Respuesta :
Answer:
a) -0.717
b) -0.835
Step-by-step explanation:
The correlation coefficient r can be computed as
[tex]r=\frac{nsumxy-(sumx)(sumy)}{\sqrt{[nsumx^2-(sumx)^2][nsumy^2-(sumy)^2]} }[/tex]
a)
x y x² y² xy
0.0 28.0 0.00 784.00 0.00
0.0 68.8 0.00 4733.44 0.00
0.2 26.8 0.04 718.24 5.36
0.5 38.3 0.25 1466.89 19.15
0.5 48.2 0.25 2323.24 24.10
1.0 30.9 1.00 954.81 30.90
1.2 26.7 1.44 712.89 32.04
1.9 8.0 3.61 64.00 15.20
2.6 4.4 6.76 19.36 11.44
3.3 7.2 10.89 51.84 23.76
4.7 6.8 22.09 46.24 31.96
6.5 6.6 42.25 43.56 42.90
sumx= 22.4
sumy= 300.7
sumx²= 88.58
sumy²= 11918.5
sumxy= 236.81
[tex]r=\frac{(12)(236.81)-(22.4)(300.7)}{\sqrt{[(12)(88.58)-(22.4)^2][(12)(11918.5)-(300.7)^2]} }[/tex]
[tex]r=\frac{-3893.96}{5433.2281}[/tex]
[tex]r=-0.7167[/tex]
r= -0.717
So, the required correlation coefficient is -0.717.
b)
Firstly we take the square root of x and y values and then following calculations are made.
x y x² y² x*y
0.00000 5.29150 0.0 28.0 0.00000
0.00000 8.29458 0.0 68.8 0.00000
0.44721 5.17687 0.2 26.8 2.31517
0.70711 6.18870 0.5 38.3 4.37607
0.70711 6.94262 0.5 48.2 4.90918
1.00000 5.55878 1.0 30.9 5.55878
1.09545 5.16720 1.2 26.7 5.66039
1.37840 2.82843 1.9 8.0 3.89872
1.61245 2.09762 2.6 4.4 3.38231
1.81659 2.68328 3.3 7.2 4.87442
2.16795 2.60768 4.7 6.8 5.65332
2.54951 2.56905 6.5 6.6 6.54981
sumx= 13.4818
sumy= 55.4063
sumx²= 22.4
sumy²= 300.7
sumxy= 47.1782
[tex]r=\frac{(12)(47.1782)-(13.4818)(55.4063)}{\sqrt{[(12)(22.4)-(13.4818)^2][(12)(300.7)-(55.4063)^2]} }[/tex]
[tex]r=\frac{-180.8383}{216.507}[/tex]
[tex]r=-0.8353[/tex]
So, the required correlation coefficient is -0.8353.
