Question

company x tried selling widgets at various prices to see how much profit they would make. the following table shows the widget selling price, x, and the total profit earned at that price, y. write a quadratic regression equation for this set of data, rounding all coefficients to the nearest tenth. using this equation, find the profit, to the nearest dollar, for a selling price of 14.75 dollars. copy values for calculator open statistics calculator

Explanation:

Step1: Input data into calculator

Input the \(x\) (price) and \(y\) (profit) values into a statistics calculator. The quadratic regression formula is \(y = ax^{2}+bx + c\).

Step2: Obtain quadratic regression equation

Using a calculator (e.g., TI - 84 Plus: STAT → EDIT (enter data), then STAT → CALC → QuadReg), we get \(y=- 3.5x^{2}+198.4x - 1258.1\) (rounded to the nearest tenth).

Step3: Substitute \(x = 14.75\) into the equation

Substitute \(x = 14.75\) into \(y=-3.5x^{2}+198.4x - 1258.1\).

$$
LATEXBLOCK0
$$

Answer:

The quadratic regression equation is \(y=-3.5x^{2}+198.4x - 1258.1\). The profit for a selling price of \(14.75\) dollars is \(907\) dollars.