Answer: Y-hat = -0.8967 + 0.9633 X1

# Why B is correct (quick reasoning) ## Check slope (\( \beta_1 \)) sign: - \( X_1 \) goes from \(-0.41\) to \(0.40\), and \( Y \) goes from \(-2\) to \(-0.11\) - As \( X_1 \) increases, \( Y \) increases → **positive slope** - This immediately eliminates options **C** and **D** (both have negative \( \beta_1 \)) ## Check intercept (\( \alpha \)) sign: - For \( X_1 = -0.41 \), with \( \beta_1 \approx 0.96 \), the slope term = \( 0.96 \times -0.41 \approx -0.39 \) - The actual \( Y \) is \(-2\), which is much lower, so \( \alpha \) must be **negative** to bring the prediction down - This eliminates option **A** ## Only option B fits: - \( \alpha = -0.8967 \) (negative), \( \beta_1 = +0.9633 \) (positive) ✅ --- # Why the others are wrong - **A**: Positive slope (ok) but positive intercept — would overpredict for negative \( X_1 \) - **C/D**: Negative slope — contradicts observed positive relationship

Author: LeetQuiz .