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

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42 views

What's the difference between the variance the mean squared error?

I'm surprised this hasn't been asked before, but I cannot find the question on stats.stackexchange. This is the formula to calculate the variance of a normally distributed sample: $\frac{\sum(X - ...
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0answers
15 views

Power spectrum of unlogged AR(1) process

Our variable of interest $X$ is nonnegative. We model $ \log(X) $ as AR(1) process. $ \log(X) $ power spectrum: $ S_{xx}(w) = \frac{\sigma^2}{1-\varphi^2} \frac{\gamma}{\omega^2 + \gamma^2} $ What ...
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0answers
6 views

Reference for explained variance situation

I have a data set with 5 parameters and 1 output. I am working on a regression problem and I've build different models by first using 1 input parameters, then 2, then 3, ..., untill the model uses 5 ...
-1
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1answer
29 views

Binomial distribution [on hold]

folks! The problems is Suppose you can make free throws at a 70% rate. Let X be the number of free throws you make in 20 tries. Model this with a binomial distribution: 1)?= E[X] 2)?=Var[X] ...
-1
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1answer
44 views

How to find the distribution of a function? [on hold]

How would one go about solving the following question: Assuming that $X \sim \mathcal{N} (μ,σ^2)$, find the distribution of $\sqrt{n}(\hat{\mu} - \mu)/σ$
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2answers
47 views

The meaning of scale and location in the Pearson correlation context

According to wikipedia, pearson correlation is scale and location invariant. Does scale refer to "variance" and location refer to "mean" ? Thanks.
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1answer
55 views

Generating data from Probit regression, cut off 0 and variance 1 necessary?

I am trying to create a dataset using a Probit regression model in R, where I have an intercept and three covariates. I first fix a set of coefficients for the three covariates, generate these ...
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0answers
9 views

Is there a need for estimamting noise variance if it is an iid? [closed]

it looks like noise variance does not need to be estimated if the noise is an iid, but on the other hand variance is constant if it is an iid? is white noise an iid? Please clarify.
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1answer
20 views

Relationships of two regressional coefficients

I have two one dimensional dataset $X$ and $Y$. I run regression and obtained $A$ from $Y = AX$. And another regression and obtain $B$ from $X = BY$. What's the relationship between $A$ and $B$? Is ...
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0answers
32 views

Why is normality assumption so important (even for large N) for Chi-square test for the Variance

In my textbook i found the note that for a Chi-square test ($\chi = \frac{(n-1) \cdot s'^2}{\sigma^2}$) the assumption of a normal distribution in the population is very important - and much more ...
3
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1answer
64 views

One sample test of uniformity in R

I have a dataset of two columns: one with IDs and one with a column of single digits (0-9) (see below). I would like a statistical significance test for whether the data is uniform. Ideally, I would ...
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0answers
13 views

variance of data of correlated poisson means?

I want to find the mean and standard deviation for the data for the following question. We have 10 houses of known different sizes. The number of people living per square meter has a poisson ...
2
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1answer
28 views

Why is the variance of a moving average process calculated this way?

I have a moving average process that looks like: $$ Y_{t}=\frac{e_{t}+e_{t-1}}{2} $$ And I can see that the variance has been calculated as follows: $$ {Var}\left ( Y_{t} \right )={Var}\left \{ ...
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0answers
39 views

Wrong variance of mean

I'm told that the $Var(\overline{x}) \approx Var(X)/N$, where $\overline{x}$ is the mean of $N$ elements from $X$. However, I have a data set where these variances seem to differ by a factor of about ...
0
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1answer
22 views

Variance of the beta coefficient in linear regression

I have a linear regression equation: $y=bx + a$. Also standard error of the slope $b$ estimate is given and the sample size. Is it possible with this information to infer the variance of $b$?
0
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1answer
37 views

standard deviation VS variance

Problem statment: What is the different between standard deviation and variance? What context should it be used for both of them?
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0answers
13 views

leave-one-out error estimate variance

What would be the lower bound for the variance of the leave-one-out error estimate? Not necesary has to hold for all distribution. Any example would be nice. Also the classifier for the example could ...
0
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0answers
21 views

