Solution
XYXYX2Y2122143618936483216645105025100714984919681612864256∑X=28∑Y=56∑XY=328∑X2=164∑Y2=656
Now, Correlation coefficient between X and Y is
(r)=∑XY−(∑X)(∑Y)N√∑X2−(∑X)2N√∑Y2−(∑Y)2N
=328−28×566√164−(28)26√656−(56)26
=328−15686√164−7846√656−31366
=328−261.33√164−130.67√655−522.67
=66.675.77×11.55
=66.666.6
=1
As the correlation coefficient between the two variables is +1, so the two variables are perfectly positive correlated.
How is correlation calculated?
The correlation coefficient is determined by dividing the covariance by the product of the two variables' standard deviations. Standard deviation is a measure of the dispersion of data from its average. Covariance is a measure of how two variables change together.
How do you find the correlation between X and Y in R?
Summary.
Use the function cor. test(x,y) to analyze the correlation coefficient between two variables and to get significance level of the correlation..
Three possible correlation methods using the function cor.test(x,y): pearson, kendall, spearman..
How do you find the correlation between X and Y in Excel?
Follow these steps:.
Open Excel. ... .
Install the Analysis Toolpak. ... .
Select “Data” from the top bar menu. ... .
Select “Data Analysis” in the top right-hand corner. ... .
Select Correlation. ... .
Define your data range and output. ... .
Evaluate your correlation coefficient..
How do you find a correlation between two functions?
For the given functions X and X2 with X∼(μ,σ2) being a normal random variable, finding cov(X,X2) is relatively easy, and then the (Pearson) correlation coefficient can be found as ρ=cov(X,X2)√var(X)var(X2).