UPSC NDA 2 2021 Mathematics Solved Paper

Concept:The regression line of $Y$ on $X$ is $Y = b_1 X + b_0$ and the regression line of $X$ on $Y$ is $X = a_1 Y + a_0$, where $b_1$ and $a_1$ are regression coefficients.Explanation:Statement 1 gives $y = \frac{3}{4}x + 2$.Rewriting: $4y = 3x + 8$, or $3x - 4y + 8 = 0$.Statement 2 gives $x = \frac{3}{4}y + \frac{1}{4}$.Rewriting: $4x = 3y + 1$, or $4x - 3y - 1 = 0$.Both equations are in the standard linear form for regression lines.The product of the regression coefficients is $\frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$, which lies between $0$ and $1$, satisfying a necessary condition for regression lines.Therefore, both statements correctly represent valid regression lines for a bivariate data set.Answer:Both statements 1 and 2 are correct. Option C.