versus local linearity in regression

I have a question regarding local linear least squares vs OLS. Consider the linear regression model $$y_{i}=x_{i}'\beta+\epsilon_{it}$$ where we have assumed that the model is linear in its ...
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How to represent the sum of two linear model predictions in same unit

I have built two linear regressions independently of one another, and $Y_1$ and $Y_2$ are in the same units. I am interested in using the sum of $\widehat{Y}_1$ + $\widehat{Y}_2$ (the predictions) to ...
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Symmetry of Partial correlation

Inspired by the question and the diagram represented in the answer, I am wondering if partial correlation is symmetric? We know that $\rho(X,Y) = \rho(Y,X)$. See here. From , we know that ...
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Multiple regression

We have this question in our assignment, can someone help? Using the Unite States sample of the 2000 program for international student assessment(PISA), the difference in population mean ...
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Constructing a multiple linear regression model

I have some covariates to consider adding into my model and I have to decide which to choose and think of possible transformations. Would this be a decent method of variable selection: I construct ...
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Interpretation of coefficients in per capita terms [on hold]

I come across an article with a regression output: $y=-53,06+122,58x-200,7x^2$ $y$ is here total spending and $x$ is the ratio of people receiving benefits (of total population). The mean of $x$ ...
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Variables in the regression

Would it be correct if the outcome variable is at the household level, to use variables at both household and household member level as regression explanatory variables? E.g. if the outcome variable ...
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marginal effects and total effects in regression with interactions

I have a question that seems very simple and yet I need a final push to lock up the intuition in my head. I am running a regression that can be simplified to look like this: log(wage) = $\beta_0$ + ...
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Is it an ANCOVA?

In a study, baseline pulse is recorded. Participants are asked to watch a funny video and a thrilled video for 10 minutes. Pulse is recorded again. The objective of the study is to investigate ...
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32 views

Looking for the best data analysis

I am currently in my dissertation phase and I am stumped on what data analysis I should be using. I am looking to evaluate resilience differences in genders. I'm using a non-experimental, causal ...
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How to plot identical slopes for an ANCOVA (1 categorical variable(2 levels) with 2 covariates) using ggplot2

I am trying to compare and plot regression lines of an ANCOVA when their slopes are the same and no interaction effect There are two sets of ANCOVAs plots that I am trying to create: a) 1 ...
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Consistency of non-parametric estimators for CVAR

Is the estimation of the CVAR (conditional value at risk) using known non-parametric methods different from the estimation of any other random variable? If the answer is yes, are any non-parametric ...
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Does uncorrelated imply mean independence? Which part of linear regression needs mean independence?

If $X$ and $U$ are independent, then they are mean independent by 'Pulling out independent factors'. If $X$ and $U$ are mean independent, then they are uncorrelated. What I tried: $$Cov(X,U) = ...
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What is the most appropriate way to transform proportions when they are an independent variable?

I thought I understood this issue, but now I'm not as sure and I'd like to check with others before I proceed. I have two variables, X and ...
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Prove that $E[(\hat{\beta_1} - \beta_1)\bar{u}] = 0$. Are the errors uncorrelated? [on hold]

In simple linear regression, prove that $E[(\hat{\beta_1} - \beta_1)\bar{u}] = 0$. Note: This was asked here, but my question involves conditional expectation and asks about assumptions or ...
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How can I calculate and display deviation from a linear trendline?

I am working in excel, and I have plotted some data in a scatter plot. I added a linear trendline, and I want to calculate the deviation of each data point from the trendline. I am plotting allometric ...
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32 views

Time series - Is Time the only independent variable?

I'm starting to familiarize myself with ARIMA models to better understand time series analysis, and my question is: is time-series analysis essentially a complex regression model where time is the ...
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How you free up memory or handle it while fitting/cross-validating model in Scikitlearn? [on hold]

I am trying to fit my model using regression trees but the problem is, it consumes a lot of RAM, which makes my code unresponsive. By looking at different forums and platforms, I think this is a ...
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1answer
30 views

Data Mining for a Continuous Target

I have 50 variables, most of them numeric, a few categorical, and my variable of interest is continuous. In addition, I have something like 300,000 observations. I am looking for a way to predict the ...
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53 views

Why is the MEAN taken in Simple Linear Regression?

