Question

calculate a quadratic regression. a) y = 0.7x² - 5.1 + 14.9 b) y = - 4.8x² - 11.6x + 14.9 c) none of these d) y = 1.8x - 11.6

Explanation:

Step1: Recall quadratic regression formula

The general form of a quadratic regression equation is $y = ax^{2}+bx + c$. One would typically use statistical software or a calculator with regression - capabilities and input the data points $(x_1,y_1),(x_2,y_2),\cdots$ to find the values of $a$, $b$, and $c$. Since we are not given the process of calculation but only the options, we can assume the calculations have been done.

Step2: Check the form of the quadratic equations in options

We are looking for an equation in the form $y = ax^{2}+bx + c$. Option A: $y=0.7x^{2}-5.1 + 14.9$ is not in the correct form (missing the $x$ term in the linear part). Option B: $y=-4.8x^{2}-11.6x + 14.9$ is in the correct quadratic - regression form $y = ax^{2}+bx + c$ where $a=-4.8$, $b = - 11.6$ and $c = 14.9$. Option C: "None of these" is incorrect as option B is a valid quadratic regression equation. Option D: $y - 1.8x-11.6$ is not a quadratic equation.

Answer:

B. $y=-4.8x^{2}-11.6x + 14.9$