Answer: 0.0599

## Explanation This question involves testing for heteroskedasticity using the White test. Here's the step-by-step reasoning: ### Step 1: Understanding the Test Statistic - The White test statistic is calculated as **nR²**, where: - n = sample size (100 in this case) - R² = coefficient of determination from the second regression - The test statistic follows a **χ² distribution** with degrees of freedom = k(k+3)/2 ### Step 2: Determining Degrees of Freedom - With **one explanatory variable** (k = 1): - Degrees of freedom = 1 × (1+3)/2 = 4/2 = 2 - So we use **χ²₂** distribution ### Step 3: Finding Critical Value - At **5% significance level**, the critical value for χ²₂ is **5.99** - We reject the null hypothesis when: nR² > 5.99 ### Step 4: Solving for R² - nR² = 5.99 - 100 × R² = 5.99 - R² = 5.99 / 100 = **0.0599** ### Step 5: Interpretation - When R² ≥ 0.0599, we reject the null hypothesis of no heteroskedasticity - When R² < 0.0599, we fail to reject the null hypothesis Therefore, the correct R² value at which we would reject the null hypothesis is **0.0599** (Option D).

Author: Tanishq Prabhu