ajumbaretu

2022-11-20

What is the benefit of OU vs regression for modeling data, say data in the form of ($x,y$) pairs?

reinmelk3iu

Beginner2022-11-21Added 21 answers

Stochastic processes and regression analysis are just two sides of the same coin. Namely, Assume that you have a realization from a univariate time process and you postulate that the process that generated this data was autoregression of order $1$, however with an unknown coefficient $\varphi $. I.e., ${X}_{t}=\varphi {X}_{t-1}+{\u03f5}_{t}$, hence you can use statistics (regression analysis) in order to estimate $\varphi $. Now, assume that you are not sure what process generated your data and you are willing to test a set of AR(I)MA models. Here too the statistics might help you to select the most appropriate model. Namely, parametric-regression models allow you to approximate the data-generating process by a linear regression. Note that not every stochastic process can be well approximated by a linear-parametric regression model. And, basically, stochastic analysis assume that you know the properties of the process and you can work with them, while regression analysis assume that you don't know the data-generating process and you try to recover its properties by using the data.

Which of the following statements is not correct for the relation R defined by aRb, if and only if b lives within one kilometre from a?

A) R is reflexive

B) R is symmetric

C) R is not anti-symmetric

D) None of the aboveA line segment is a part of a line as well as a ray. True or False

Which characteristic of a data set makes a linear regression model unreasonable?

Find the meaning of 'Sxx' and 'Sxy' in simple linear regression

In the least-squares regression line, the desired sum of the errors (residuals) should be

a) zero

b) positive

c) 1

d) negative

e) maximizedCan the original function be derived from its ${k}^{th}$ order Taylor polynomial?

Should the independent (or dependent) variables in a linear regression model be normal or just the residual?

What is the relationship between the correlation of two variables and their covariance?

What kind of technique is to be adopted if I have to find an equation or model for say, $D$ depends on $C$, $C$ changes for a set of $B$, which changes for different $A$.

Correlation bound

Let x and y be two random variables such that:

Corr(x,y) = b, where Corr(x,y) represents correlation between x and y, b is a scalar number in range of [-1, 1]. Let y' be an estimation of y. An example could be y'=y+(rand(0,1)-0.5)*.1, rand(0,1) gives random number between 0, 1. I am adding some noise to the data.

My questions are:

Is there a way where I can bound the correlation between x, y' i.e. Corr(x,y')?I mentioned y' in light of random perturbation, I would like to know what if I don't have that information, where I only know that y' is a estimation of y. Are there any literature that cover it?Can you determine the correlation coefficient from the coefficient of determination?

How can one find the root of sesquilinear form with positive definite matrix?

From numerical simulation and regression analysis I discovered that the root-mean-square amplitude of white noise with bandwidth $\mathrm{\Delta}\phantom{\rule{negativethinmathspace}{0ex}}f$ is proportional to $\sqrt{\phantom{\rule{negativethinmathspace}{0ex}}\mathrm{\Delta}\phantom{\rule{negativethinmathspace}{0ex}}f}$. How can this be derived mathematically ?

In a Simple Linear Regression analysis, independent variable is weekly income and dependent variable is weekly consumption expenditure. Here $95$% confidence interval of regression coefficient, ${\beta}_{1}$ is $(.4268,.5914)$.

How to find AIC values for both models using $R$ software?