 # Get help with inferential statistics problems

Recent questions in Inferential Statistics Kendall Oneill 2022-05-08

### What do you mean by a distribution is homoscedastic (ie, $\sigma \left(Y|X=x\right)=\sigma$) in the context of simple linear regression? Why do we need this assumption in simple linear regression? What will happen to the regession if a distribution is not homoscedastic? Carley Haley 2022-05-08

### In Linear regression, we have $\theta ={\left({X}^{T}X\right)}^{-1}{X}^{T}y$.In Ridge regression, we have $\theta ={\left(\lambda I+{X}^{T}X\right)}^{-1}{X}^{T}y$.I learnt somewhere that while ${X}^{T}X$ is not guaranteed to be invertible, $\lambda I+{X}^{T}X$ is guaranteed to be invertible.Is this true? If so, why? Porter Mccullough 2022-05-03

### Table of values$\begin{array}{cccccc}x& 1& 2& 3& 4& 5\\ y& 3& 6& 8& 9& 0\\ y& 4& 6& 1& 2& 4\end{array}$and know that it is a simple linear regression model, what is the value of $n$? I think it is either $5$ or $10$ but am not sure which one. juniorychichoa70 2022-05-02

### I am getting ${f}_{X,Y}\left(x,y\right)={f}_{X}\left(x\right){f}_{Y}\left(y\right)$ even if the correlation coefficient $\rho \ne 0$ znacimavjo 2022-05-01

### Suppose you have two sequences of complex numbers ${a}_{i}$ and ${b}_{i}$ indexed over the integer numbers such that they are convergent in ${l}^{2}$ norm and a has norm greater than b in the sense$\mathrm{\infty }>\sum _{i}|{a}_{i}{|}^{2}\ge \sum _{i}|{b}_{i}{|}^{2}.$Suppose moreover they are uncorrelated over any time delay, meaning$\sum _{i}{a}_{i}\overline{{b}_{i-n}}=0\phantom{\rule{1em}{0ex}}\mathrm{\forall }n\in \mathbb{Z}.$Is it true that the polinomial $a\left(z\right)=\sum _{i}{a}_{i}{z}^{-i}$ is greater in absolute value than $b\left(z\right)=\sum _{i}{b}_{i}{z}^{-i}$ for any unit norm complex number z? gaitaprepeted05u 2022-04-30
### Two random variables, X and Y, have the joint density function:$f\left(x,y\right)=\left\{\begin{array}{ll}2& 0Calculate the correlation coefficient between X and Y. ga2t1a2dan1oj 2022-04-07