For the quadratic model with regression function $\mu _ { i\cdot x } = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$ , the parameters $\beta _ { 0 } , \beta _ { 1 } \text {, and } \beta _ { 2 }$ characterize the behavior of the function near
A) x = 2.0
B) x = 1.5
C) x = 1.0
D) x = .05
E) x = 0.0

Question

Quizplus · Accepted Answer

The parameters $\beta _ { 0 } , \beta _ { 1 } \text {, and } \beta _ { 2 }$ in a quadratic regression model characterize the behavior of the function for all values of $x$, but they are not specific to any particular value of $x$ like 2.0, 1.5, 1.0, or .05. However, $\beta_0$ represents the intercept, which is the value of the function when $x = 0$, making option E the most directly related to the parameters mentioned.

For the Quadratic Model with Regression Function μi⋅x=β0+β1x+β2x2\mu _ { i\cdot x } = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }μi⋅x​=β0​+β1​x+β2​x2

For the Quadratic Model with Regression Function $\mu _ { i\cdot x } = \beta _ { 0 } + \beta _ { 1 } x + \beta _ { 2 } x ^ { 2 }$