GLM over two groups with unequal variance in the dependent variable

I have a dataset of patients and controls and would like to model the group specific effect of a certain predictor PRED (brain imaging, marker of structural connectivity) onto one behavioral measure, ...
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0answers
17 views

R limma voom function trend in mean-variancerelationship

I am new to the Limma package and when using voom I get this. I am really not sure what it means. I wonder if anyone here have seen something like this before, or ...
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0answers
6 views

Variance decomposition of fixed factors and stochsticity

I am running a model sensitivity analysis of a model that yield results based on several (fixed) input parameters and some randomness (stochasticity). So in order to get the sensitivity of the model's ...
0
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1answer
17 views

Accounting For Increase In Volume

I'm not very good at statistics but today at work we were in a meeting where manager stood at the top of the room and told us our quality performance in manufacturing our goods had dropped but our ...
0
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1answer
22 views

Variance calculation RELU function (deep learning)

weight initialization is important for modern deep learning. To understand [1,2], I would like to understand the following: $$ E[x^2] = 0.5 Var[y], $$ where $x= max(0,y)$, $E[.]$ is the expectation, ...
3
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0answers
24 views

Comparing variation of two datasets of dimensionless quantities

I have a biological dataset in which we measured two dimensionless quantities $x$ and $y$. Let $X = \{x_1,\dots,x_N\}$ and $Y = \{y_1,\dots, y_N\}$ be the vectors holding this data. I want to argue ...
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0answers
12 views

Description of how the variance in `Y` changes with the discrete variable `X`?

Let Y be a continuous response variable and X be a discrete explanatory variable. I am interested in developing a statistical ...
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0answers
19 views

Bias-variance trade-off regarding K-Fold Cross-Validation

In the book An Introduction to Statistical Learning (4th Edition), while discussing bias-variance trade-off in the context of k-fold cross-validation vs. ...
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0answers
32 views

How would you solve for var of Y-bar given a set of Xi iid random var and a single Y random var?

Say I have $X_1, ..., X_n$ iid RV, each has variance $\sigma^2$. Say I have a $Y_k=X_k - X_{k-1}$ for $k = 1$ to $n$ and that the sample $Y$ ($\bar{Y}$) is equal to the the summation from $k$ to $n$ ...
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0answers
28 views

Estimating variance of a function of multiple random variables?

What are some strategies for estimating the variance of a statistic that is an arbitrary function of multiple random variables? I am familiar with the Delta method which uses asymptotics to estimate ...
1
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1answer
48 views

Covariance of product

A question has been asked regarding the Variance of product of dependent variables. I am interested in the case in which $X$ is a vector and $Y$ is a scalar and the two variables are independent. ...
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0answers
17 views

What is the variance of the sample mean $\bar{x}$

Let $X_1, X_2, ... , X_n$ be a random sample of size $n$ from a distribution (population) with mean $μ$ and variance $σ^2$. What is the variance of sample mean $\bar{x}$? I know that var($\bar{x}$) = ...
1
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1answer
31 views

Understanding proportion of variance in PCA

One of my exam question was as follows: Assume the covariance matrix of your dataset $X $ is $\Sigma$ and while doing Principal Component Analysis, you found $\Sigma = CDC^T $. Here $D $ is the ...
0
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0answers
12 views

(Pretty) large sample size, unequal variance, unequal sample sizes, non-normal distribution. T-test alternative?

So, I've never had all these problems at the same time before, but I have: - Likert data, from a 9 point scale - n = 317 v 177 respectively - SD = 2.08 v. .274; 1.9 v. 2.6; 2.5 v. 2.9 etc. (you get ...
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0answers
27 views

Comparing R2 between Different Samples

Good Evening All, I'm looking to directly compare the variance explained by the same regression model (same IVs, DV) between two different samples. The way I'm conceptualizing it is like Fisher's ...
0
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1answer
19 views

What is the estimated variance of residuals? From R [duplicate]

I am trying to figure out what is the estimated variance (i.e. the estimated "error") of residuals around a fitted line. ...
0
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1answer
22 views

Breusch-Pagan Test using R [duplicate]

I'm currently working on the Breusch-Pagan Test using RStudio through the command ncvTest. I've used the dataset pipeline.txt in ...
1
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1answer
105 views