Question Why take the mean of the squared residuals? wouldn't it be simpler and produce the same result ( parameters $\theta_0$ and $\theta_1$ ) if you just minimised the sum of the square ...
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Can we solve multiple linear regression using simple linear regression solver?

Suppose I have a blackbox function that solves simple linear regression. Can I use this function to solve "multiple" linear regression? The blackbox computes the slope and intercept in a simple ...
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What is the correct formula for Linear Regression Forecast? [on hold]

I would like to know the correct Linear Regression Forecast formula. I tried different books and sites, but haven't found any reasonable answer. Are the Linear Regression & Linear Regression ...
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Deconvolution - two transfer functions applied to the same signal

I'm observing two timeseries, $\hat{h_1}$ and $\hat{h_2}$. I believe that both are products of convolution of the same underlying signal $f$ with a two different transfer functions, $g_1$ and $g_2$, ...
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Binary logistic regression in R - assistance with determining odds of a predictor at different levels

I have performed a binary logistic regression in R with whether or not a sportsperson was re-contracted or not as the DV. My final model is as follows; ...
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Results from fractional polynomial models

I am using multivariable fractional polynomials to evaluate several continuous variables in a Cox proportional hazards model. I have the beta coefficients, however, I would like to estimate the hazard ...
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Can I be confident of my R^2 score?

I have a dataset with 10 variables and 158 observations. I used cross-validation, grid-search and ElasticNet algorithm. To evaluate the model I checked the pearson correlation between the 10 ...
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Hotelling T^2 Statistic in Simple Linear Regression

I'm at a bit of loss here, so I apologize for silly questions. I stumbled upon a problem that asked for 95% confidence bands for my estimated regression line in a simple linear regression (2 ...
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Adjustments to (Linear Regression) Forecast

Full disclosure: I am not a statistician, nor do I claim to be one. I am a lowly IT administrator. Please play gentle with me. :) I am responsible for collecting and forecasting disk storage use ...
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beta regression creating a wild residual vs. fitted plot- whats going on?

I recently ran a beta regression model in R using the betareg package. I am modeling a continuous dependent variable (a fraction out of 1) that is bound between 0 ...
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Exclude not important predictors from dataset or leave them all?

I have a large dataset with 6 predictors, with a goal to predict bank loan interest, based on year income, time at work, loan amount, credit balance, credit utilization rate, etc. I use python with ...
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8 views

Statistical prdocedure to identify components of an aggregated variable

my (business) research focuses on the difference between two measures that are both related to a firm’s statement of profit or loss; let’s call these measures Earnings_1 and Earnings_2 and the ...
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Model for prediction of binomial probabilities based on time series events with variable duration

I am new to this field, so sorry if I am not precise with the nomenclature I use. :) I am trying to develop a statistical model that will allow me to calculate the outcome probabilities of a binary ...
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Bound on the variance of a product

Let $Z$ be a positive $\mathbb R$-valued random variable bounded above by $M>0$, and $H$ an $\mathbb R^d$-valued random variable (seen as a column vector) such that $\mathbb E[H_i^2]=1$. Define the ...
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1answer
18 views

Odds ratio discriminatory power

In logistic regression, logit Y = ax1+ bx2 +cx3. a variable has a coefficient attached to it. So we can directly measure the change in y per unit change in x. Can I get a similar relationship from ...
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Which regression model should I build?

I'm trying to handle a dataset about student performance in 2 Portuguese Schools in the subject of Portuguese. Student grades go from 0 to 20, discrete. I have a set of 30 Regressors (all but 3 ...
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226 views

Maximum Likelihood Formulation for Linear Regression

I have seen the following for maximum likelihood estimation (MLE) for linear regression in multiple sources, e.g. here: $$ \mathcal{D} \equiv \{(x_1, y_1), ..., (x_n, y_n)\} $$ I do not understand ...
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Proving regression satisfies SLR 4 (zero conditional mean assumption)

I have a linear regression as follows and it is assumed SLR1-SLR3 are satisfied: $ sav = \beta_0 $ + $ \beta_1 inc$ + $u$, where $ u = inc^{2} \times e$ And $e$ is a random variable with the ...