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