A data set has n=10 pairs of X and Y values. This data has SSx=10, SSy= 20 and SP=10. Compute the Pearson correlation and explain
r=sp/√ssx ssy =
10/√10*20=
10/√200
Simplify 200 under radical= 200 as 10^2⋅2. √(〖10〗^2 )×2= 10/10√2 or decimal form 14.14213562
Therefore, 10/10√2is the final answer
To compute the Pearson correlation (r) given SSx (sum of squares of X values), SSy (sum of squares of Y values), and SP (sum of products of X and Y values), you can use the formula r = SP / √(SSx * SSy).
In this case, SSx = 10, SSy = 20, and SP = 10. Plugging these values into the formula, we have:
r = 10 / √(10 * 20)
To simplify the expression under the square root, we can break down 200 as 10^2 * 2:
r = 10 / √(10^2 * 2)
Taking the square root of 10^2 gives us 10, so we have:
r = 10 / (10 * √2)
Simplifying further, we have:
r = 1 / √2
To rationalize the denominator, we multiply both the numerator and denominator by √2:
r = (1 * √2) / (√2 * √2)
Simplifying the expression, we have:
r = √2 / 2
Therefore, the Pearson correlation (r) for this data set is √2 / 2.