Chapter: Linear Regression· Mathematics & Statistics (Commerce) Part 2
For a bivariate data \(\bar{x} = 10,\ \bar{y} = 12,\ V(X) = 9,\ \sigma_y = 4\) and \(r = 0.6\). Estimate \(y\) when \(x = 5\)Solution : Line of regression of Y on X is \(Y - \bar{y} = \square\,(X - \bar{x})\)\(\therefore Y - 12 = r\cdot\dfrac{\sigma_…
Q.6 (C)(i)
For a bivariate data \(\bar{x} = 10,\ \bar{y} = 12,\ V(X) = 9,\ \sigma_y = 4\) and \(r = 0.6\). Estimate \(y\) when \(x = 5\)
Solution : Line of regression of Y on X is \(Y - \bar{y} = \square\,(X - \bar{x})\)
\(\therefore Y - 12 = r\cdot\dfrac{\sigma_y}{\sigma_x}(X - 10)\)
\(\therefore Y - 12 = 0.6 \times \dfrac{4}{\square}(X - 10)\)
\(\therefore\) When \(x = 5\): \(Y - 12 = \square\,(5 - 10)\)
\(\therefore Y - 12 = -4\)
\(\therefore Y = \square\)