Answer to Question #153927 in Statistics and Probability for sathish

Question

Ten students obtained the following percentage of marks in the college internal test (x) and in the final university examination (y). Find the correlation coefficient between the marks of the two test. x 51 63 63 49 50 60 65 63 46 50 y 49 72 75 50 48 60 70 48 60 56

Answer 1

x y x2 y2 xy

51 49 2601 2401 2499

63 72 3969 5184 4536

63 75 3969 5625 4725

49 50 2401 2500 2450

50 48 2500 2304 2400

60 60 3600 3600 3600

65 70 4225 4900 4550

63 48 3969 2304 3024

46 60 2116 3600 2760

50 56 2500 3136 2800

560 588 31850 35554 33344

r$=\frac{n(∑xy)−(∑x∑y)​}{\sqrt{ [n∑x^2−(∑x)^2][n∑y^2−(∑y)^2]}}$

=$\frac{(10*33344)-560*588}{\sqrt{ [10*31850-560^2] [10*35554-588^2]}}$

r=0.6004