For the second-order polynomial model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$ ,the shape of the curve will be determined by the relative sizes of $\beta _ { 1 }$ and $\beta _ { 2 }$ and on their signs.

Question

Quizplus · Accepted Answer

The coefficients determine the shape of the curve, with $\beta _ { 1 }$ determining whether the curve is upwards or downwards sloping, and $\beta _ { 2 }$ determining the concavity or convexity of the curve. The signs of these coefficients also play a role in determining the shape of the curve.

For the Second-Order Polynomial Model E(y)=β0+β1x+β2x2E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }E(y)=β0​+β1​x+β2​x2

For the Second-Order Polynomial Model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$