Correlation Coefficient Online Tutoring

Tutoring is one of the best ways for receiving help in various subjects. Some of the common tools for online tutoring include whiteboard, chat and audio call. There are number of Websites available for online tutoring.(Example: www.tutorvista.com). Correlation is nothing but calculate the strength of the linear relationship between two variables x and y. Correlation will always between -1 and +1. There are two types of correlation. Positive correlation and negative correlation.

Correlation(r) =`[ (NsumXY - (sumX)(sumY)) / sqrt([NsumX^2 - (sumX)^2]xx[NsumY^2 - (sumY)^2])] `

where, N = Number of elements in the set of data. Now, we are going to see some of the problems on correlation coefficient.


Example problem- correlation coefficient online tutoring:

Example problem:

Calculate the correlation coefficient of the following data
x 50 51 52 53 54 55
y 2.1 2.4 2.6 2.8 3 3.3

Solution:

Step 1: First count the number of values.
N = Number of elements in the set of data = 6

Step 2: Next, find XY, X2, Y2
x y X*Y X*X Y*Y
50 2.1 105 2500 4.41
51 2.4 122.4 2601 5.76
52 2.6 135.2 2704 6.76
53 2.8 148.4 2809 7.84
54 3 162 2916 9
55 3.3 181.5 3025 10.89


Step 3: Then, find ΣX, ΣY, ΣXY, ΣX2, ΣY2.
Sum of all values of x = ΣX = 315
Sum of all values of y =  ΣY = 16.2
Sum of all values of xx = ΣXY = 854.5
Sum of square values of x = ΣX2 = 16555
Sum of square values of y =ΣY2 = 44.66

Step 4: Now, Substitute in the above formula given.
Correlation(r) =`[ (NsumXY - (sumX)(sumY)) / sqrt([NsumX^2 - (sumX)^2]xx[NsumY^2 - (sumY)^2])]`


= `((6)xx(854.5)-(315)xx(16.2)) / sqrt([(6)xx(16555)-(315)^2]xx[(6)xx(44.66)-(16.2)^2])`

= `(5127 - 5103) / sqrt([99330 - 99225]xx[267.96 - 262.44])`

= `24 / sqrt(105xx5.52)`

= `24 / sqrt(579.6)`

= `24/24.0749`

= 0.9968

So, the correlation coefficient (r) of the given data= 0.9968.

Practice problem-correlation coefficient online tutoring:

Practice problem:

Calculate Correlation Co-efficient of the following data
x 40 41 42 43 44 45
y 1.1 1.4 1.6 1.8 2 2.3

Answer: Correlation coefficient (r) = 0.9968.