All Questions
6 questions
4
votes
2
answers
521
views
Why do we use $R^2$ instead of $R$ in linear regression?
$R^2$ equals the "amount of variance explained by the model".
However, we rarely use variance in descriptive statistics. We say a sample's weight is 78 ± 13 kg, which is $\bar x$ ± $\sigma$ (...
- 51
0
votes
0
answers
55
views
Variance of the sum of N correlated random variables with equal variance [duplicate]
According to this Wikipedia article,
In general, the variance of the sum of $n$ variables is the sum of their covariances.
So if the variables have equal variance ${\sigma}^2$ and the average ...
- 101
1
vote
0
answers
76
views
If the coefficient of determination is a measure based on variance, then what about standard deviation instead?
Background: I've been teaching a very simple course of introductory Statistics for a few years now and we cover linear correlation and the Correlation Coefficient ($r$). I want to introduce the ...
2
votes
0
answers
1k
views
Correlation coefficient with standard deviation
I quite often find myself testing hypotheses in which the standard deviation of one (Normally distributed) variable is linked to (the mean of) another variable. I would like to be able to express the ...
- 7,752
6
votes
1
answer
3k
views
Why would we ever use Covariance over Correlation and Variance over Standard Deviation?
I am unable to understand the practical use of Covariance and Variance.
In my understanding, Covariance and Correlation are both measures of how one variable changes with respect to another. The only ...
- 163
8
votes
3
answers
13k
views
Covariance greater than Variance?
It is straightforward to verify that for two random variables $X$ and $Y$ with variances $\sigma^2_X \neq \sigma^2_Y$, we have that
$$\Big|{\rm Cov}(X, Y)\Big| \leq \max\{\sigma^2_X,\, \sigma^2_Y\}$$
...