# Tagged Questions

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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### Standard deviation of sample mean - unknown equation answered

Does anyone recognize mathematically or statistically what this formula's purpose is. If it is not statistically useful what does dividing a value by a constant and taking a square root mean? For ...
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### Variance of a distribution of multi-level categorical data

I am currently analyzing large data sets with various characteristics (such as city). I wanted to find a measure which would essentially say how much or how little of a variance there was across the ...
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### Unbiased weighted variance with reliability/importance weights

I need to provide a reference for the use of a modified version of the formula in wikipedia for the unbiased weighted variance with reliability (aka. importance or non-random) weights: https://en....
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### Intuition (geometric or other) for $Var(X+Y) = Var(X)+Var(Y) + 2 \ Cov(X, Y)$

Is there any way to make sense out of this formula intuitively? I rederived it algebraically (took me a while...), which made me happy because I used to be incapable of doing that kind of stuff, but ...
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### estimating variance using only data at the tails without resorting to Gibbs sampling

Suppose we know that the population size is $n=1,000$ but for whatever reason, we only have the bottom $n_1=100$ observations and the top $n_2 = 200$ observations. Furthermore, suppose we know the ...
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### Expected value of a semi-partial correlation

Say I have 4 random variables. $X^{(1)}$ and $X^{(2)}$ are jointly multivariate normal with mean 0 and covariance $\Sigma_X$, and $Y^{(1)}$ and $Y^{(2)}$ are jointly multivariate normal with mean 0 ...
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### Why do loadings of princomp in R report identical proportion of variance for all principal components? [duplicate]

I'm trying to run a few tests using princomp in R. In princomp there is a value called <...
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### Variance of error $Y* = y_i/c_i$

If I have this model: $Y_i = B_1 + B_2logx_i + 2e_i$ $e_i$ ~ $N(0, σ^2)$ how to solve this $Y* = y_i/c_i$ --------> if : $V(Y*) = σ^2$ ? the constant is $c_i = 1/2$?
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### Is there easiest way to derive variance of continuation-ratio logit estimator?

I wanted to calculate the variance of continuation-ratio logit estimator that defined as $\hat{\theta}^+_j=\ln\frac{\pi_j}{\sum_{k=1}^{j-1}\pi_k}$, for $j=2,...,C$, where $C$ is number of categories. ...
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### Variance of stationary VAR process

Suppose we are given stationary VAR(p) process. How to estimate variance of its components: $y_{1t}, y_{2t}...y_{mt}$? Will be very grateful for help!
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### How do i use PCA? [duplicate]

I am not sure i understood the concept of PCA that well. I know it is used to reduce the dimensionality by the help of the eigenvector and eigenvalues of the covariance matrix, and thereby compute ...
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### How can I quantify the multivariate variances of several characters in different groups?

I have a multivariate dataset of linear measurements. Where I measured several characters (e.g. skull length, skull width, skull height, ...) for several different species. My questions is, if the ...
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### Help Beginner Q: Explanation on pooled variance and when it is used

If I am conducting a difference in means hypothesis test, when do we use the pooled variance and why? Lets say the population variance was unknown for two samples, the sample sizes for the two means ...
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### Is this controversial that in PCA, we want the variance as large as possible, while in bayesian, a large variance means a low precision?

I am wondering about the variance. We say the variance is inverse proportional to precision, then we also say the variance is proportional to the information, which means that a large variance means ...
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### Why is my kalman filter trusting so much my observations?

This question follows the one asked there. I am trying to filter an equity index (Stoxx 600) time series using kalman filter. I'm using the R package dlm and my code is inspired from the dlm ...
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### Higher variance in sample mean or sample median? [duplicate]

The variance of the sample median depends on the distribution you are sampling from. This is also true for the variance of the mean. But can one say that the variance of the sample mean is always ...