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If the regression line of y on x and of x and y are given by 2x 3y = -1 and 5x 6y = -1 then the arithmetic means of x and y are given by?
Most Upvoted Answer
If the regression line of y on x and of x and y are given by 2x 3y =...
Solution:
Given regression lines are:
2x + 3y = -1 ...(1)
5x + 6y = -1 ...(2)
We know that the regression line of y on x is given by:
bx + a = ŷ
where b is the slope and a is the intercept.
Similarly, the regression line of x on y is given by:
by + c = x̂
where c is the intercept and b is the slope.
Let's find the slope and intercept of regression line of y on x:
2x + 3y = -1
3y = -2x - 1
y = (-2/3)x - 1/3
So, the slope is -2/3 and the intercept is -1/3.
Now, let's find the slope and intercept of regression line of x on y:
5x + 6y = -1
5x = -6y - 1
x = (-6/5)y - 1/5
So, the slope is -6/5 and the intercept is -1/5.
Arithmetic means of x and y
The arithmetic means of x and y are given by:
x̄ = (Σx)/n
ȳ = (Σy)/n
where Σx is the sum of all the values of x, Σy is the sum of all the values of y, and n is the number of observations.
To find the arithmetic means of x and y, we need to know the values of x and y. However, these values are not given in the question. Therefore, we cannot find the arithmetic means of x and y.
Hence, the answer is "Arithmetic means of x and y cannot be determined from the given information."
Given regression lines are:
2x + 3y = -1 ...(1)
5x + 6y = -1 ...(2)
We know that the regression line of y on x is given by:
bx + a = ŷ
where b is the slope and a is the intercept.
Similarly, the regression line of x on y is given by:
by + c = x̂
where c is the intercept and b is the slope.
Let's find the slope and intercept of regression line of y on x:
2x + 3y = -1
3y = -2x - 1
y = (-2/3)x - 1/3
So, the slope is -2/3 and the intercept is -1/3.
Now, let's find the slope and intercept of regression line of x on y:
5x + 6y = -1
5x = -6y - 1
x = (-6/5)y - 1/5
So, the slope is -6/5 and the intercept is -1/5.
Arithmetic means of x and y
The arithmetic means of x and y are given by:
x̄ = (Σx)/n
ȳ = (Σy)/n
where Σx is the sum of all the values of x, Σy is the sum of all the values of y, and n is the number of observations.
To find the arithmetic means of x and y, we need to know the values of x and y. However, these values are not given in the question. Therefore, we cannot find the arithmetic means of x and y.
Hence, the answer is "Arithmetic means of x and y cannot be determined from the given information."
Community Answer
If the regression line of y on x and of x and y are given by 2x 3y =...
X=1 and y=-1
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If the regression line of y on x and of x and y are given by 2x 3y = -1 and 5x 6y = -1 then the arithmetic means of x and y are given by? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the regression line of y on x and of x and y are given by 2x 3y = -1 and 5x 6y = -1 then the arithmetic means of x and y are given by? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the regression line of y on x and of x and y are given by 2x 3y = -1 and 5x 6y = -1 then the arithmetic means of x and y are given by?.
If the regression line of y on x and of x and y are given by 2x 3y = -1 and 5x 6y = -1 then the arithmetic means of x and y are given by? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the regression line of y on x and of x and y are given by 2x 3y = -1 and 5x 6y = -1 then the arithmetic means of x and y are given by? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the regression line of y on x and of x and y are given by 2x 3y = -1 and 5x 6y = -1 then the arithmetic means of x and y are given by?.
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