Answer: 8.289%

## Explanation This is a linear regression prediction problem where: - Dependent variable (Y) = Inflation rate - Independent variable (X) = Money supply growth rate **Step 1: Calculate the slope coefficient (β)** \[ \hat{\beta} = \frac{\hat{\sigma}_{XY}}{\hat{\sigma}_X^2} = \frac{0.007668}{0.02320} = 0.33051 \] Where: - \(\hat{\sigma}_{XY} = 0.007668\) (covariance between money supply growth and inflation) - \(\hat{\sigma}_X^2 = 0.02320\) (variance of money supply growth) **Step 2: Calculate the intercept (β₀)** \[ \hat{\beta}_0 = \bar{Y} - \hat{\beta}\bar{X} = 0.03 - 0.33051 \times 0.09 = 0.0002541 \] Where: - \(\bar{Y} = 0.03\) (mean inflation rate = 3%) - \(\bar{X} = 0.09\) (mean money supply growth rate = 9%) **Step 3: Form the regression equation** \[ \hat{Y} = 0.0002541 + 0.33051X \] **Step 4: Predict inflation rate when X = 25% (0.25)** \[ \hat{Y} = 0.0002541 + 0.33051 \times 0.25 = 0.0828816 \approx 8.289\% \] **Step 5: Compare with options** - A. 7.234% ❌ - B. 8.289% ✅ Correct - C. 6.345% ❌ - D. 8.756% ❌ **Key Concepts:** - Simple linear regression: \(Y = \beta_0 + \beta_1X + \epsilon\) - Slope coefficient: \(\beta_1 = \frac{Cov(X,Y)}{Var(X)}\) - Intercept: \(\beta_0 = \bar{Y} - \beta_1\bar{X}\) - Prediction: Substitute X value into regression equation

Author: Nikitesh Somanthe