In: Math
Let x =independent variable =Time spent studying before the exam.
Let y =dependent variable =Marks obtained in the exam.
Let us take a sample of 10 students.
So, the sample size, n =10
Finding correlation coefficient, r:
x: Time spent studying (in hours) | y: Marks obtained (in %) | x2 | y2 | xy |
2 | 30 | 4 | 900 | 60 |
4 | 29 | 16 | 841 | 116 |
5 | 32 | 25 | 1024 | 160 |
9 | 40 | 81 | 1600 | 360 |
14 | 50 | 196 | 2500 | 700 |
18 | 48 | 324 | 2304 | 864 |
22 | 56 | 484 | 3136 | 1232 |
25 | 63 | 625 | 3969 | 1575 |
30 | 70 | 900 | 4900 | 2100 |
34 | 75 | 1156 | 5625 | 2550 |
x =163 | y =493 | x2 =3811 | y2 =26799 | xy =9717 |
Thus, the correlation coefficient, r =0.991
Calculation of degrees of freedom, df:
Degrees of freedom, df =n - 2 =10 - 2 =8