# 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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52 views

### Variance-stabilizing transformation on a simple linear regression

I am currently working with variance-stabilizer method and readed something about it from my textbook. I want to understand it better so I would like to consider a case where I for instance have a ...
11 views

### Intuition of R-squared in a quantile

I assume, R-squared (correlation of determination) can be used as a measure of the goodness-of-fit in a quantile plot (QQ-plot). In a QQ-plot we measure between empirical quantiles (the ranked sample) ...
18 views

### Alternative Regression

Consider the least square regression $y ∈ R^n$ on $X ∈ R^{n\times k}$, and the alternative regression on $Z = XC$, where $C ∈ R^{k×k}$ is a invertible matrix. Compare the least square estimators and ...
38 views

105 views

### finding optimal entry and exit points in a time series of prices

given an initial 1000 dollars cash value, and a time series of bid price, ask price, assuming constraints of transaction costs, e.g. 1 dollar every time we buy or sell, what is the best approach to ...
85 views

### What makes inequality true in proof of Gauss Markov theorem

Elsewhere on this site, I found a very compact proof of the Gauss-Markov theorem, seen below. I don't understand the justification for the middle step with the inequality. Specifically, what property ...
24 views

### Show that $𝑌^𝑡𝑌= \hat{𝑌}^{t}\hat{𝑌}+ 𝑒^𝑡𝑒$

I'm trying to solve this property of multiple linear regression $𝑌^𝑡𝑌= \hat{𝑌}^{t}\hat{𝑌}+ 𝑒^𝑡𝑒$ Any suggestions would be great!
36 views

### Test which functional form that best explains data

I had this question in an exam lately and I was not sure how to answer it. Now the exam is done, and I can't go back, but it's been in my head ever since and I'm really curious about the answer. ...
80 views

### Can I determine if two random variables are independent if I know their expected values and the variances?

I have two random variables $X$ and $Y$. I know the expected values $E\left[X\right]$ and $E\left[Y\right]$, as well as their respective variances $V\left[X\right]$ and $V\left[Y\right]$ (I have them ...
17 views

### low $p$-value and low explained variation connection in multiple regression analysis

I've just started studying multiple linear regression and I'm stuck at creating a dataset for which a multiple regression model would have a low $p$-value (the coefficients are non zero) and also low ...
30 views

### How to handle an integral or derivative as a collinear variable in regression?

I would like to regress multiple unknowns relating a dependent variable to an second variable both of which are functions of third independent variable. I can relate the integral of the first ...
55 views

### what is your opinion for the best function can be fitted to these plots?

I have three sets of data (x,f(x)) as follows: ...
23 views

### Standard deviation formula for coefficients in multiple regression analysis

I am trying to understand how to calculate the individual deviation in this regression analysis table. $(HH Size)_{se} =$ $stderr \over \sqrt{S_{xx}}$ $=$ ${0.444400903 \over \sqrt{10}} = 0.14053$ ...
33 views

### Relationship between correlation coefficient and the agle between two regression lines

From: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient Geometric interpretation Regression lines for y = gX(x) [red] and x = gY(y) [blue] Regression lines for y = gX(x) [red] and x = gY(...
61 views

### How do I judge the accuracy of a model with 3 variables?

For my high-school maths exploration, I have chosen to simulate heat flow in a one-dimensional rod using GNU Octave. I will then solve the heat equation and judge the accuracy of the heat equation in ...
29 views

### QMLE for correlated Bernouli model parameter

9Consider a binary dependent variable of the form $$y_t=\begin{cases} 1, & \ \text{with probability} \ p(y_t=1|x_t) \\ 0, & \ \text{with probability} \ 1- p(y_t=1 |x_t) \end{cases}$$ Suppose ...
1 vote
22 views

### Analytic solution of regression problem

I have a regression problem as below. $$A^* = \operatorname*{argmin}_A \| Y - AX \|_F^2$$ where $Y$ and $X$ are matrices, and $A$ is a mapping matrix between these two matrices. There are analytic ...
21 views

### In Twisk (2013) on the equation describing a generalized estimating equation (GEE), why is there a subscripted '1' after beta?

In his book on Applied Longitudinal Data Analysis for Epidemiology, page 60 there is an equation that describes a generalized estimating equations (GEE) model. This equation models the relationship ...
50 views

### Statistical significance in context of financial data?

I understand statistical significance in the general sense: we take a sample from a population and compute some parameter from the sample to infer what is the propulsion parameter to some degree of ...
1 vote
59 views

### On the difference in nonparametric regression models

I recently read the wikipedia article about nonparametric regression. It contains the following quote: In nonparametric regression, we have random variables $X$ and $Y$ and assume the following ...
105 views

### Maximum likelihood variance estimator of simple linear regression is biased

Colleagues, I understand that bias is defined as $b(\theta)=\mathbb{E}(\hat{\theta})-\theta$. How can one show that the variance estimator for maximum likelihood estimators of simple simple linear ...
40 views

### supervised model for car accidents?

I can't seem to figure out how I would fit a multinomial distribution here? I think I've managed to produce the linear combination as: yi = α0 + α1x 1,i + α2 x2,i I'd be hugely grateful for any ...
1 vote
74 views

### Translate my GLM model with coefficients into a formula

I wasn't sure whether to post here or on stats.stackexchange, but trying here first since my goal is to find/derive a math formula for my r generated model. If you look at my post history you can see ...
58 views

### Find Best Fit Equation From 4 Data Points [closed]

I have thousands of rows which each contain 4 different data values. Data example: A = 799, B = 190.68, C = 131.74, Y = 48.65 A = 1209, B = 9.67, C = 9.67, Y = 311.36 A = 932, B = 212.23, C ...
1 vote
27 views

### Solving gradient expression as a differential equation

I study horizontal gravity gradient $\frac{\Delta g}{\Delta l}$ in certain field. We measure $\Delta g$ and $\Delta l$ thhrough several profiles and same direction. Something like that: enter image ...
122 views

### Why square of pearson correlation does not match with r2 score?

As per link of correlation and R2 , it is mathematically shown that square of pearson correlation is equal to r2. However, I am trying to replicate these results with my data in python and I do not ...
68 views

### Regression and stress management

Participants were randomly allocated to one of two stress management therapy groups (group A vs. group B), or a waiting list control group. Their baseline levels of stress were measured before ...
Consider the real matrices $V, W, X, Y$. Define the function $L(W, V) := \frac 1 2 \| Y - V W X \|_2^2$. How can it be shown that $L$ non-convex, as claimed here? Tnx. I have tried to look first at ...