Mathematics Stack Exchange
Mathematics Stack Exchange

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').

(Wikipedia) Regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed.

Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed.

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Non-linear regression problem

A physical phenomenon I'm studying obeys the simple law (harmonic oscillator): $$\theta=\theta_0\cos(\omega t),$$ where $\theta$ is an angle, $\theta_0$ the amplitude of the oscillation, $\omega$ its angular frequency and $t$ is time. I have a large…
Gert
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Meaning of dimensional reduction in principal components regression.

When performing principal components regression (PCR) on a high-dimensional dataset we are often looking for a few informative predictor variables in an ocean of uninformative variables. Principal components (linear combinations of the original…
cjkilimanjaro
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What are the prerequisites for regression analysis?

I want to be able to read this book: Data Analysis using Multilevel and Hierarchal models? I have read "Think Stats" published by O'Reilly and have taken some higher math classes in algebra and analysis. Not a lot of probability and statistics…
Moriarty Snarly
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data point on an exponential line in excel

I plotted a trend line in excel. The formula is y = 41899e1E-07x. What I need is to know what the points are on the trend line. I cannot figure out how to use this formula. I don't know what the e and the E mean. Ideally, I want to show the labels…
Talani Casariego
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Frisch-Waugh Theorem for different regressions

I'm stuck on the question when the residual vectors of different regressions are numerically equal according to the above mentioned theorem. Let \begin{equation} y=Xb+e=X_{1}b_1+X_{2}b_2+e \label{eq:1} \end{equation} where $b_1, b_2$ are the OLS…
Flowsen_95
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Prove that mean independence implies zero conditional expectation in regression model

Let $Y,X_i$ for $i=1,2,3$ be random variables and let $$Y=\beta_0+\beta_1X_1+\beta_2X_2+\beta_3X_3+U$$ s.t. $E(Y)=0$. Suppose that $$E\left(U \mid X_1X_2X_3\right)=E\left(U\mid X_1X_2\right)=E\left(U\mid X_1X_3\right)=E\left(U\mid X_2X_3\right)$$…
user375432
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backward selection

In the procedure of backward selection, after dropping the variable with the largest p-value, should I do likelihood ratio test of the reduced model with the original model first, and then check the variable with the largest p-value again or should…
user3404321
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Strategy to analyse whether unknown function is injective

I have an unknown function $x \to f(x)$, $f:\mathbb{R}^4 \to \mathbb{R}^4$. All elements $x_i$ are within a closed interval. Every function evaluation is quite expensive. How can I made a statement about the "injectivity" of my function in terms of…
user2911557
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Simple Linear regression Slope and Intercept

Why do we find confidence interval for slope and intercept in Simple Linear Regression Model ? What does it indicate?
Milan Amrut Joshi
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Linear Regression with variables at different times

I want to do a sensitivity analysis on two variables. I'm trying to do a basic linear regression on the variables $X$ and $Y$ where $X$ is my exogenous variable and $Y$ is my dependent variable. The data I was given for $X$ is given hourly for every…
Daniel
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