# Understanding Inferential Statistics through Examples

Recent questions in Inferential Statistics
Annie French 2022-11-11

## Is it a "standard" Math/Numerical-Analysis hack to add a relatively small number e.g. 1*10E-5 to the diagonal of a squared matrix to ensure LU Decomposition (or whichever decomposition algorithm is applicable)? As opposed to "partially/totally pivoting"?

Siena Erickson 2022-11-11

## What is degree of freedom in statistics?

Mark Rosales 2022-11-11

## How can we fit a set of data points to a hyperbola, a square root function or a logarithmic function?

Kayley Dickson 2022-11-10

## Show that if ${x}_{t+l}=A{x}_{t}$ , then $\rho \left(l\right)=1$ if $A>0$, and $\rho \left(l\right)=-1$ if $A<0$.

klasyvea 2022-11-09

## How do you write an exponential function to model the situation. Then estimate the value of the function after 5 years. A population of 290 animals that increases at an annual rate of 9%?

Yaretzi Mcconnell 2022-11-09

## What is the meaning of :$:s$ after a mathematical symbol?

Cael Dickerson 2022-11-09

## Correlation matrix with same pairwise correlation coefficientQuestionCorrelation matrix. Consider 𝑛 random variables with the same pairwise correlation coefficient ${\rho }_{n}$. Find the highest possible value of ${\rho }_{n}$fora) n=3b) n=4c) general, n $\ge$2HINT: Correlation matrix must be positive semi-definite.My WorkingsThis is what I infer from "same pairwise coefficients":$\left(\begin{array}{ccc}1& {\rho }_{n}& {\rho }_{n}\\ {\rho }_{n}& 1& {\rho }_{n}\\ {\rho }_{n}& {\rho }_{n}& 1\end{array}\right)$Because a correlation matrix is positive semi-definite, all principal minors have to be positiveFor n=3, the principal minors calculations yield$\mid {H}_{1}\mid$=1$\mid {H}_{2}\mid$=1-${\rho }_{n}^{2}$ $\ge 0$ $⇒$${\rho }_{n}$ $\le 1$$\mid {H}_{3}\mid ={\rho }_{n}^{2}$ - ${\rho }_{n}$$\ge 0$ $⇒$ ${\rho }_{n}$ $\ge 1$$\mid {H}_{4}\mid =\left({1}^{3}$+2${\rho }_{n}^{3}$)-(3${\rho }_{n}^{2}$)$\ge 0$ . I solved for the roots and found 1Conclusion: For n=3, max ${\rho }_{n}$=1I did the same method for n=4 and found max ${\rho }_{n}$=1 againMy ProblemResult looks too simple and false. Method is tediousI have no idea how to do the general case. (by induction ?)Thank you for your helpINDUCTION ATTEMPT${H}_{0}$$\left(\begin{array}{cc}1& {\rho }_{2}\\ {\rho }_{2}& 1\end{array}\right)$$⇒-\frac{1}{2-1}\le {\rho }_{2}\le 1$${H}_{n}$: Pn: Suppose that for a nxn correlation matrix An with same pairwise coefficients ${\rho }_{n}$, $-\frac{1}{n-1}\le {\rho }_{n}\le 1$ holds${H}_{n+1}$$-\frac{1}{n-1}\le {\rho }_{n}\le 1$$⇐⇒$$-\frac{1}{\left(n+1\right)-1}\le {\rho }_{n+1}\le 1$$⇐⇒$$-\frac{1}{n}\le {\rho }_{n+1}\le 1$And because for all $-\frac{1}{n}\ge -\frac{1}{n-1}$$-\frac{1}{n-1}\le {\rho }_{n+1}\le 1$

Kale Sampson 2022-11-09

## Whether there is some connection between fitting probability distribution on some data set and linear regression? Or this two tools are for different problems?

Rosemary Chase 2022-11-07

## Can you determine the coefficient of determination from the correlation coefficient?

Ricky Arias 2022-11-07

## Explain what does it mean this denotation: $\underset{w}{min}||Xw-y|{|}_{2}^{2}$

Alice Chen 2022-11-07

## Correlation FunctionLet X,Y be random variables. If $\rho \left(X,Y\right)=a$ (Correlation), where $a\in \left(0,1\right)$, what can be said about the relationship between X and Y? Is it true that Y=bX+c+Z, where Z is a random variable? If it is true then how is $|Z|$ related to the correlation a?

klasyvea 2022-11-06

## What are the prerequisites for regression analysis?

Messiah Sutton 2022-11-06

## Why is the standardized regression coefficient in a regression model with more than one independent variable not the same as the correlation coefficient between x we interested in and y in a regression model with more than one independent variable?$\stackrel{^}{{\beta }_{i}}=\mathrm{c}\mathrm{o}\mathrm{r}\left({Y}_{i},{X}_{i}\right)\cdot \frac{\mathrm{S}\mathrm{D}\left({Y}_{i}\right)}{\mathrm{S}\mathrm{D}\left({X}_{i}\right)}$So$\mathrm{c}\mathrm{o}\mathrm{r}\left({Y}_{i},{X}_{i}\right)=\stackrel{^}{{\beta }_{i}}\cdot \frac{\mathrm{S}\mathrm{D}\left({X}_{i}\right)}{\mathrm{S}\mathrm{D}\left({Y}_{i}\right)}$The formula for the standardized regression coefficient is also:$standardizedBeta=\stackrel{^}{{\beta }_{i}}\cdot \frac{\mathrm{S}\mathrm{D}\left({X}_{i}\right)}{\mathrm{S}\mathrm{D}\left({Y}_{i}\right)}$So shouldn't it be$standardizedBeta=\mathrm{c}\mathrm{o}\mathrm{r}\left({Y}_{i},{X}_{i}\right)$?

drogaid1d8 2022-11-05

## How can you estimate the parameters of a normal distribution?

Jaslyn Sloan 2022-11-05

## Find the function that describes a real life curve

vidamuhae 2022-11-05

## What is the generalized R-Squared?

Nola Aguilar 2022-11-05