# Tagged Questions

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### Summing variance of autocorrelated timeseries

Problem: When trying to calculate the variance of timeseries sums I get a negative variance, mostly due to autocovariances at large lag steps. Does not seem realistic. I have a timeseries which is ...
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### How is covariation and homoscedasticity related?

How is covariation and homoscedasticity related? In my lecture notes for stats class we're told that an assumption pf Pearons correlation coefficient is that covariation must be linear, which I ...
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### Variance of a difference in marginal proportions in a three-way contingency table

Let a multivariate distribution be given by $P(Y,S_1,S_2)$, where all three variables are discrete, $Y$ is multivalued, $S_1=(0,1)$ and $S_2=(0,1)$, respectively, and all may be dependent. Define the ...
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### What is a numerical example of $Var(X_1 + X_2) = Var(X_1) + Var(X_2)$

I need a numerical example to illustrate cases where $Cov(X_1, X_2) = 0$. Can you think of examples involving functions or matrices?
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### Why is Pearson's correlation coefficient defined the way it is?

$$r = \frac{{\rm Cov}(X,Y)}{ \sigma_{X} \sigma_{Y}}$$ I do not understand this equation at all. Where does it come from? From my personal understanding ${\rm Cov}(X,Y)$ comes from that fact that ...
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### How to diagonalize a covariance matrix into Identity matrix

Given a symmetric, positive definite, covariance matrix $S$, how can I calculate a matrix $C$ such that $CSC^T$ is the Identity matrix $I$?
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### Variance and covariance of binary data

The variance of a set of $n$ binary variables $D = <x_1, \ldots, x_n>$ is $${\rm var(D)} = \frac{k(n-k)}{n^2},$$ where $k$ denotes the number of $1$s in $D$ (see ...
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### How to normalize data prior to computation of covariance matrix

In all my self-study, I have come across many different ways in which people seem to normalize their data, prior to the computation of the covariance matrix. I am confused as to what ways are ...
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### How do I create a random variance matrix (x'x)/N with confidence that it will be invertible?

I see some similar threads, but no answer that I know how to apply to this question. I wish to create a variance matrix for a (pseudo)random matrix $X$ with dimensions $K \times N$, where each row $k$ ...
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### Interpretation of Variance and Covariance

I am totally new to statistics and I have to create a variance and covariance analysis. I am using SPSS for this. I have created the covariance table: Hopefully it is the right thing. The first 3 ...