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If u 5x=6 and 3y-7v=20 and the correlation coefficient b/w x and y is 0.58 then what would be the correlation coefficient b/w u and v?
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If u 5x=6 and 3y-7v=20 and the correlation coefficient b/w x and y is ...
Solution:
Given:
Calculating Correlation Coefficient between u and v:
Solving Equations:
Multiplying the first equation by 5, we get:
15y - 35v = 20
Adding this equation to the second equation, we get:
15y - 35v + 0 = 20 + 6
15y - 35v = 26
Dividing both sides by 15, we get:
y - (7/3)v = 26/15
Solving for y, we get:
y = (7/3)v + 26/15
Now, we can use the formula for correlation coefficient to find the correlation coefficient between u and v.
The formula for correlation coefficient is:
r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]
where n is the number of data points, Σxy is the sum of the products of x and y, Σx is the sum of x values, Σy is the sum of y values, Σx^2 is the sum of squares of x values, and Σy^2 is the sum of squares of y values.
In our case, we have n = 1, since we only have one pair of values for u and v. We also have:
x = 6/5
y = (7/3)v + 26/15
Σx = 6/5
Σy = (7/3)Σv + 26/15
Σxy = (6/5)(7/3)Σv + (6/5)(26/15)
Σx^2 = (6/5)^2
Σy^2 = ((7/3)Σv + 26/15)^2
Given:
- 5x=6
- 3y-7v=20
- Correlation coefficient between x and y is 0.58
Calculating Correlation Coefficient between u and v:
- From the equation 5x=6, we can find the value of x as x=6/5
- Substituting the value of x in the equation 3y-7v=20, we get 3y-7v=20 becomes 3y-7v=20
- Now, we have two equations: 3y-7v=20 and 5x=6
- Let's solve the equations simultaneously to find the values of y and v
Solving Equations:
- From the equation 5x=6, we get x=6/5
- Substituting the value of x in the equation 3y-7v=20, we get 3y-7v=20 becomes 3y-7v=20/5=4
- Now, we have two equations: 3y-7v=4 and 5x=6
- Let's solve these equations simultaneously to find the values of y and v
Multiplying the first equation by 5, we get:
15y - 35v = 20
Adding this equation to the second equation, we get:
15y - 35v + 0 = 20 + 6
15y - 35v = 26
Dividing both sides by 15, we get:
y - (7/3)v = 26/15
Solving for y, we get:
y = (7/3)v + 26/15
Now, we can use the formula for correlation coefficient to find the correlation coefficient between u and v.
The formula for correlation coefficient is:
r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)]
where n is the number of data points, Σxy is the sum of the products of x and y, Σx is the sum of x values, Σy is the sum of y values, Σx^2 is the sum of squares of x values, and Σy^2 is the sum of squares of y values.
In our case, we have n = 1, since we only have one pair of values for u and v. We also have:
x = 6/5
y = (7/3)v + 26/15
Σx = 6/5
Σy = (7/3)Σv + 26/15
Σxy = (6/5)(7/3)Σv + (6/5)(26/15)
Σx^2 = (6/5)^2
Σy^2 = ((7/3)Σv + 26/15)^2
Community Answer
If u 5x=6 and 3y-7v=20 and the correlation coefficient b/w x and y is ...
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If u 5x=6 and 3y-7v=20 and the correlation coefficient b/w x and y is 0.58 then what would be the correlation coefficient b/w u and v?
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If u 5x=6 and 3y-7v=20 and the correlation coefficient b/w x and y is 0.58 then what would be the correlation coefficient b/w u and v? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If u 5x=6 and 3y-7v=20 and the correlation coefficient b/w x and y is 0.58 then what would be the correlation coefficient b/w u and v? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If u 5x=6 and 3y-7v=20 and the correlation coefficient b/w x and y is 0.58 then what would be the correlation coefficient b/w u and v?.
If u 5x=6 and 3y-7v=20 and the correlation coefficient b/w x and y is 0.58 then what would be the correlation coefficient b/w u and v? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If u 5x=6 and 3y-7v=20 and the correlation coefficient b/w x and y is 0.58 then what would be the correlation coefficient b/w u and v? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If u 5x=6 and 3y-7v=20 and the correlation coefficient b/w x and y is 0.58 then what would be the correlation coefficient b/w u and v?.
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