calculateorigion corelation cofeciant betwen x and y

Question

x=5,10,15,20,25,30,35 y=100,180,360,350,500,2240,600

Answer 1

To do this manually we need a table:

X	Y	XY	X2	Y2
5	100	500	25	10000
10	180	1800	100	32400
15	360	5400	225	129600
20	350	7000	400	122500
25	500	12500	625	250000
30	2240	67200	900	5017600
35	600	21000	1225	360000
140	4330	115400	3500	5922100

The correlation coefficient is given by:

r=(n∑XY-∑X∑Y)/√([(n∑X²-(∑X)²][(n∑Y²-(∑Y)²]). n=7, the number of data pairs.

The summations are in the last row of the table:

r=(7×115400-140×4330)/√([(7×3500-140²][7×5922100-4330²]),

r=201600/√(4900×22705800)=0.6044 approx.

This is a rather weak correlation, probably caused by the outlier (X,Y)=(30,2240). Without this outlier r=0.974.