Linked Questions

0
votes
1answer
68 views

Why is correlation formula the way it is? Or Say how it formed? [duplicate]

I am really being confused by why the correlation formula is called the correlation of two variables $X$ and $Y$. Also how is it derived? The part where we divide covariance by product of standard ...
196
votes
10answers
115k views

How would you explain covariance to someone who understands only the mean?

...assuming that I'm able to augment their knowledge about variance in an intuitive fashion ( Understanding "variance" intuitively ) or by saying: It's the average distance of the data ...
91
votes
2answers
165k 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?
48
votes
4answers
5k views

Does correlation = 0.2 mean that there is an association “in only 1 in 5 people”?

In The Idiot Brain: A Neuroscientist Explains What Your Head is Really Up To, Dean Burnett wrote The correlation between height and intelligence is usually cited as being about $0.2$, meaning ...
13
votes
4answers
15k 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 ...
12
votes
3answers
50k views

Do correlation or coefficient of determination relate to the percentage of values that fall along a regression line?

Correlation, $r$, is a measure of linear association between two variables. Coefficient of determination, $r^2$, is a measure of how much of the variability in one variable can be "explained by" ...
16
votes
1answer
7k views

Question on how to normalize regression coefficient

Not sure if normalize is the correct word to use here, but I will try my best to illustrate what I am trying to ask. The estimator used here is least squares. Suppose you have $y=\beta_0+\beta_1x_1$, ...
11
votes
3answers
1k views

Why does the product of the bivariate regression coefficients of the $y$-on-$x$ line and $x$-on-$y$ line equal the square of the correlation?

There's regression model where $Y = a + bX$ with $a = 1.6$ and $b=0.4$, which has a correlation coefficient of $r = 0.60302$. If $X$ and $Y$ are then switched around and the equation becomes $X = c + ...
5
votes
2answers
2k views

Proof of Point-Biserial Correlation being a special case of Pearson Correlation

I have been examining the use of the Point Biserial correlation as a statistic to measure the relationship between a dichotomous variable and a continuous one. Wikipedia et. al. seem to concur that ...
0
votes
1answer
1k views

z-score for two variables

Can we study the relationship between two variables using z score? For example: Let us say that we have two classes A, B and we have 5 students in each class and we know the age and the grade for ...
3
votes
1answer
817 views

correlation coefficient - dot and cross products

I refer to 'Thirteen Ways to Look at the Correlation Coefficient' by Rodgers & Nicewander (1988), specifically to 2 of the 13 ways of looking at the correlation coefficient, namely: No. 6 "...
3
votes
1answer
257 views

Exact meaning of correlation coefficient

What is the exact meaning of the entries of a correlation coefficients matrix? I have spent time researching this, but could find only approximate interpretations which give me no good understanding ...
2
votes
2answers
108 views

How do you calculate the statistical significance of a correlation between $Y$ and $X$?

Can one just fit a linear model between $Y$ and $X$, and then take the p-values of the $t$-test done on the slope (or beta) of the linear model? Since presumably correlation would be in the same ...
0
votes
0answers
52 views

Formulas for correlation coefficient

I'm taking an online stats class. Currently we are on the topic of a correlation coefficient. Several formulas for $r$ were given in the reading material. The formulas are below. Unfortunately it was ...