Question
Download Solution PDFGiven the regression lines X + 2Y - 5 = 0, 2X + 3Y - 8 = 0 and Var(X) = 12, the value of Var(Y) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
Regression lines
x + 2y - 5 = 0
2x + 3y - 8 = 0
var(x)= σx = 12
Calculation
x + 2y - 5 = 0 ------(i)
Let y = - x/2 + 5/2 be the regression line of y on x [ from equation 1]
2x + 3y - 8
x = -(3/2)y + 8/2 be the regressiopn line of x on y
⇒ byx = -1/2 and bxy = -3/2
bxy = Regression line of y on x
byx = Regression line of x on y
We know that regression coefficient = r = √(byx × bxy)
⇒ r = √(-1/2 × -3/2)
Since both bxy and byx are negative r is also negative
∴ r = -√3/2 < 1
σx = \(\sqrt{12}\) = 2√3
We know that byx = r (σy/σx)
⇒ -1/2 = -√3/2 (σy/2√3)
⇒ σy = 2
∴ var(y) = variance of y =(2)2 = 4
Last updated on Jul 10, 2025
-> The SSC CGL Application Correction Window Link Live till 11th July. Get the corrections done in your SSC CGL Application Form using the Direct Link.
-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.
-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.
-> Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.
-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.
-> The CGL Eligibility is a bachelor’s degree in any discipline.
-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.
-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.