Q.Using the advertising-expenditure (X, ₹'000) and sales (Y, ₹ lakh) data from the previous question [X: 2, 4, 6, 8, 10; Y: 3, 6, 7, 10, 14], find the regression equation of Y on X, and use it to estimate sales when advertising expenditure is ₹12,000 (X = 12).

The regression of Y on X reuses the same Σxy and Σx² already computed for correlation, just combined differently to build a predictive equation. …

From the previous question, $\bar X = 6$, $\bar Y = 8$, $\sum xy = 52$, $\sum x^2 = 40$.

Step 1 — regression coefficient of Y on X:

Step 2 — regression equation:

Step 3 — estimate at X = 12:

$Y = 1.3(12) + 0.2 = 15.6 + 0.2 = 15.8$ …

Compute $b_{yx}=\Sigma xy/\Sigma x^2$ using the already-found deviation sums; substitute into $Y-\bar Y=b_{yx}(X-\bar X)$ to get the equation in Y = …

Using $b_{xy}=\Sigma xy/\Sigma y^2$ (the coefficient for regressing X ON Y) when the question asks for Y on X — the two regression coefficients divide by diffe …