Inferential Statistics Examples and Solutions Never be so Available

Recent questions in Inferential Statistics

misurrosne 2022-06-15

regression $x (t) = a t + b$ , number of trials, and $R_{2}$ of the regression. How do I find the value and $95 %$ 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
$Y = α + β X + μ$
It also holds that $E (μ) = 0$ , $Var (μ) = σ_{μ}^{2}$ , $Var (X) = σ_{X}^{2}$ , $Var (Y) = σ_{Y}^{2}$ , $Corr (X, Y) = r$ and $Corr (X, μ) = r_{X μ}$ . Find $β$ . I tried to solve this as follows:
For simple linear regression $β = \frac{Cov (X, Y)}{Var (X)}$ and $Corr (X, Y) = \frac{Cov (X, Y)}{σ_{X} σ_{Y}} = r$ so that:
$β = \frac{Corr (X, Y) \cdot σ_{X} σ_{Y}}{σ_{X}^{2}} = r \frac{σ_{Y}}{σ_{X}}$
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
$e_{i} = y_{i} - a x_{i} - b$
$e_{i} = (y_{i} - \bar{y}) - a (x_{i} - \bar{x}) - (b - \bar{y} + a \bar{x})$

Paul Webster 2022-06-04

Short version, I need to find a regression to this: $a \equiv t (\mod Δ)$ , $a$ and $Δ$ 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 $Δ$ , 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 $m Δ$ .

Paul Webster 2022-06-04

Short version, I need to find a regression to this: $a \equiv t (\mod Δ)$ , $a$ and $Δ$ 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 $Δ$ , 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 $m Δ$ .

Chandini Pamulapati2022-06-03

Among 157 African-American men, the mean systolic blood pressure was 146 mm Hg with a standard deviation of 27. We wish to know if on the basis of these data, we may conclude that the mean systolic blood pressure for a population of African-American is greater than 140.
- Setup the null and alternate hypothesis
- Determine the type of the test
- Use a=0.01, conduct the test and accept or reject the hypothesis on the basis of the test.

Jornelecrearlqx2un 2022-06-02

If the joint density function of $X$ and $Y$ is given by:
$f (x, y) = {\begin{cases} 1 / 2, & for | x | + | y | \leq 1 \\ 0, & otherwise \end{cases}$
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 $x^{T} W y = z$ , where $x$ and $y$ are real valued vectors. For example, two images.
Breaking it into a more familiar form:
$x^{T} W y = \sum_{i j} w_{i j} x_{i} y_{j} = z$
This essentially looks very similar to polynomial regression with only interactions between features (without the polynomials). i.e.
$z = f_{w} (x) = \sum_{i} w_{i} x_{i} + \sum_{i} \sum_{j = i + 1} w_{i j} x_{i} x_{j}$
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 $2 D$ dimensions (fitting a function $f (x, y)$ to a set of data $X, Y$ , and $Z$ )? And is there a way to apply a condition to the regression in $2 D$ that requires all functions fitted to go through the axis line $x = 0$ ?

agdv9m 2022-05-24

set $S$ of coordinates $(x, y)$ , and am estimating $f (x) = a x + b$ where $a > 0$ . I also happen to know that $\forall x, y ((x, y) \in S ⟹ y < f (x))$ .
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 $g (x)$ and then construct $g^{'} (x) = g (x) + c$ , with $c$ being the lowest number such that $\forall x, y ((x, y) \in S ⟹ y \leq g^{'} (x))$ , e.g. such that $g^{'} (x)$ 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

A random sample of size $n$ from a bivariate distribution is denoted by $(x_{r}, y_{r}), r = 1, 2, 3, . . ., n$ . Show that if the regression line of $y$ on $x$ passes through the origin of its scatter diagram then
$\bar{y} \sum_{r = 1}^{n} x_{r}^{2} = \bar{x} \sum_{r = 1}^{n} x_{r} y_{r}$
where $(\bar{x}, \bar{y})$ is the mean point of the sample.

Cody Lowe2022-05-11

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 $ρ$ , 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,
$ρ_{X, Y} (f (X), g (Y))$
where f, g are non-linear functions such that it measures other kinds of dependce (take for example $f (s) = g (s) = s^{2}$ for quadratic dependence).

ga2t1a2dan1oj 2022-05-08

$X =$ Lot & $Y =$ Cost
Give a broken line linear model with a breakpoint at $250$ :
$Y = B_{0} + B_{1} X_{1} + B_{2} X_{2} + B_{3} X_{3} + e$
where $X_{2} = 0$ or $1$ depending on whether the lot size is $\geq 250$ or $< 250$ and $X_{3} = X_{1} \cdot X_{2} .$ .
Which hypothesis statement is equivalent to the statement: The two regression lines have the same intercept term?
$H_{0} : B_{0} = 0 H_{0} : B_{1} = 0 H_{0} : B_{2} = 0 H_{0} : B_{3} = 0$
$B_{0}$ is obviously the intercept for simple linear regression models, however, the broken line phrasing is causing me to be confused on this. My initial instinct was to assume $B_{0}$ hypothesis was appropriate, but now I'm wondering if $B_{2} = 0$ makes more sense.

velinariojepvg 2022-05-08

If I have built two linear regression models over sets $A$ and $B$ , and now want a linear regression over set $A \cup B$ .Is there a way to reuse what I already have?

Jayla Faulkner 2022-05-08

Is the total sum of squares for multiple regression the same as the total sum of squares for anova?
Is anova a test for bivariate correlation or multiple regression?

Kendall Oneill 2022-05-08

What do you mean by a distribution is homoscedastic (ie, $σ (Y | X = x) = σ$ ) 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 $θ = {(X^{T} X)}^{- 1} X^{T} y$ .
In Ridge regression, we have $θ = {(λ I + X^{T} X)}^{- 1} X^{T} y$ .
I learnt somewhere that while $X^{T} X$ is not guaranteed to be invertible, $λ I + X^{T} X$ 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.

In simple terms, inferential statistics is an approach where you use measurements from the sample of specific subjects as you conduct an experiment. The purpose is to make an outcome based on generalization regarding the greater population of subjects. You may use equations if there are questions that are related to a particular approach. You can get inferential statistics help as we provide a list of answers with good samples to start with. There are related topics like correlation problems that will help you with financial statistics and the coordination of variables

Inferential Statistics

Understanding Inferential Statistics through Examples