Linked Questions

2
votes
2answers
2k views

Does the magnitude of covariance have any real meaning? [duplicate]

I am not able to understand logic behind coming up with this formula for covariance. We know that the sample covariance formula is: $${\rm Cov}(x,y)=\frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{n-1}$$ ...
0
votes
0answers
28 views

The covariance of a gaussian random variable and another one in its variance linear combination [duplicate]

Assume $y$ is a Gaussian random variable with $\text{Var}(y)= \sigma_y^2=\sum_i a_i^2\sigma_i^2$, where $\sigma_i$ corresponds to $x_i$, all $x_i$ are independent. $\mu_y = \sum a_i\mu_i$. I want to ...
0
votes
0answers
12 views

Covariance vs Correlation Definition [duplicate]

I am having a tough time understanding the difference between both terms. Could someone please clear up what both terms mean and in the process of doing so, explain the difference between them?
121
votes
6answers
217k views

How would you explain the difference between correlation and covariance?

Following up on this question, How would you explain covariance to someone who understands only the mean?, which addresses the issue of explaining covariance to a lay person, brought up a similar ...
93
votes
10answers
65k views

Understanding “variance” intuitively

What is the cleanest, easiest way to explain someone the concept of variance? What does it intuitively mean? If one is to explain this to their child how would one go about it? It's a concept that I ...
104
votes
2answers
191k views

What is covariance in plain language?

What is covariance in plain language and how is it linked to the terms dependence, correlation and variance-covariance structure with respect to repeated-measures designs?
54
votes
7answers
63k views

Effect of switching response and explanatory variable in simple linear regression

Let's say that there exists some "true" relationship between $y$ and $x$ such that $y = ax + b + \epsilon$, where $a$ and $b$ are constants and $\epsilon$ is i.i.d normal noise. When I randomly ...
26
votes
7answers
15k views

Why are symmetric positive definite (SPD) matrices so important?

I know the definition of symmetric positive definite (SPD) matrix, but want to understand more. Why are they so important, intuitively? Here is what I know. What else? For a given data, Co-...
22
votes
5answers
10k views

What exactly does a non-parametric test accomplish & What do you do with the results?

I have a feeling this may have been asked elsewhere, but not really with the type of basic description I need. I know non-parametric relies on the median instead of the mean to compare... something. ...
17
votes
4answers
21k views

Prove the equivalence of the following two formulas for Spearman correlation

From wikipedia, Spearman's rank correlation is calculated by converting variables $X_i$ and $Y_i$ into ranked variables $x_i$ and $y_i$, and then calculating Pearson's correlation between the ranked ...
16
votes
2answers
23k views

How does one find the mean of a sum of dependent variables?

I know that the mean of the sum of independent variables is the sum of the means of each independent variable. Does this apply to dependent variables as well?
13
votes
5answers
5k views

Intuition on the definition of the covariance

I was trying to understand the Covariance of two random variables better and understand how the first person that thought of it, arrived at the definition that is routinely used in statistics. I went ...
11
votes
4answers
772 views

Why Are Measures of Dispersion Less Intuitive Than Centrality?

There seems to be something in our human understanding that creates difficulties in grasping intuitively the idea of variance. In a narrow sense the answer is immediate: squaring throws us off from ...
15
votes
1answer
2k views

How to understand the correlation coefficient formula?

Can anyone help me understand the Pearson correlation formula? the sample $r$ = the mean of the products of the standard scores of variables $X$ and $Y$. I kind of understand why they need to ...
7
votes
2answers
2k views

Calculate variance without calculating the mean

Can we calculate the variance without using the mean as the 'base' point?

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