NDA 2 2024 Maths, question 101

Topic: Statistics

Q101

Let $x-3y+4=0$ and $2x-7y+8=0$ be two lines of regression computed from some bivariate data. If $b_{yx}$ and $b_{xy}$ are regression coefficients of lines of regression of $y$ on $x$ and $x$ on $y$ respectively, then what is the value of $b_{xy}+7b_{yx}$ ?

(a) $-2$
(b) $1$
(c) $2$
(d) $5$ Correct answer

Solution.

Answer: (d) $5$

Regression coefficients have product r²≤1.
Taking b_yx=1/3 and b_xy=7/2 would give 7/6>1, impossible.
Therefore b_yx=2/7 from the second line and b_xy=3 from the first.
The required value is 3+7(2/7)=5.