Given Y-hat = a + b1 X1 + b2 X2 with a = 3, b1 = 4, b2 = -1, X1 = 3, X2 = 6, what is the predicted value of Y?

Given Y-hat = a + b1 X1 + b2 X2 with a = 3, b1 = 4, b2 = -1, X1 = 3, X2 = 6, what is the predicted value of Y?

• A. 9
• B. 12
• C. 3
• D. 0

Answer: (A)

The model predicts Y-hat by adding the intercept to the weighted contributions of each predictor: Y-hat = a + b1 X1 + b2 X2. Plugging in the values: 3 + 4*3 + (-1)*6. Compute 4*3 = 12 and (-1)*6 = -6, then 3 + 12 - 6 = 9. So the predicted Y is 9. This shows how each predictor shifts the prediction: X1 adds 4 for each unit, while X2 subtracts 1 for each unit, starting from the baseline of 3.

The model predicts Y-hat by adding the intercept to the weighted contributions of each predictor: Y-hat = a + b1 X1 + b2 X2. Plugging in the values: 3 + 4*3 + (-1)6. Compute 43 = 12 and (-1)*6 = -6, then 3 + 12 - 6 = 9. So the predicted Y is 9. This shows how each predictor shifts the prediction: X1 adds 4 for each unit, while X2 subtracts 1 for each unit, starting from the baseline of 3.