Suppose that the sample regression equation of a second-order model is given by $\tilde { y } = 2.50 + 0.15 x + 0.45 x ^ { 2 }$ .Then,the value 4.60 is the:
A) predicted value of y for any positive value of x.
B) predicted value of y when x = 2.
C) estimated change in y when x increases by 1 unit .
D) intercept where the response surface strikes the x-axis.

Question

Quizplus · Accepted Answer

The value 4.60 is the predicted value of y when x=2. This can be calculated by substituting x=2 in the given sample regression equation and solving for y:

$\tilde { y } = 2.50 + 0.15 x + 0.45 x ^ { 2 }$

$\tilde { y } = 2.50 + 0.15(2) + 0.45 (2)^{2}$

$\tilde { y } = 2.50 + 0.30 + 0.90$

$\tilde { y } = 4.70$

Therefore, option B is the correct answer. Option A is incorrect because the predicted value of y varies for different values of x. Option C is incorrect because the estimated change in y when x increases by 1 unit would be given by the coefficient of x (0.15), not the predicted value of y. Option D is incorrect because the intercept where the response surface strikes the x-axis would be given by setting y=0 in the regression equation and solving for x, which is not relevant to the question.

Suppose That the Sample Regression Equation of a Second-Order Model y~=2.50+0.15x+0.45x2\tilde { y } = 2.50 + 0.15 x + 0.45 x ^ { 2 }y~​=2.50+0.15x+0.45x2

Suppose That the Sample Regression Equation of a Second-Order Model $\tilde { y } = 2.50 + 0.15 x + 0.45 x ^ { 2 }$