Question

Using the data below, calculate the correlation of these samples. Round your answer to 1 decimal place.

seed_mass	seedling_height
2.06	7.91
5.06	7.22
2.2	7.29
5.91	8.91
5.6	6.93
4.54	6.62
6.6	8.47
4.79	2.87
6.15	9.18
5	6.14
5.77	6.34
4.33	2.22
5.38	7.7
4.25	2.77
5.41	8.29
5.01	7.66
6.26	6.73
5.07	6.26
5.5	2.89
5.23	7.14
4.24	2.48
5.89	8.36
5.32	6.26
5.56	6.04
4.95	6.97

Answer 1

seed_Height(y_i)   
7.91
7.22
7.29
8.91
6.93
6.62
8.47
2.87
9.18
6.14
6.34
2.22
7.70
2.77
8.29
7.66
6.73
6.26
2.89
7.14
2.48
8.36
6.26
6.04
6.97

seed_mass(x_i)
2.06
5.06
2.20
5.91
5.60
4.54
6.60
4.79
6.15
5.00
5.77
4.33
5.38
4.25
5.41
5.01
6.26
5.07
5.50
5.23
4.24
5.89
5.32
5.56
4.95

we have calculated the value of x_i*y_i, for all i=1,2,3,............,24,25 as follows

x_i*y_i
16.2946
36.5332
16.0380
52.6581
38.8080
30.0548
55.9020
13.7473
56.4570
30.7000
36.5818
9.6126
41.4260
11.7725
44.8489
38.3766
42.1298
31.7382
15.8950
37.3422
10.5152
49.2404
33.3032
33.5824
34.5015

now the formula of correlation coefficient is

where,

here n=25

Hence covariance(x_i,y_i)=0.53802

var(x_i)=1.140306

var(y_i)= 4.378825

So,

and the scatter plot is ,

from the above value of coorelation =0.2407725 and the scatter plotit is clear that the Seed mass and seedimg height are positively correlated that is if value of one increases, the value of other also increases and vice versa.