Question

An example of a correlation problem ( finding degrees of freedom)

I need an example of any correlation problem , including finding the degrees of freedom. Provide any exsmple of a correlation math problem

Answer 1

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