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Given the following equation : 2x-3y=10 and 3x 4y=15 , which one is on regression equation of x on y?
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Given the following equation : 2x-3y=10 and 3x 4y=15 , which one is on...
Regression Equation of X on Y
Regression analysis is a statistical tool that is used to establish the relationship between two or more variables. The regression equation of x on y is a formula used to predict the value of x given the value of y. In other words, it shows how changes in the dependent variable (y) affect the independent variable (x).
Step 1: Find the slope of the regression line
The slope of the regression line is given by:
b = r * (Sy / Sx)
Where r is the correlation coefficient, Sy is the standard deviation of y and Sx is the standard deviation of x.
Step 2: Find the intercept of the regression line
The intercept of the regression line is given by:
a = y - b * x
Where y is the mean of y, x is the mean of x and b is the slope of the regression line.
Step 3: Plug in the values
Now that we have the slope and intercept, we can plug them into the regression equation:
x = a + b * y
This equation tells us how to predict the value of x given the value of y.
Applying the steps to the given equations
Let's apply these steps to the given equations:
2x - 3y = 10
3x + 4y = 15
Step 1: Find the slope of the regression line
First, we need to solve for x in both equations:
2x - 3y = 10
2x = 3y + 10
x = (3/2)y + 5
3x + 4y = 15
3x = -4y + 15
x = (-4/3)y + 5
Now we can calculate the correlation coefficient:
r = (-4/3) * (Sy / Sx)
r = (3/4) * (Sy / Sx)
Step 2: Find the intercept of the regression line
We can find the mean of x and y:
x̄ = (5 + 5) / 2 = 5
ȳ = (10/3 + 5/4) / 2 = 2.9167
Now we can calculate the intercept:
a = ȳ - b * x̄
a = 2.9167 - (3/4) * 5
a = -0.8333
Step 3: Plug in the values
Finally, we can plug in the values to get the regression equation:
x = -0.8333 + (3/4) * y
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Given the following equation : 2x-3y=10 and 3x 4y=15 , which one is on regression equation of x on y?
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Given the following equation : 2x-3y=10 and 3x 4y=15 , which one is on regression equation of x on y? 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 Given the following equation : 2x-3y=10 and 3x 4y=15 , which one is on regression equation of x on y? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given the following equation : 2x-3y=10 and 3x 4y=15 , which one is on regression equation of x on y?.
Given the following equation : 2x-3y=10 and 3x 4y=15 , which one is on regression equation of x on y? 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 Given the following equation : 2x-3y=10 and 3x 4y=15 , which one is on regression equation of x on y? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given the following equation : 2x-3y=10 and 3x 4y=15 , which one is on regression equation of x on y?.
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