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If the relationship between two variables x and u is u 3x 15 = 0 and between two other variables y and v is 2y 5y = 23, and regression coefficient of yon x is known as 0.80, what would be the regression coefficient of v on u?
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If the relationship between two variables x and u is u 3x 15 = 0 a...
Given Information
- Equation for x and u: u = 3x - 15 = 0
- Equation for y and v: 2y + 5y = 23
- Regression coefficient of y on x is 0.80
Regression Coefficient of v on u
To find the regression coefficient of v on u, we need to follow the below steps:
- First, we need to find the regression equation of y on x.
- Using the regression equation, we can find the predicted value of y for each value of x.
- We can then substitute these predicted values of y in the equation for y and v to get the predicted values of v for each value of x.
- We then use these predicted values of v and the actual values of u to find the regression equation of v on u.
- The slope of the regression equation of v on u will give us the regression coefficient of v on u.
Finding the Regression Equation of y on x
Let's find the regression equation of y on x using the given information:
- We know that the regression coefficient of y on x is 0.80.
- We also know that the equation for y and v is 2y + 5y = 23, which simplifies to 7y = 23.
Using the regression equation, we can write:
$$\hat{y} = b_0 + b_1x$$
where $\hat{y}$ is the predicted value of y, $b_0$ is the intercept, $b_1$ is the slope, and x is the independent variable (in this case, x is u).
We know that the slope of the regression equation of y on x is 0.80. Let's assume that the intercept is 0. We can then write:
$$\hat{y} = 0 + 0.80x$$
Substituting the equation for x and u, we get:
$$\hat{y} = 0 + 0.80u$$
$$\hat{y} = 0 + 0.80(3x - 15)$$
$$\hat{y} = 0.80(3x) - 0.80(15)$$
$$\hat{y} = 2.40x - 12$$
So, the regression equation of y on x is $\hat{y} = 2.40x - 12$.
Finding the Regression Equation of v on u
Now that we have the regression equation of y on x, we can use it to find the regression equation of v on u:
- We know that the equation for y and v is 2y + 5y = 23, which simplifies to 7y = 23.
- Substituting the regression equation of y on x, we get:
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If the relationship between two variables x and u is u 3x 15 = 0 and between two other variables y and v is 2y 5y = 23, and regression coefficient of yon x is known as 0.80, what would be the regression coefficient of v on u?
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If the relationship between two variables x and u is u 3x 15 = 0 and between two other variables y and v is 2y 5y = 23, and regression coefficient of yon x is known as 0.80, what would be the regression coefficient of v on u? 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 the relationship between two variables x and u is u 3x 15 = 0 and between two other variables y and v is 2y 5y = 23, and regression coefficient of yon x is known as 0.80, what would be the regression coefficient of v on u? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the relationship between two variables x and u is u 3x 15 = 0 and between two other variables y and v is 2y 5y = 23, and regression coefficient of yon x is known as 0.80, what would be the regression coefficient of v on u?.
If the relationship between two variables x and u is u 3x 15 = 0 and between two other variables y and v is 2y 5y = 23, and regression coefficient of yon x is known as 0.80, what would be the regression coefficient of v on u? 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 the relationship between two variables x and u is u 3x 15 = 0 and between two other variables y and v is 2y 5y = 23, and regression coefficient of yon x is known as 0.80, what would be the regression coefficient of v on u? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the relationship between two variables x and u is u 3x 15 = 0 and between two other variables y and v is 2y 5y = 23, and regression coefficient of yon x is known as 0.80, what would be the regression coefficient of v on u?.
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