Question

What is the quadratic regression equation for the data set?

Answer 1

`y=0.056x^2+1.278x-0.886`

Explanation:

`"substitute the given values for x into the equations and"`
`"check result against the corresponding value of y"`

`"the 'simplest ' value to start with is x = 10"`

`" starting with the first equation and working down"`

`"looking for an answer of "x=10toy=17.48`

`y=0.056x^2+1.278xto(color(red)(1))`

`color(white)(y)=(0.056xx100)+(1.278xx10)`

`color(white)(y)=5.6+12.78=18.38!=17.48`

`y=0.056x^2-1.278x-0.886to(color(red)(2))`

`color(white)(y)=(0.056xx100)-(1.278xx10)-0.886`

`color(white)(y)=5.6-12.78-0.886=-8.066!=17.48`

`y=0.056x^2+1.278to(color(red)(3))`

`color(white)(y)=(0.056xx100)+1.278`

`color(white)(y)=5.6+1.278=6.878!=17.48`

`y=0.056x^2+1.278x-0.886to(color(red)(4))`

`color(white)(y)=(0.056xx100)+(1.278xx10)-0.886`

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

`"this appears to be the correct equation"`

`"As a further test choose some other values of x "`