Pearson correlation coefficient is a type of correlation coefficient which denotes the relationship between two variables that are measured on the same interval.
SSx = Σ ( X - Mx ) 2 SSy = Σ ( Y - My ) 2 X = X Values Y = Y Values Mx = Mean of x values My = Mean of y values Σ ( X - Mx ) , Σ ( Y - My ) = Sum of deviation scores Σ ( X - Mx )2 , Σ ( Y - My )2 = Sum of deviation squared
Find the pearson correlation coefficient for this data set.
x values | y values |
2 | 3 |
4 | 6 |
6 | 4 |
2 | 2 |
5 | 1 |
Find Mx and My , Mx = [ 2 + 4 + 6 + 2 + 5 ] / 5 Mx = 3.8 My = [ 3 + 6 + 4 + 2 + 1 ] / 5 My = 3.2
Then, find the following values,
( X - Mx ) | ( Y - My ) | ( X - Mx )2 | ( Y - My )2 | ( X - Mx ) * ( Y - My ) |
-1.8 | -0.2 | 3.24 | 0.04 | 0.36 |
0.2 | 2.8 | 0.04 | 7.84 | 0.56 |
2.2 | 0.8 | 4.84 | 0.64 | 1.76 |
-1.8 | -1.2 | 3.24 | 1.44 | 2.16 |
1.2 | -2.2 | 1.44 | 4.84 | -2.64 |
Σ ( X - Mx )=3.6 | Σ ( Y - My )=0 | Σ ( X - Mx ) 2=12.8 | Σ ( Y - My ) 2=14.8 | Σ (X - Mx)*(Y - My)=2.2 |
Substitute the given values in the formula = 2.2 / √ [ 12.8 * 14.8 ] = 2.2 / √189.44 = 2.2 / 13.76372 = 0 . 159 Therefore, the pearson correlation coefficient r = 0 . 16