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Given the following data Variable X Y Mean 40 60 SD 3 5 Coefficient of correlation 0.4 What is the most likely value of „X” when Y= 50?
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Given the following data Variable X Y Mean 40 60 SD 3 5 Coefficient of...
Calculation of Most Likely Value of X when Y= 50
Given data:
- X Mean = 40
- Y Mean = 60
- X SD = 3
- Y SD = 5
- Coefficient of Correlation = 0.4
Formula:
- Regression Equation: Y = a + bX
- b = r(SD of Y/SD of X)
- a = Y Mean - b(X Mean)
Calculation:
- b = 0.4(5/3) = 0.67
- a = 60 - 0.67(40) = 34.8
- Y = 50
- X = (Y - a)/b = (50 - 34.8)/0.67 = 22.69
Answer:
The most likely value of X when Y = 50 is 22.69.
Explanation:
The given data is used to calculate the regression equation, which is used to find the most likely value of X when Y = 50. The formula for the regression equation is Y = a + bX, where a is the intercept and b is the slope. The slope is calculated using the formula b = r(SD of Y/SD of X), where r is the coefficient of correlation, SD of Y is the standard deviation of Y, and SD of X is the standard deviation of X. The intercept is calculated using the formula a = Y Mean - b(X Mean).
Once the regression equation is calculated, the value of X is found by plugging in the value of Y. In this case, the value of Y is 50. The formula X = (Y - a)/b is used to find the value of X. This formula rearranges the regression equation to solve for X when Y is known.
Therefore, the most likely value of X when Y = 50 is 22.69.
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Given the following data Variable X Y Mean 40 60 SD 3 5 Coefficient of correlation 0.4 What is the most likely value of „X” when Y= 50?
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Given the following data Variable X Y Mean 40 60 SD 3 5 Coefficient of correlation 0.4 What is the most likely value of „X” when Y= 50? 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 data Variable X Y Mean 40 60 SD 3 5 Coefficient of correlation 0.4 What is the most likely value of „X” when Y= 50? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given the following data Variable X Y Mean 40 60 SD 3 5 Coefficient of correlation 0.4 What is the most likely value of „X” when Y= 50?.
Given the following data Variable X Y Mean 40 60 SD 3 5 Coefficient of correlation 0.4 What is the most likely value of „X” when Y= 50? 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 data Variable X Y Mean 40 60 SD 3 5 Coefficient of correlation 0.4 What is the most likely value of „X” when Y= 50? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given the following data Variable X Y Mean 40 60 SD 3 5 Coefficient of correlation 0.4 What is the most likely value of „X” when Y= 50?.
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