# Get help with inferential statistics problems

Recent questions in Inferential Statistics
Poftethef9t 2022-06-21

### Given $X$ and $Y$ sample data as something like$\left[\begin{array}{cc}1& 2\\ 2& 3\end{array}\right]$$\left[\begin{array}{c}7\\ 8\end{array}\right]$In such an arrangement how do I include B3? I would think I would want to add it in as always 1 in $X$. IE$\left[\begin{array}{cc}1& 2\\ 2& 3\\ 1& 1\end{array}\right]$

Averi Mitchell 2022-06-16

### Can I maximize the correlation between a linear combination of variables and some other variable?

Amber Quinn 2022-06-15

### Why is the following true for the covariance $cov\left(X,Y\right)$ and variances $Var\left(X\right)$ , $Var\left(Y\right)$ of two rvs X and Y:$\frac{Cov\left(cX,Y\right)}{\sqrt{Var\left(cX\right)Var\left(Y\right)}}=\frac{cCov\left(X,Y\right)}{\sqrt{{c}^{2}Var\left(X\right)Var\left(Y\right)}}=\frac{Cov\left(X,Y\right)}{\sqrt{Var\left(X\right)Var\left(Y\right)}}$

misurrosne 2022-06-15

### regression $x\left(t\right)=at+b$, number of trials, and ${R}_{2}$ of the regression. How do I find the value and $95\mathrm{%}$ confidence interval for the value of $V=x/t$?

manierato5h 2022-06-15

### Let's say we have two random variables $Y$ and $X$ used to form regression model$Y=\alpha +\beta X+\mu$It also holds that $E\left(\mu \right)=0$, $\text{Var}\left(\mu \right)={\sigma }_{\mu }^{2}$, $\text{Var}\left(X\right)={\sigma }_{X}^{2}$, $\text{Var}\left(Y\right)={\sigma }_{Y}^{2}$, $\text{Corr}\left(X,Y\right)=r$ and $\text{Corr}\left(X,\mu \right)={r}_{X\mu }$. Find $\beta$. I tried to solve this as follows:For simple linear regression $\beta =\frac{\text{Cov}\left(X,Y\right)}{\text{Var}\left(X\right)}$ and $\text{Corr}\left(X,Y\right)=\frac{\text{Cov}\left(X,Y\right)}{{\sigma }_{X}{\sigma }_{Y}}=r$ so that:$\beta =\frac{\text{Corr}\left(X,Y\right)\cdot {\sigma }_{X}{\sigma }_{Y}}{{\sigma }_{X}^{2}}=r\frac{{\sigma }_{Y}}{{\sigma }_{X}}$Is this as simple as this?

Damon Stokes 2022-06-10

### We have to determine the effect of a predictor variable on an outcome variable using simple linear regression. We have lots of data (about 300 variables) and we may include some other covariates in our regression model. Why would we include other covariates and how do you decide which of those 300 variables we want to include in our regression model?

shmilybaby4i 2022-06-09

### Help to understand${e}_{i}={y}_{i}-a{x}_{i}-b$${e}_{i}=\left({y}_{i}-\overline{y}\right)-a\left({x}_{i}-\overline{x}\right)-\left(b-\overline{y}+a\overline{x}\right)$

Paul Webster 2022-06-04

### Short version, I need to find a regression to this: $a\equiv t\phantom{\rule{0.444em}{0ex}}\left(\mathrm{mod}\phantom{\rule{0.333em}{0ex}}\mathrm{\Delta }\right)$, $a$ and $\mathrm{\Delta }$ are the unknowns constants.Any idea where I should start looking?Some context, because I may be wording it in a confusing way: I am trying to find the tempo of time-stamped events ${t}_{i}$ for some real time musical analysis. They have a typical interval of $\mathrm{\Delta }$, but there isn't an event at every "tick", so no linear regression, and there may be more than one event for a given "tick". In other words, ${t}_{n+1}-{t}_{n}$ may be $0$ or any $m\mathrm{\Delta }$.

