# Understanding Inferential Statistics through Examples

Recent questions in Inferential Statistics
Ayanna Jarvis 2022-10-12

## Find the upper estimate for the total amount of water that leaked out by using five rectangles? Give your answer with one decimal place.

Janessa Benson 2022-10-07

## Probability of infection by staphylococcus aureusPlease forgive my innumeracy, but I have a question with which I am hoping someone might be able to help me.Suppose the following be true. The chance of a prosthetic hip joint becoming infected by staphylococcus aureus is one per cent. The chance of a natural hip joint becoming infected by staphylococcus aureus is 0.1%. In other words (in case I am misusing the word 'chance'), one in one hundred people with prosthetic hip joints will become infected by staphylococcus aureus, whereas only one in one thousand people with natural hip joints will become so infected.Now suppose that X has a prosthetic hip joint and that X's hip joint becomes infected by staphylococcus aureus.Given only the information provided here, is it correct to say that X's hip joint probably would not have become infected but for the fact that X has a prosthetic hip joint (instead of a natural hip joint)? In other words (to make it clear what I mean by 'probably'), is it correct to say that there is a greater than 50 per cent chance that X's hip joint would not have become infected but for the fact that X has a prosthetic hip joint? Why or why not?

Cindy Noble 2022-10-05

## Based on the estimates $\mathrm{log}\left(2\right)=.03$ and $\mathrm{log}\left(5\right)=.7$, how do you use properties of logarithms to find approximate values for ${\mathrm{log}}_{5}\left(2\right)$?

Leonel Schwartz 2022-10-02

## Please, give examples of two variables that have a perfect positive linear correlation and two variables that have a perfect negative linear correlation.

garnirativ8 2022-09-30

## Let us define the correlation coefficient as $\rho \left(X,Y\right)=\frac{Cov\left(X,Y\right)}{\sqrt{Var\left(X\right)Var\left(Y\right)}}$ .Are the following statements true or false?If $\rho \left(X,Y\right)=\rho \left(Y,Z\right)=0$ then $\rho \left(X,Z\right)=0$If $\rho \left(X,Y\right)>\rho \left(Y,Z\right)>0$ then $\rho \left(X,Z\right)>0$If $\rho \left(X,Y\right)<\rho \left(Y,Z\right)<0$ then $\rho \left(X,Z\right)<0$I think they are false, but I can't find counterexamples. Could you help me?

ecoanuncios7x 2022-09-30

## Linear Regression:$Y=a+bX+ϵ$For $R$ squared in linear regression, in the form of ratio between $\left({y}_{i}-{y}^{bar}\right)$, or in terms of$\left({S}_{xy}{\right)}^{2}/\left({S}_{xx}{S}_{yy}\right)$Not sure if you guys come across this form:${R}^{2}=\frac{Var\left(bX\right)}{V\left(bX\right)+V\left(ϵ\right)}$?

Aidyn Crosby 2022-09-29

## A and B have negative correlation, so -A and -B have positive?

Aidyn Crosby 2022-09-29

## What is the main difference between correlation and causation? (Answer the question in a short paragraph (roughly 3-5 sentences). If necessary, explain the concept and/or give examples)

elisegayezm 2022-09-29

## Based on the estimates $\mathrm{log}\left(2\right)=.03$ and $\mathrm{log}\left(5\right)=.7$, how do you use properties of logarithms to find approximate values for $\mathrm{log}\left(0.25\right)$?

eukrasicx 2022-09-29

## Proof that given 2 variables X and Y with correlation ${\rho }_{X,Y}$ and given $U=a+bX$ and $V=c+dY$ then ${\rho }_{X,Y}={\rho }_{U,V}$ if $bd>0$

garnirativ8 2022-09-28

## How do you determine the value of an x-ray machine after 5 year if it cost \$216 thousand and Margaret Madison, DDS, estimates that her dental equipment loses one sixth of its value each year?

