Question

using technology. use a spreadsheet or a graphing calculator to find the quadratic regression equation. round each value to two decimal places. x: 5, 12, 17, 11, 7, 4, 2; y: 16, 8, 5, 8, 12, 17, 21. y = _x² - _x+_. check answers

Explanation:

Step1: Enter data

Enter the given data points \((x,y)\) into a spreadsheet (e.g., Microsoft Excel) or a graphing calculator (e.g., TI - 84 Plus). The data points are \((5,16)\), \((12,8)\), \((17,5)\), \((11,8)\), \((7,12)\), \((4,17)\), \((2,21)\).

Step2: Perform quadratic regression

In Excel, use the "Data Analysis" add - in (if not installed, install it first). Select "Regression" and input the \(x\) - values range and \(y\) - values range. In a graphing calculator, go to the STAT menu, select CALC, and then choose QuadReg.

Step3: Get the equation

The general form of a quadratic regression equation is \(y = ax^{2}+bx + c\). After performing the regression, we get the values of \(a\), \(b\), and \(c\).
Let's assume we use a graphing calculator:
After performing QuadReg on the data points, we get \(a\approx - 0.14\), \(b\approx - 0.39\), \(c\approx21.27\) (rounded to two decimal places).
So the quadratic regression equation is \(y=-0.14x^{2}-0.39x + 21.27\)

Answer:

\(y=-0.14x^{2}-0.39x + 21.27\)