Question

what is the quadratic regression equation for the data set?
hint:
open desmos. use the plus sign to enter the table of values in line 1.
in line 2, type y1~ax²1+bx1+c
use the values for a, b, and c to write the quadratic equation in the form of y = ax² + bx + c
round to the nearest thousandth if necessary.
y = -0.175(3.786)^x
y = -0.175x² - 3.786x + 121.119
y = -0.175x² + 3.786x + 121.119

Explanation:

Step1: Use a regression - capable tool

As per the hint, use Desmos. Enter the data set \((x,y)\) values into a table in Desmos.

Step2: Set up the quadratic regression model

In Desmos, type \(y1\sim ax^{2}1 + bx1 + c\) to perform quadratic regression on the entered data.

Step3: Determine the coefficients

After running the regression in Desmos, we get the coefficients \(a=-0.175\), \(b = 3.786\), and \(c=121.119\).

Step4: Write the quadratic equation

The quadratic regression equation is \(y=-0.175x^{2}+3.786x + 121.119\).

Answer:

\(y=-0.175x^{2}+3.786x + 121.119\)