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If the covariance between two variables is 20 and the variance of one variable is 16 what would be the variance of the other variable?
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If the covariance between two variables is 20 and the variance of one ...
Answer:
Given:
Covariance between two variables = 20
Variance of one variable = 16
Formula:
Covariance of two variables = (Sum of (xi - x̄) * (yi - ȳ)) / (n - 1)
Variance of a variable = Sum of (xi - x̄)² / (n - 1)
Step 1: Find the correlation coefficient
Correlation coefficient (ρ) = Covariance of two variables / (Standard deviation of variable 1 * Standard deviation of variable 2)
Standard deviation of variable 1 = square root of Variance of variable 1 = square root of 16 = 4
ρ = 20 / (4 * Standard deviation of variable 2)
Step 2: Find the standard deviation of variable 2
Standard deviation of variable 2 = 20 / (4 * ρ)
Step 3: Find the variance of variable 2
Variance of variable 2 = Standard deviation of variable 2² = (20 / (4 * ρ))²
Final answer:
The variance of the other variable is (20 / (4 * ρ))².
Given:
Covariance between two variables = 20
Variance of one variable = 16
Formula:
Covariance of two variables = (Sum of (xi - x̄) * (yi - ȳ)) / (n - 1)
Variance of a variable = Sum of (xi - x̄)² / (n - 1)
Step 1: Find the correlation coefficient
Correlation coefficient (ρ) = Covariance of two variables / (Standard deviation of variable 1 * Standard deviation of variable 2)
Standard deviation of variable 1 = square root of Variance of variable 1 = square root of 16 = 4
ρ = 20 / (4 * Standard deviation of variable 2)
Step 2: Find the standard deviation of variable 2
Standard deviation of variable 2 = 20 / (4 * ρ)
Step 3: Find the variance of variable 2
Variance of variable 2 = Standard deviation of variable 2² = (20 / (4 * ρ))²
Final answer:
The variance of the other variable is (20 / (4 * ρ))².
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If the covariance between two variables is 20 and the variance of one variable is 16 what would be the variance of the other variable?
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If the covariance between two variables is 20 and the variance of one variable is 16 what would be the variance of the other variable? 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 covariance between two variables is 20 and the variance of one variable is 16 what would be the variance of the other variable? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the covariance between two variables is 20 and the variance of one variable is 16 what would be the variance of the other variable?.
If the covariance between two variables is 20 and the variance of one variable is 16 what would be the variance of the other variable? 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 covariance between two variables is 20 and the variance of one variable is 16 what would be the variance of the other variable? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the covariance between two variables is 20 and the variance of one variable is 16 what would be the variance of the other variable?.
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