# What is the quadratic regression equation for the data set?

Feb 1, 2018

$y = 0.056 {x}^{2} + 1.278 x - 0.886$

#### Explanation:

$\text{substitute the given values for x into the equations and}$
$\text{check result against the corresponding value of y}$

$\text{the 'simplest ' value to start with is x = 10}$

$\text{ starting with the first equation and working down}$

$\text{looking for an answer of } x = 10 \to y = 17.48$

$y = 0.056 {x}^{2} + 1.278 x \to \left(\textcolor{red}{1}\right)$

$\textcolor{w h i t e}{y} = \left(0.056 \times 100\right) + \left(1.278 \times 10\right)$

$\textcolor{w h i t e}{y} = 5.6 + 12.78 = 18.38 \ne 17.48$

$y = 0.056 {x}^{2} - 1.278 x - 0.886 \to \left(\textcolor{red}{2}\right)$

$\textcolor{w h i t e}{y} = \left(0.056 \times 100\right) - \left(1.278 \times 10\right) - 0.886$

$\textcolor{w h i t e}{y} = 5.6 - 12.78 - 0.886 = - 8.066 \ne 17.48$

$y = 0.056 {x}^{2} + 1.278 \to \left(\textcolor{red}{3}\right)$

$\textcolor{w h i t e}{y} = \left(0.056 \times 100\right) + 1.278$

$\textcolor{w h i t e}{y} = 5.6 + 1.278 = 6.878 \ne 17.48$

$y = 0.056 {x}^{2} + 1.278 x - 0.886 \to \left(\textcolor{red}{4}\right)$

$\textcolor{w h i t e}{y} = \left(0.056 \times 100\right) + \left(1.278 \times 10\right) - 0.886$

color(white)(y)=5.6+12.78-0.886=17.49~~17.48color(white)(x)✔︎

$\text{this appears to be the correct equation}$

$\text{As a further test choose some other values of x }$