For the quadratic regression equation = b₀ + b₁x + b₂x²,the predicted y achieves its optimum (maximum or minimum)when x is _________. A) -2b₂/b₁ B) -b₁/2b₂ C) b₁/2b₂ D) 2b₁/b₂

Question

Quizplus · Accepted Answer

The predicted y achieves its optimum (maximum or minimum) when the slope of the quadratic regression equation equals zero. In other words, when the derivative of the equation with respect to x equals zero. The derivative of the regression equation is: b₁ + 2b₂x² Setting the derivative equal to zero and solving for x, we get: b₁ + 2b₂x² = 0 2b₂x² = -b₁ x = -b₁/2b₂ Therefore, the predicted y achieves its optimum when x is -b₁/2b₂, which is answer choice B.

For the Quadratic Regression Equation = B0 + B1x

For the Quadratic Regression Equation = B₀ + B₁x