The expected squared deviation of a random variable from its mean; or, the average squared deviation of data about their mean.

learn more… | top users | synonyms

1
vote
0answers
17 views

You will randomly select 10 balls from the box with replacement what is $E(\bar X)$

A box contains 100 numbered balls - 21 with the number 1, 36 with the number 2 and 43 with the number 3. You will randomly select 10 balls from the box with replacement and you take the mean of the ...
1
vote
0answers
30 views

Minimum variance for sum of three random variables

I have been working on the following problem: Given you have VarX = 1, VarY = 4, and VarZ = 25, what is the minimum possible variance for the random variable W = X + Y + Z, or min Var(X+Y+Z)? My ...
1
vote
1answer
50 views

Is there a name or reference in a published journal/book for the following variance formula?

Variance can be combined as $$v=\frac{1}{n-1}\left(\sum_{i = 1}^{numGroups}n_{i}(m_{i}-m)^2+ \sum_{i = 1}^{numGroups}(n_{i}-1)v_{i}\right)$$ where $v$ is the combined variance, $n$ is the total ...
2
votes
0answers
26 views

Variance of difference of $x_{i,t}$ and $x_{i,t+1}$

We have $n$ observations of human performance before and after a training program. We have a random sample of $n$ individuals and assume population distributions are normal. We thus have: $x_{1,t},\ ...
5
votes
1answer
128 views

Are normally distributed residuals not necessarily homoskedastic?

Let's say I've ran a linear regression and I'm checking the model diagnostics. I made a histogram of the residuals and they appear more or less normally distributed as below. I thought for a long ...
0
votes
0answers
6 views

Scaling Specificity to larger data set

Suppose I have the following 2x2 table ...
0
votes
1answer
38 views

Variance of product of two random variables

I’m trying to calculate the variance of a function of two discrete independent functions. The first function, “f(x)”, returns a value of 0 with probability 0.243, a value of 1 with probability 0.306, ...
1
vote
0answers
49 views

Why is permutation test wrong with variance but correct with standard deviation?

I am trying to understand the limits of permutation testing. I wrote up a small permutation test example in R, and found that permutation testing seems to fail when using absolute difference in ...
1
vote
0answers
21 views

Asymptotic consistency with non-zero asymptotic variance -what does it represent?

The issue has come up before, but I want to ask a specific question that will attempt to elicit an answer that will clarify (and classify) it: In Poor Man's Asymptotics, one keeps a clear distinction ...
2
votes
1answer
34 views

Calculating the expected value and variance of an estimator of a normal quantile

I don't quite understand how to use the estimator function and the variance function and plug in the sample mean. I expected that we would plug in the value $\bar X - 1.645s$ into $E(s)$ and $V(s)$. ...
2
votes
1answer
44 views

Almost sure convergence and limiting variance goes to zero

Say an estimator converges with probability one and at the same time its variance goes to zero in the limit. How is it different than an estimator that converges with probability one but its variance ...
0
votes
0answers
21 views

Convergence of an estimator with infinite variance

Is it true that an estimator with infinite variance can converge both in probability and with probability one?
0
votes
0answers
28 views

Inter-cluster variance

Can you please help me understand how is inter-cluster (between clusters) variance defined? As opposed to intra-cluster variance which is pretty straightforward, I have not managed to found a clear ...
0
votes
0answers
23 views

Finite variance of harmonic mean estimator when samples are bounded

Harmonic mean estimator is notorious for the possibility of having infinite variance. Now I want to show that it has finite variance when samples are bounded. I am wondering whether my following ...
1
vote
0answers
15 views

Variance of weighted importance sampling when random variables are bounded

I am trying to find out whether the variance of weighted importance sampling can be shown to be bounded when the original samples are bounded. More specifically, say $Y_1, \cdots, Y_n\in\mathbb{R}$ ...
0
votes
1answer
31 views

Variance decomposition time series hypothesis testing

I'm doing biological gene expression data. For the genes I analysed, each gene can produce two isoforms, one dominant (Gene isoform 1) one minus can be treated as a by-product (Gene isoform 2). I'm ...
0
votes
1answer
19 views

Best estimate of variation for duplicate data?

