Given the set of numbers Y = 5,15,12,6,30,6,10 and X = 10,5,8,20,2,24,8 the equation of a simple linear regression model becomes: Y = -0.77461X +20.52073.
When X is equal to 15, the equation predicts a Y value of 8.90158.
Next, to calculate the Pearson Correlation Coefficient, we use the equation r = (sum(x-xbar)(y-ybar))/(root(sum(x-xbar)^2 sum(y-ybar)^2)).
Next, inserting values, the equation becomes r = (-299)/(root((386)(458))) = -299/420.4617,
Therefore, Pearson's Correlation Coefficient is -0.71112
Finally, to calculate Spearman's Correlation, we use the following equation: p = 1 - [((6(sum(d^2))/(n(n^2-1))]
To use the equation we first rank the data, calculate the difference in rank as well as the squared difference in rank. The sample size, n, is 7 and the sum of the square of rank differences is 94
Solving p = 1 - ((6)(94))/(7(7^2-1) = 1 - (564)/(336) = 1 - 1.678571 = -0.67857
Therefore, Spearman's Correlation is -0.67857