Paul Webster 2022-06-04

### Short version, I need to find a regression to this: $a\equiv t\phantom{\rule{0.444em}{0ex}}\left(\mathrm{mod}\phantom{\rule{0.333em}{0ex}}\mathrm{\Delta }\right)$, $a$ and $\mathrm{\Delta }$ are the unknowns constants.Any idea where I should start looking?Some context, because I may be wording it in a confusing way: I am trying to find the tempo of time-stamped events ${t}_{i}$ for some real time musical analysis. They have a typical interval of $\mathrm{\Delta }$, but there isn't an event at every "tick", so no linear regression, and there may be more than one event for a given "tick". In other words, ${t}_{n+1}-{t}_{n}$ may be $0$ or any $m\mathrm{\Delta }$.

Jornelecrearlqx2un 2022-06-02

### If the joint density function of $X$ and $Y$ is given by:Show that $Y$ has constant regression with respect to $X$ and/but that $X$ and $Y$ are not independant.

dokezwa17 2022-05-28

### A similarity/metric learning method that takes in the form of ${x}^{T}Wy=z$, where $x$ and $y$ are real valued vectors. For example, two images.Breaking it into a more familiar form:${x}^{T}Wy=\sum _{ij}{w}_{ij}{x}_{i}{y}_{j}=z$This essentially looks very similar to polynomial regression with only interactions between features (without the polynomials). i.e.$z={f}_{w}\left(x\right)=\sum _{i}{w}_{i}{x}_{i}+\sum _{i}\sum _{j=i+1}{w}_{ij}{x}_{i}{x}_{j}$I was curious to see if the optimization for the matrix $W$ is the same as doing optimization for multivariate linear/polynomial regression, since $x$ and $y$ are fixed, and the only variate is the weight matrix $W$?

Mackenzie Rios 2022-05-24

### Is there a method for polynomial regression in $2D$ dimensions (fitting a function $f\left(x,y\right)$ to a set of data $X,Y$, and $Z$)? And is there a way to apply a condition to the regression in $2D$ that requires all functions fitted to go through the axis line $x=0$?

agdv9m 2022-05-24

### set $S$ of coordinates $\left(x,y\right)$, and am estimating $f\left(x\right)=ax+b$ where $a>0$. I also happen to know that $\mathrm{\forall }x,y\left(\left(x,y\right)\in S\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}y.The question is how I can utilize this knowledge of the upper bound on values to improve the regression result?My intuition is to run a "normal" linear regression on all coordinates in $S$ giving $g\left(x\right)$ and then construct ${g}^{\prime }\left(x\right)=g\left(x\right)+c$, with $c$ being the lowest number such that $\mathrm{\forall }x,y\left(\left(x,y\right)\in S\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}y\le {g}^{\prime }\left(x\right)\right)$, e.g. such that ${g}^{\prime }\left(x\right)$ lies as high as it can whilst still touching at least point in $S$. I do, however, have absolutely no idea if this is the best way to do it, nor how to devise an algorithm that does this efficiently.

Rachel Villa 2022-05-23

2022-05-17

### The incomplete dot plot shows the result of a survey in which each student was asked how many dimes were in their pockets or wallets. The results for “4 dimes” are not shown. Each dot represents one student. It is known that 12.5% of the students had one dime.a)Find the number of students surveyed. Then complete the dot plot.b)What percent of the students had either 0 or 6 dimes?c)What percent of the students had either 1 or 5 dimes?d)Briefly describe the distribution of the data

Cody Lowe 2022-05-11

### According to government data, the probability that an adull was never in a museum is 15%. In a random survey of 10 adults, what is the probability that at least eight were in a museum? Round to three decimal places

Merati4tmjn 2022-05-09

### It is known that $\rho$ , the pearson correlation, is a measure for the linear dependence of two random variables say X, Y. But can't you say just transform X and Y such that we have,${\rho }_{X,Y}\left(f\left(X\right),g\left(Y\right)\right)$where f, g are non-linear functions such that it measures other kinds of dependce (take for example $f\left(s\right)=g\left(s\right)={s}^{2}$ for quadratic dependence).

ga2t1a2dan1oj 2022-05-08