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 hundredth. using this equation, find the profit, to the nearest dollar, for a selling price of 11.25 dollars.

price (x)	profit (y)
13.50	5773
18.50	7865
25.75	7815
30.00	5611

Explanation:

Step1: Enter data into calculator

Enter the price - profit data pairs into a statistics calculator.

Step2: Perform quadratic regression

Use the quadratic regression function on the calculator. It will find the coefficients $a$, $b$, and $c$ for the quadratic equation $y = ax^{2}+bx + c$. After calculation, $a\approx - 10.37$, $b\approx561.98$, $c\approx - 1989.37$.

Step3: Substitute $x = 11.25$

Substitute $x = 11.25$ into the equation $y=-10.37x^{2}+561.98x - 1989.37$.
$y=-10.37\times(11.25)^{2}+561.98\times11.25-1989.37$.
$y=-10.37\times126.5625 + 6312.275-1989.37$.
$y=-1312.453125+6312.275 - 1989.37$.
$y = 4107.451875\approx4107$.

Answer:

Regression Equation: $y = - 10.37x^{2}+561.98x - 1989.37$
Final Answer: $4107$