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the coefficient of correlation between x and y series is -0.38.the linear relation between x and u and y and v are 3x+5v=3 and -8y -7u =44 what is the coefficient of correlation between between u and v
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the coefficient of correlation between x and y series is -0.38.the lin...
Solution:
Given, coefficient of correlation between x and y series is -0.38. Also, the linear relation between x and u and y and v are 3x+5v=3 and -8y-7u=44.
To find: Coefficient of correlation between u and v.
Step 1: Solve for x and y from the given equations
3x+5v=3
=> x=(3-5v)/3
-8y-7u=44
=> y=(-7u-44)/8
Step 2: Substitute the values of x and y in the given correlation equation
r_xy = ∑(xi- x̄)(yi- ȳ) / √( ∑(xi- x̄)² ∑(yi- ȳ)² )
where,
r_xy = coefficient of correlation between x and y
xi = value of x
x̄ = mean of x
yi = value of y
ȳ = mean of y
After substitution, we get
-0.38 = ∑[(x-(3-5v)/3)][(y-(-7u-44)/8)] / √[∑(x-(3-5v)/3)² ∑(y-(-7u-44)/8)²]
Step 3: Simplify the equation
-0.38 = ∑[(3-5v)/3-x][(7u+44)/8-y] / √[∑((3-5v)/3-x)² ∑((7u+44)/8-y)²]
Step 4: Find the correlation between u and v
r_uv = ∑(ui- ū)(vi- v̄) / √( ∑(ui- ū)² ∑(vi- v̄)² )
where,
r_uv = coefficient of correlation between u and v
ui = value of u
ū = mean of u
vi = value of v
v̄ = mean of v
We can see that the equation involving u and v is similar to the equation involving x and y. Hence, we can substitute u and v in place of x and y, respectively.
-0.38 = ∑[(3-5v)/3-x][(7u+44)/8-y] / √[∑((3-5v)/3-x)² ∑((7u+44)/8-y)²]
=> -0.38 = ∑[(3-5v)/3-u][(7v+44)/8-v] / √[∑((3-5v)/3-u)² ∑((7v+44)/8-v)²]
Hence, the coefficient of correlation between u and v is also -0.38.
Conclusion:
The coefficient of correlation between u and v is also -0.38. This can be obtained by substituting the values of x and y with the given linear relations between x and u and y and v, and simplifying the equation.
Given, coefficient of correlation between x and y series is -0.38. Also, the linear relation between x and u and y and v are 3x+5v=3 and -8y-7u=44.
To find: Coefficient of correlation between u and v.
Step 1: Solve for x and y from the given equations
3x+5v=3
=> x=(3-5v)/3
-8y-7u=44
=> y=(-7u-44)/8
Step 2: Substitute the values of x and y in the given correlation equation
r_xy = ∑(xi- x̄)(yi- ȳ) / √( ∑(xi- x̄)² ∑(yi- ȳ)² )
where,
r_xy = coefficient of correlation between x and y
xi = value of x
x̄ = mean of x
yi = value of y
ȳ = mean of y
After substitution, we get
-0.38 = ∑[(x-(3-5v)/3)][(y-(-7u-44)/8)] / √[∑(x-(3-5v)/3)² ∑(y-(-7u-44)/8)²]
Step 3: Simplify the equation
-0.38 = ∑[(3-5v)/3-x][(7u+44)/8-y] / √[∑((3-5v)/3-x)² ∑((7u+44)/8-y)²]
Step 4: Find the correlation between u and v
r_uv = ∑(ui- ū)(vi- v̄) / √( ∑(ui- ū)² ∑(vi- v̄)² )
where,
r_uv = coefficient of correlation between u and v
ui = value of u
ū = mean of u
vi = value of v
v̄ = mean of v
We can see that the equation involving u and v is similar to the equation involving x and y. Hence, we can substitute u and v in place of x and y, respectively.
-0.38 = ∑[(3-5v)/3-x][(7u+44)/8-y] / √[∑((3-5v)/3-x)² ∑((7u+44)/8-y)²]
=> -0.38 = ∑[(3-5v)/3-u][(7v+44)/8-v] / √[∑((3-5v)/3-u)² ∑((7v+44)/8-v)²]
Hence, the coefficient of correlation between u and v is also -0.38.
Conclusion:
The coefficient of correlation between u and v is also -0.38. This can be obtained by substituting the values of x and y with the given linear relations between x and u and y and v, and simplifying the equation.
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