2
votes
2answers
518 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: $${\rm Cov}(x,y)=\frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{n-1}$$ ...
97
votes
6answers
194k 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 ...
72
votes
9answers
53k 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 ...
82
votes
2answers
146k 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?
38
votes
4answers
31k 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 ...
22
votes
5answers
8k 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. ...
18
votes
8answers
4k 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-...
12
votes
4answers
12k 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 ...
7
votes
2answers
11k 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?
10
votes
5answers
4k 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
533 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 ...
14
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 ...
11
votes
4answers
2k views

How to conceptualize error in a regression model?

I am attending a data analysis class and some of my well-rooted ideas are being shaken. Namely, the idea that the error (epsilon), as well as any other sort of variance, applies only (so I thought) to ...
18
votes
1answer
3k views

Link between variance and pairwise distances within a variable

Please, prove that if we have two variables (equal sample size) $X$ and $Y$ and the variance in $X$ is greater than in $Y$, then the sum of squared differences (i.e., squared Euclidean distances) ...
5
votes
2answers
744 views

Pearson correlation between a variable and its square

Here is my R code to get familiarised with Pearson's correlation. I generate values of $X$ from 1 to 100, then find the correlation between $X$ and $X^2$: ...

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