Mangle Woods2022-09-27

## what ia the probability of obtaining ten heads in a row when flipping a coin? Interpret this probability. the probability of obtaining ten heads in a row when flipping a coin it?

Parker Pitts 2022-09-27

## Multiple Regression Forecast"Part C: asks what salary would you forecast for a man with 12 years of education, 10 months of experience, and 15 months with the company."This is straight forward enough just reading off the coefficients table. $y=3526.4+\left(722.5\right)\left(1\right)+\left(90.02\right)\left(12\right)+\left(1.269\right)\left(10\right)+\left(23.406\right)\left(15\right)=5692.92$but"Part D: asks what salary would you forecast for men with 12 years of education, 10 months of experience, and 15 months with the company."I know that the answer to this must be different from C, but I have no idea why, I would of just done exactly the same as in part C,What is wrong with my train of thought or intuition and how might I go about calculating the salary for men, rather than a man?

trkalo84 2022-09-27

## What is $Var\left[b\right]$ in multiple regression?Assume a linear regression model $y=X\beta +ϵ$ with $ϵ\sim N\left(0,{\sigma }^{2}I\right)$ and $\stackrel{^}{y}=Xb$ where $b=\left({X}^{\prime }X{\right)}^{-1}{X}^{\prime }y$. Besides $H=X\left({X}^{\prime }X{\right)}^{-1}{X}^{\prime }$ is the linear projection from the response space to the span of $X$, i.e., $\stackrel{^}{y}=Hy$Now I want to calculate $Var\left[b\right]$ but what I get is an $k×k$ matrix, not an $n×n$ one. Here's my calculation:What am I doing wrong?Besides, are $E\left[b\right]=\beta$, $E\left[\stackrel{^}{y}\right]=HX\beta$, $Var\left[\stackrel{^}{y}\right]={\sigma }^{2}H$, $E\left[y-\stackrel{^}{y}\right]=\left(I-H\right)X\beta$, $Var\left[y-\stackrel{^}{y}\right]=\left(I-H\right){\sigma }^{2}$ correct (this is just on a side note, my main question is the one above)?

Melina Barber 2022-09-26

## Pearson Correlation Coefficient InterpretationLet X=(1,2,3,...,20). Suppose that $Y=\left({y}_{1},{y}_{2},...,{y}_{20}\right)$ with ${y}_{i}={x}_{i}^{2}$ and $Z=\left({z}_{1},{z}_{2},...,{z}_{20}\right)$ with ${z}_{i}={e}^{{x}_{i}}$. Pearson correlation coefficient is defined by formula$\rho \left(X,Y\right)=\frac{\sum _{i=1}^{20}\left({x}_{i}-\overline{x}\right)\left({y}_{i}-\overline{y}\right)}{\sqrt{\left(\sum _{i=1}^{20}\left({x}_{i}-\overline{x}{\right)}^{2}\right)\left(\sum _{i=1}^{20}\left({y}_{i}-\overline{y}{\right)}^{2}\right)}}$If $\rho \left(X,Y\right)=1$, we can say that X and Y have a linear correlation. If $0.7\le \rho \left(X,Y\right)<1$ then X and Y has a strong linear correlation, if $0.5\le \rho \left(X,Y\right)<0.7$ then X and Y has a modest linear correlation, and if $0\le \rho \left(X,Y\right)<0.5$ then X and Y has a weak linear correlation. Using this formula, we get $\rho$(X,Y)=0.9 and $\rho$(X,Z)=0.5. However, the relationship between X and Y is actually quadratic but they have the high correlation coefficient that indicate linear correlation.So, my question is what is "linear correlation" actually between X and Y ? Since $\rho$(X,Z)=0.5 indicate the modest correlation coefficient, what is another intepretation of this value? What is the difference between $\rho$(X,Y) and $\rho$(X,Z), noting that Y and Z is not a linear function of X.

malaana5k 2022-09-26