calculate the correlation of the data set Round to two decim

calculate the correlation of the data set. Round to two decimal places. (3,2,), (3,3), 6,4) f(x)= ?

Solution

values are (3,2) , ( 3,3) , ( 6,4)..
mean(x) =4..mean(y) =3..cov(x,y) =1..var(x) =2..so, slope = cov(x,y) / var(x) =1 / 2 =0.5..

and intercept =(mean of y) - (slope * mean of x) = 3 - ( 0.5 * 4) = 1...
f(x) = 1 + 0.5*x....
s.d(x) = 1.414214.......s.d(y) = 0.816497.....
correlation = cov(x,y) / ( s,d(x) * s.d(y) ) = 1 / ( 1.414214*0.816497) = 0.866025.... = 0.87(rounded)