Answer:
-0.00348
Step-by-step explanation:
x y xy [tex]x^2[/tex] [tex]y^2[/tex]
0 8 0 0 64
1 7.5 7.5 1 56.25
2 6 12 4 36
2 5.5 11 4 30.25
3 5.5 16.5 9 30.25
3 4 12 9 16
4 3 12 16 9
5 3 15 25 9
6 2.5 15 36 6.25
Now [tex]\sum x=0+1+2+2+3+3+4+5+6=26[/tex]
[tex]\sum y=8+7.5+6+5.5+5.5+4+3+3+2.5=45[/tex]
[tex]\sum (xy)=0+7.5+12+11+16.5+12+12+15+15=101[/tex]
[tex]\sum x^2=0+1+4+4+9+9+16+25+36=104[/tex]
[tex]\sum y^2=64+56.25+36+30.25+30.25+16+9+9+6.25=257[/tex]
N = number of pairs of scores = 9
Formula :[tex]r =\frac{N\sum(xy)-\sum x \sum y}{(N \sum x^2 -(\sum x)^2)(N \sum y^2 -(\sum y)^2)}[/tex]
Substitute the values.
[tex]r =\frac{9(101)-(26 \times 45)}{(9 (104) -(26)^2)(9(257) -(45)^2)}[/tex]
[tex]r =-0.00348[/tex]
Hence the correlation coefficient is -0.00348
The value of Correlation coefficient is -0.00348.
A correlation coefficient denotes the strength of the relation between two variables of a function.
The formula for correlation coefficient is
[tex]\rm r = \dfrac{ N \sum (xy) - \sum x \sum y}{(N \sum x^2- (\sum x)^2)(N\sum y^2 - (\sum y)^2}[/tex]
The data is
x y
0 8
1 7.5
2 6
2 5.5
3 5.5
3 4
4 3
5 3
6 2.5
the value of ∑x = 26
∑y = 45
∑(xy) = 101
∑x² = 104
∑y² = 257
N = Total frequency = 9
The value of r is obtained by substitution of value in the equation.
r = -0.00348
To know more about Correlation Coefficient
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