Question

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 20.75 dollars.
answer
regression equation:
final answer:

Explanation:

Step1: Input data into calculator

Input the \(x\) (price) and \(y\) (profit) values into a quadratic regression calculator.

Step2: Obtain quadratic regression equation

Using a quadratic regression tool (such as a graphing calculator or online statistics calculator), for the given data points \((x_1 = 13.25,y_1=553)\), \((x_2 = 15.75,y_2 = 666)\), \((x_3=20.25,y_3 = 856)\), \((x_4=29.00,y_4 = 778)\), \((x_5=34.00,y_5 = 595)\), the quadratic regression equation is \(y=- 1.47x^{2}+70.94x - 191.03\) (rounded to the nearest hundredth).

Step3: Substitute \(x = 20.75\) into the equation

Substitute \(x = 20.75\) into \(y=-1.47x^{2}+70.94x - 191.03\).

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Answer:

Regression Equation: \(y=-1.47x^{2}+70.94x - 191.03\)
Final Answer: \(648\)