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: $${\rm Cov}(x,y)=\frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{n-1}$$ ...
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 ...
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?
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 ...
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 ...
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?
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 ...
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-...
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. ...
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 ...
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?
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 ...
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 ...
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 ...