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If mean of X and Y variables is 20 and 40 respectively and the regression coefficient Y on X is 1.608 then the regression line of Y on X is :?
Most Upvoted Answer
If mean of X and Y variables is 20 and 40 respectively and the regress...
Solution:
Given data:
- Mean of X variable = 20
- Mean of Y variable = 40
- Regression coefficient of Y on X = 1.608
To find:
- Regression line of Y on X
Regression equation:
- The regression equation of Y on X is given as:
Y = a + bX
- Where a is the intercept and b is the slope of the regression line.
- The slope b can be calculated as:
b = r(Sy/Sx)
Where r is the correlation coefficient between X and Y variables, Sy is the standard deviation of Y variable, and Sx is the standard deviation of X variable.
- The intercept a can be calculated as:
a = Y - bX
Where Y is the mean of Y variable and X is the mean of X variable.
Calculation:
- Given: Mean of X variable = 20, Mean of Y variable = 40, Regression coefficient of Y on X = 1.608
- Let us assume that the standard deviation of X variable is 1.
- Then, the standard deviation of Y variable can be calculated as:
Sy = (r)(Sx)(Sy/Sx) = (r)(1)(Sy)
Sy = (1.608)(Sy)
Sy = Sy(1.608)
1 = 1.608
This is not possible, as the value of r cannot be greater than 1.
- Therefore, let us assume that the standard deviation of Y variable is 1.
- Then, the standard deviation of X variable can be calculated as:
Sx = (r)(Sy)(Sx/Sy) = (r)(Sx)(1)
Sx = (1.608)(Sx)
Sx = Sx(1.608)
1 = 1.608
This is not possible, as the value of r cannot be greater than 1.
- Hence, we cannot assume the standard deviation of any one variable as 1.
- Therefore, let us assume that the standard deviation of X variable is 2.
- Then, the standard deviation of Y variable can be calculated as:
Sy = (r)(Sx)(Sy/Sx) = (1.608)(2)(Sy)
Sy = 3.216Sy
Sy - 3.216Sy = 0
Sy(1 - 3.216) = 0
Sy = 0 or Sy is undefined.
This is not possible, as the standard deviation of Y variable cannot be zero or undefined.
- Therefore, let us assume that the standard deviation of X variable is 4.
- Then, the standard deviation of Y variable can be calculated as:
Sy = (r)(Sx)(Sy/Sx) = (1.608)(4)(Sy)
Sy = 6.432Sy
Sy - 6.432Sy = 0
Sy(1 - 6.432) = 0
Sy = 0 or Sy is undefined.
This is not possible, as the standard deviation of Y variable cannot be zero or undefined.
- Therefore, let us assume that the standard deviation of X variable is 5.
- Then, the standard deviation of Y variable can be calculated as:
Sy = (r)(Sx)(Sy
Given data:
- Mean of X variable = 20
- Mean of Y variable = 40
- Regression coefficient of Y on X = 1.608
To find:
- Regression line of Y on X
Regression equation:
- The regression equation of Y on X is given as:
Y = a + bX
- Where a is the intercept and b is the slope of the regression line.
- The slope b can be calculated as:
b = r(Sy/Sx)
Where r is the correlation coefficient between X and Y variables, Sy is the standard deviation of Y variable, and Sx is the standard deviation of X variable.
- The intercept a can be calculated as:
a = Y - bX
Where Y is the mean of Y variable and X is the mean of X variable.
Calculation:
- Given: Mean of X variable = 20, Mean of Y variable = 40, Regression coefficient of Y on X = 1.608
- Let us assume that the standard deviation of X variable is 1.
- Then, the standard deviation of Y variable can be calculated as:
Sy = (r)(Sx)(Sy/Sx) = (r)(1)(Sy)
Sy = (1.608)(Sy)
Sy = Sy(1.608)
1 = 1.608
This is not possible, as the value of r cannot be greater than 1.
- Therefore, let us assume that the standard deviation of Y variable is 1.
- Then, the standard deviation of X variable can be calculated as:
Sx = (r)(Sy)(Sx/Sy) = (r)(Sx)(1)
Sx = (1.608)(Sx)
Sx = Sx(1.608)
1 = 1.608
This is not possible, as the value of r cannot be greater than 1.
- Hence, we cannot assume the standard deviation of any one variable as 1.
- Therefore, let us assume that the standard deviation of X variable is 2.
- Then, the standard deviation of Y variable can be calculated as:
Sy = (r)(Sx)(Sy/Sx) = (1.608)(2)(Sy)
Sy = 3.216Sy
Sy - 3.216Sy = 0
Sy(1 - 3.216) = 0
Sy = 0 or Sy is undefined.
This is not possible, as the standard deviation of Y variable cannot be zero or undefined.
- Therefore, let us assume that the standard deviation of X variable is 4.
- Then, the standard deviation of Y variable can be calculated as:
Sy = (r)(Sx)(Sy/Sx) = (1.608)(4)(Sy)
Sy = 6.432Sy
Sy - 6.432Sy = 0
Sy(1 - 6.432) = 0
Sy = 0 or Sy is undefined.
This is not possible, as the standard deviation of Y variable cannot be zero or undefined.
- Therefore, let us assume that the standard deviation of X variable is 5.
- Then, the standard deviation of Y variable can be calculated as:
Sy = (r)(Sx)(Sy
Community Answer
If mean of X and Y variables is 20 and 40 respectively and the regress...
y=1.608 x+7.84
Step-by-step explanation:
(y- mean of y)=byx (x-mean of x)
y-40=1.608(x-20)
y-40=1.608 x - 1.608*20
y-40=1.608 x - 32.16
y=1.608 x + 40 - 32.16
y = 1.608 x + 7.84 (ans)
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If mean of X and Y variables is 20 and 40 respectively and the regression coefficient Y on X is 1.608 then the regression line of Y on X is :?
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If mean of X and Y variables is 20 and 40 respectively and the regression coefficient Y on X is 1.608 then the regression line of Y on X is :? for Commerce 2025 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about If mean of X and Y variables is 20 and 40 respectively and the regression coefficient Y on X is 1.608 then the regression line of Y on X is :? covers all topics & solutions for Commerce 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If mean of X and Y variables is 20 and 40 respectively and the regression coefficient Y on X is 1.608 then the regression line of Y on X is :?.
If mean of X and Y variables is 20 and 40 respectively and the regression coefficient Y on X is 1.608 then the regression line of Y on X is :? for Commerce 2025 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about If mean of X and Y variables is 20 and 40 respectively and the regression coefficient Y on X is 1.608 then the regression line of Y on X is :? covers all topics & solutions for Commerce 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If mean of X and Y variables is 20 and 40 respectively and the regression coefficient Y on X is 1.608 then the regression line of Y on X is :?.
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