I'm simplifying a bit here, but my dataset contains 10 stations, each with measurements of growth at time increments. For each measurement, there are between 1-4 duplicates measured at the same ...
2
votes
0answers
58 views

Variance along the regression line

I have two random variables $X$ and $Y$ of unknown distribution which I sample $n$ times to get a set of $n$ random points. I do simple linear regression on this set and arrive at an equation for a ...
0
votes
0answers
60 views

Distributions where higher variance in sample estimates leads to smaller loss when estimating mean

Let's say I have an unknown distribution a. I do not know the shape, mean or variance of this distribution but I have access to another distribution ...
1
vote
0answers
31 views

Estimating of variance of dependent normal distribution

Let $X_1,\dots,X_n$ are independent and identically unobservable variable on $\Omega$. Suppose that $f:\Omega\times\Omega\mapsto \mathbb R$ be unknown function such that we know the value of ...
2
votes
2answers
61 views

Maximum Likelihood estimator of population variance and its derivation process

I have 2 questions about maximum likelihood and using it to calculate variance: Question #1: The question is about finding the derivative of the score function with respect to the parameter $ ...
0
votes
0answers
25 views

Top K variable that represent entire dataset

There are 100 variables in the dataset. Also, i have extracted some additional information about each variable viz Var1 is correlated (Pearson correlation) to Var21,Var25,Var34,Var45,Var55 ; Var2 is ...
2
votes
0answers
59 views

Maximum minus average?

I have some legacy code that is doing some stats that I can't figure out. It's taking the maximum value of a data set, and subtracting the average of the data set. I've tried looking into what this is ...
0
votes
0answers
11 views

Derive covariance of coefficients in simple linear regression [duplicate]

i just need help showing my work to show that Cov(b0,b1)=-xσ^2(sxx) i know that Cov(b0,b1)=E(b0b1)−E(b0)E(b1)=E(b0b1)−β0β1 and i know that var(b0,b1)=σ^2*(X'X)^-1
2
votes
1answer
42 views

Variance problem

I found on the book Casella & Berger: "Statistical Inference" the following theorem (2.3.4): If $X$ is a random variable with finite variance, then for any constants $a$ and $b$ ...
1
vote
2answers
64 views

Adding two (or more) means and calculating the new standard deviation

There are a load of discussions online about adding means and recalculating the standard deviation, but on none have I found answer to this question. I have two sub groups with mean $x_1$ and $x_2$, ...
0
votes
0answers
21 views

What is the variance? [duplicate]

I'm trying to find an answer to this question everywhere, but I'm having a lot of troubles understanding the answers that people are giving; they only confuse me more. I understand that it is a ...
0
votes
2answers
26 views

Understanding COVARIANCE when using same scale

Assuming that an experiment has 3 variables. Time, Temperature inside, Temperature outside. Also, considering that both the temperatures are measured using the same scale say Degree Celsius. If the ...
2
votes
0answers
10 views

average difference between two sets of values

I've been keeping track of my car's gas mileage by calculating gallons divided by miles traveled. The car itself calculates this mileage as well, but its values are always a little higher than the ...
4
votes
2answers
213 views

Can I model standard deviations in a linear model?

Is it possible to put standard deviations or variances into a linear model, as the data to be explained? I have a predictor which I think will linearly increase the standard deviation of a measure, ...
0
votes
0answers
17 views

How to calculate the lag 1 autocovariance for the difference of two variables from the individual autocovariances of the two variables

Is it possible to calculate the auto-covariance of the difference of two variables, from the auto-covariances of two variables being differenced? I have a situation where: Y=βx x is 3*3 matrix of ...
0
votes
1answer
40 views

Computing conditional variance

Is there a package in R that does that? How could I compute the conditional variance $\mathrm{var}(y|x)$ of a sample? I also don't know what to do in case where there are not enough $y$ for each ...
2
votes
2answers
21 views

Finite Population Variance for a Changing Population

How does the addition of one unit affect the population variance of a finite population if everything else remains unchanged? What are the conditions such that the new unit leaves the variance ...
0
votes
0answers
11 views

How to compare the volatility of quarterly p&l of two firms in the same sector?

