using technology. use a spreadsheet or a graphing calculator to find the quadratic regression equation…

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

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

Answer

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)