# Questions tagged [regression-analysis]

This tag is for questions about regression analysis. In statistical modeling, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables (or 'predictors').

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### Technique for finding expected value Weighted Ridge Regression Coefficients

Context: We would like to approximate a linear function $f(\mathbf{x})$ at the point $\boldsymbol{\xi} \in \mathbb{R}^D$ using samples of size $N$ around $\boldsymbol{\xi}$. Assume that the input data ...
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### Is there a way to modelize a partial predictor in a classification problem with an unbalanced target?

I would like to share with you a classification issue I faced during the modelling process. I have to create a model for an unbalanced binary target by 4 predictors where one of them has 45% of wrong ...
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### Appropriateness of one observation per unique combination of dummy variables

I am wondering what conclusions you can draw regarding the coefficients of an OLS model when you only have one observation per combination of unique dummy variables. I have seen someone else do this ...
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### How to use Multiple Regression Analysis to get to linear equation

I am working on a paper about MQ gas sensors and found this other study (https://www.researchgate.net/publication/...
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### Degrees of Freedom in PCA

Suppose we are doing PCA over a historic time series of temperatures. The feature for the PCA to be explained is the time when the temperature was observed every hour. Let’s say for the sake of ...
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### Understanding Cook's Distance

Does Cooks Distance tell us how much the estimated parameter values change when the ith observation is removed or how much the fitted values change when the ith observation is removed? I'm being told ...
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### How to calculate sample standard deviation of the intercepts that are obtained from all possible combinations (having $n \ge 3$ points)?

Starting with an example: Having the points $P_1(1,29),P_2(2,50),P_3(4,88)$. Then there are $4$ possible ways to choose points to find the "best" line (using ordinary least-squares). The $4$ ...
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### Regression calculation of initial individual weight considering variations in weighing dates and missing data

I need to determine the initial individual weight of each animal as accurately as possible, taking into account the following challenges: The animals may be weighed on different days. There may be ...
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### Linear Algebra/Matrices Reference Request

I am learning multivariate regression, with matrix equations and heavy use of: Transposes Inverses Identity, idempotent matrices Can anyone refer some books where I can learn the properties of ...
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### When does averaging affect a linear regression?

Given the following: data $(x_{data},y_{data})$, where x values may be measured multiple times. For example, $$x_{data} = ( 1, 2, 2, 3,3,3, 4 )$$ $$y_{data}=(8,10,9,1,2,1.5,−7)$$ And a fitting ...
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### Covariance of Residuals and Fitted Values in Linear Regression

Consider the simple linear regression model $Y_i = \beta_0 + \beta_1x_i + \epsilon_i$ where $\epsilon_i \sim^{indep} N(0, \sigma^2)$ for $i = 1,...,n$. Let $\hat{\beta_{0}}$ and $\hat{\beta_{1}}$ be ...
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### How to explain covariance in logistic regression + analogy to linear regression

Introduction Linear model In linear regression we predict continuous variable $Y \in R^n$ with use of $n \times p$ deterministic plan matrix $X$ and theoretical model (let's ignore intercept ...
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### Econometrics/Statistics Regression Question [closed]

As you can see from the provided picture given Heart attack given rate per 100,000 population. I was able to successfully ran my regression; but now I am trying to figure out how to alter my ...
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### Use regression to find common noise component

Suppose I have three mutually independent non-Gaussian noise $E_A$, $E_B$, $E_C$. There are two variables generated by linear combinations of these noise components: $M=pE_A+qE_B$, $N=rE_B$. By linear ...
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I recently read about logistic regression model. $$y=\frac{1}{1+e^{-(\beta_0+\beta_1x)}}$$ where y is a categorical variable with either 0 or 1 output. What seems to be perplexing to me is, I can see ...