I want to compare the volatility of the historical quarterly profit and loss (p&l) data of two or more firms operating in the same sector and determine whether the volatility of p&l of these ...
0
votes
0answers
17 views

Comparison of average variances between groups of different size

I have 3 groups, split by highest degree of education. For each individual in a group, i calculate the variance of her income in a five year window. Let's for simplicity assume that i only do this ...
1
vote
0answers
12 views

How do I determine the variance of a collection of groups?

I’m trying to compute the variance of how much pumpkins weigh across pumpkins from 125 farms. However, I only have, for each farm, three pieces of data: (1) the variance of weights for pumpkins from ...
7
votes
2answers
154 views

Why is the standard deviation defined as sqrt of the variance and not as the sqrt of sum of squares over N?

Today I taught an introductory class of statistics and a student came up to me with a question, which I rephrase here as: "Why is the standard deviation defined as sqrt of variance and not as the sqrt ...
0
votes
1answer
33 views

Variance and asymmetry on relative frequency class distribution

I don't know how to resolve this (easy) exercise. I've calculated the first output. But I don't know if it's correct. Calculate arithmetic mean, variance (standard deviation^2), concentration and ...
1
vote
0answers
36 views

Bias-variance decomposition with sklearn BaggingRegressor

There is an example given on the Scikit-Learn site that compares the bias-variance decomposition of the rmse of a single SVR model against a bagging ensemble. Unfortunately, the data is being ...
2
votes
0answers
24 views

Determine how much and why a sample differs from its population

I'd like to be able to determine a) how much and b) why a non-random sample “differs” from the population (there's probably a better word than “differs”; I was tempted to use “does not represent” but ...
0
votes
0answers
26 views

Covariance Matrix using Delta Method

I am trying to get the variance-covariance matrix of a transformation using the Delta Method. Originally, I have coefficients (let's call them X1, X2, etc...) and their variance-covariance matrix. ...
0
votes
1answer
23 views

Inverse-variance weighting

I'm writing a Bachelor Thesis in engineering an a small part of it has two deal with assigning weights to independent measurements. This is from the thesis: I am pretty sure that what equations ...
0
votes
0answers
15 views

Summary statistics & CIs for sample variances from multiple populations

Suppose $X_i$ are $n$ random variables that are all distributed normally, but with differing means and standard deviations: $X_i \sim N(\mu_i, \sigma_i)$. Now suppose $y_{ij}$ is the $j$-th random ...
1
vote
0answers
29 views

Distribution of sample variance for non-normal random variable [duplicate]

For a sample of size $n$ of non-normal random variables $x_1,...,x_n$. Is it possible to know which distribution the sample variance estimator follows? Details: The distribution of $x_i$'s is not ...
2
votes
1answer
77 views

How to calculate variance of Gaussian given mean and average deviation

I want to calculate the variance sigma of a Gaussian (normal) distribution given its mean mu and average deviation d (i.e. average of absolute value of difference from the mean). How can I do this? ...
2
votes
1answer
53 views

What is the name of the distribution of unbiased sample variance for a sample from Gaussian distribution?

Suppose $X_i$'s are iid Gaussian random variables with mean $\mu$ and variance $\sigma^2$. The distribution of $\sum_i (X_i - \bar{X}_i)^2 / (n-1)$ isn't Chi square. What is its distribution called? ...
7
votes
2answers
324 views

In simple linear regression, where does the formula for the variance of the residuals come from?

According to a text that I'm using, the formula for the variance of the $i^{th}$ residual is given by: $\sigma^2\left ( 1-\frac{1}{n}-\frac{(x_{i}-\overline{x})^2}{S_{xx}} \right )$ I find this hard ...
0
votes
0answers
14 views

Adequacy of forecasted volatility vs realized volatility. GARCH model

Below I have performed forecasting of volatility, in my simple case of 6 days: ...
0
votes
0answers
22 views

How to study the property of a score e.g. its variance in R

I'm trying to develop a score for biomarker discovery in two-class high throughput biological data. At this stage the significance of the score (p-value) is estimated by permutation of the class ...
0
votes
3answers
84 views

Calculating the Variance (Standard Error Estimation)

I am studying the book "An Introduction to Statistical Learning: with Applications in R", on page 66 While the book explains how to calculate $\beta_0$ and $\beta_1$, it skips how the actual ...