Linked Questions

1
vote
0answers
60 views

Understanding “we lose degrees of freedom in product deviations”? [duplicate]

I'm having a tricky time understanding the statement: we lose $n−1$ [degrees of freedom] by computing the product deviations [in $cov(x,y)$] I'm not necessarily looking for an overview of ...
4
votes
0answers
56 views

Sample Covariance [duplicate]

The sample covariance is defined as $\hat{\sigma}_{xy}:=\frac1{n-1} \sum_{i=1}^n (x_i -\bar{x})(y_i-\bar{y})$. What is the intuition for using the correction term $n-1$ instead of $n-2$. Because we ...
2
votes
0answers
36 views

Degrees of freedom in covariance calculation [duplicate]

When calculating the sample covariance, why do we divide by $n-1$ instead of $n-2$? Don't we lose two degrees of freedom since we need to calculate two sample means? For example, when estimating the ...
2
votes
0answers
27 views

Why does computing product derivations eliminate degrees of freedom? [duplicate]

I'm trying to get an intuition as to why degrees of freedom is n - 1 when calculating sample covariance. This is what I found: 1) Start with 2n degrees of freedom from the bivariate data 2) Lose 2 ...
0
votes
0answers
15 views

Sample covariance vs population variance of means [duplicate]

Was looking at this link and wondering why for population covariance, the denominator is n, while for sample covariance, denominator is n-1. How does this 1/n(n-1) replace the 1/n^2 in the proof in ...
4
votes
2answers
4k views

Covariance of two sample means

I am trying to derive the covariance of two sample means and get confused at one point. Given is a sample of size $n$ with paired dependent observations $x_i$ and $y_i$ as realizations of RVs $X$ and $...
6
votes
2answers
3k views

Variance and covariance in the context of deterministic variables

Questions: Can we talk about: variance of a deterministic variable?; covariance between a deterministic variable and a stochastic variable?; covariance between two deterministic variables? Are these ...
8
votes
1answer
4k views

Efficient way to compute distances between centroids from distance matrix

Let us have square symmetric matrix of squared euclidean distances $\bf D$ between $n$ points and vector lengthed $n$ indicating cluster or group membership ($k$ clusters) of the points; a cluster may ...
5
votes
2answers
686 views

Why is Covariance Useful?

There are a number of topics related to covariance on this site. What I am having trouble grasping: why is covariance a useful thing to calculate? As far as I see it, covariance is not a helpful ...
1
vote
2answers
653 views

When are OLS linear regression parameters inaccurate?

Q1: Show quantitatively that OLS regression can be applied inconsistently for linear parameters estimation. We show an example of linear OLS inaccuracy from inappropriate application to bivariate ...
5
votes
2answers
3k views

Variance of the sum of random vectors

Let $X_1, X_2, \dots , X_n \sim G$ where $G$ is some distribution and the samples are not independent. If $X_i \in \mathbb{R}$, then I know that $$\text{Var}\left(\sum_{i=1}^{n} X_i \right) = n\text{...
2
votes
1answer
559 views

Uncorrected sample standard deviation in correlation coefficient

There seems to be a common use of the uncorrected sample standard deviation in calculating the correlation coefficient: http://www.experts-exchange.com/articles/2728/Covariance-and-Correlation-in-MS-...
0
votes
1answer
493 views

formula for sample covariance: Bessel's correction

Two options for the sample covariance between X and Y: 1)(with Bessel's) COV(X,Y) = $1/(n-1)$ * $\Sigma$ $(Xi - mean(X))$*$(Yi - mean(Y))$ 2)(without) COV(X,Y) = $1/n$ * $\Sigma$ $(Xi - mean(X))$*$(...
3
votes
1answer
367 views

Dividing by degrees of freedom [duplicate]

When estimating parameters such as (I don't care about this specific instance particularly) Variance of a random variable X, one usually adopts Bessel's correction, i.e. using the formula $\hat{Var}{(...
1
vote
2answers
229 views

Standard Deviation is to variance as ____ is to covariance?

I'm looking at the bivariate relationships among a set of time-series data that have the same units. I have computed the covariance matrix and am working on interpreting it. My hunch is that it would ...

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