Correlation Equations

Question 1

Sample Standard Deviation

Answer 1

sqrt(1/n-1 x (sum(x - meanx)^2))

Question 2

Sample Pearson Correlation

Answer 2

1/n-1 x ((sum(x-meanx)(y-meany)) / sx x sy)
where
sx = sample standard deviation of x
sy = sample standard deviation of y

Question 3

Standard Deviation

Answer 3

sqrt((sum(x - meanx)^2)/N)

Question 4

Sample Variance

Answer 4

(sum(x - meanx)^2)/N-1

Question 5

Covariance

Answer 5

E(XY) - (EX)(EY)
1/N x sum(x-meanx)(y-meany)

Question 6

Sample covariance

Answer 6

1/N-1 x sum(x-meanx)(y-meany)

Question 7

Pearson product-moment correlation

Answer 7

cov(X,Y) / (σ_X)(σ_Y)

Question 8

Sample correlation coefficient

Answer 8

sum((x-meanx)(y-meany)) / sqrt(sum((x-meanx)^2) x (sum((y-meany)^2))

Question 9

Empirical Rule

Answer 9

68-95-99.7

Question 10

Confidence level interval

Answer 10

(x - z* x (σ/sqrt(n)), x - z* x (σ/sqrt(n))).