Question

How do you calculate the correlation coefficient?

Answer 1

Correlation(r) = NΣXY - (ΣX)(ΣY) / Sqrt([NΣX2 - (ΣX)2][NΣY2 - (ΣY)2])

Explanation:

Correlation Coefficient Formula :

Correlation(r) = NΣXY - (ΣX)(ΣY) / Sqrt([NΣX2 - (ΣX)2][NΣY2 - (ΣY)2])

Where,

N = Number of Values or Elements
X = First Score
Y = Second Score
ΣXY = Sum of the Product of First and Second Scores
ΣX = Sum of First Scores
ΣY = Sum of Second Scores
ΣX2 = Sum of Square of First Scores
ΣY2 = Sum of Square of Second Scores
https://www.easycalculation.com/statistics/correlation.php

https://www.thoughtco.com/how-to-calculate-the-correlation-coefficient-3126228

Applied to the t-test in Statistics:
https://onlinecourses.science.psu.edu/stat501/node/259/

Setting up the equations for solution in Excel:
http://www.real-statistics.com/regression/hypothesis-testing-significance-regression-line-slope/