2 discrete distributions with equal mean and variance

I need to compute 2 discrete distributions with equal mean and variance. One should be a distribution taking values x and y and the other one taking values z, 0, and y. The probabilities should take ...
2
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1answer
19 views

Jitter/Variation in normal distribution

I am studying frame delay variation (FDV) in packet networks. I will explain what that is (or what I interpret it to be) in more detail in a second. I'm assuming the time difference between two ...
6
votes
1answer
95 views

How to get the variance of the residual variance in a simple linear regression model

How do you get the variance of the residual variance in a simple linear regression model? In a book I see that ${\rm Var}(S_R^2)=\frac{2\sigma^4}{n-2}$, where $S_R^2=\sum\frac{e_i^2}{n-2}$ and ...
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0answers
28 views

Generate discrete distributions with same mean and variance

I have a question concerning mean-variance analysis. I need to compute 2 discrete distributions with equal mean and variance. One should be a distribution taking values x and y and the other one ...
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0answers
13 views

Variance reduction in repeated measures multilevel model

I'm building a multilevel model where I have repeated measures of students' performance and some predictors (sex, age, studyhours, etc..). Sex does not vary with time, hours of study do vary. My ...
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0answers
37 views

LMM: How do I calculate a standard deviation on the variance explained by fixed effects?

So, building a LMM with the lmer function in lme4, you get the variance explained by the variance component. ...
1
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1answer
90 views

Show that $E[\mu_i^2|X_i]=\sigma^2$ and $Var(\mu_i|X_i)=\sigma^2$

I'm a little stuck on this review problem so help would be greatly appreciated! Q: We have the regression model $Y_i=\beta_0+\beta_1X_i+\mu_i$ and we assume that the expected errors are $0$. We also ...
0
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0answers
24 views

Comparing the Magnitude of the Difference in Variances Between Groups to Identify Selection Bias

I'm comparing two populations--private and public sector accounting firms in the state of Rhode Island--for differences in the distribution of quality/ability of the accountants who work at those ...
0
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0answers
46 views

What is variance of an election poll?

I was working through Harvard data science course: I came across this question: Assume you have $M$ polls with sample sizes $n_1,\ldots,n_M$. If the polls are independent, what is the average of the ...
1
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1answer
28 views

Forecasting Skew & Kurtosis

I have seen several models for estimating the expected value and variance of a distribution. I am curious, to learn if anyone has looked at models that extend beyond these first two moments ...
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0answers
21 views

Order Statistic Moments, INID Gaussian, Equal Variance, Unequal Means

I've been playing with this for a couple hours now and would like to figure it out if there is a well known solution. I want to calculate the mean of the order statistical distribution of N INID ...
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0answers
98 views

Explained variation ($R^2$) from MCMC glmm - Nakagawa & Schielzeth 2013

This is a follow up to a question I asked previously, where I suggested that variance-covariance matrices could be used to derive correlations, which are then usable as estimates of how much each ...
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1answer
56 views

Algebraic manipulation of $Var(Y|X)=E[(Y-E(Y|X))^2|X]$

Q: Show that $Var(Y|X)=E[(Y-E(Y|X))^2|X]$ is equal to $Var(Y|X)=E[Y^2|X]-(E[Y|X)]^2$. Answer: I know I have to use the law of iterated expectation to get to the second statement but I am having ...
1
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1answer
22 views

Randomized Block ANOVA Model: Intermediate Steps

While reading through my lecture notes, I came across a randomized block ANOVA model and some assumptions. How did the authors get to these assumptions (Expectation and Variance) from the given model? ...
2
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2answers
68 views

Mean Preserving PDF Spreading

I have a histogram representing the PDF of an unknown discrete RV. The histogram is asymmetrical. To be clear, all I have is the histogram. Is there a known way to increase/decrease the variance of ...
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3answers
123 views

Covariance greater than Variance?

It is straightforward to verify that for two random variables $X$ and $Y$ with variances $\sigma^2_X \neq \sigma^2_Y$, we have that $$\Big|{\rm Cov}(X, Y)\Big| \leq \max\{\sigma^2_X,\, \sigma^2_Y\}$$ ...