Question

The table shows a company’s profit based on the number of pounds of food produced.

Using the quadratic regression model, which is the best estimate of the profit when 350 pounds of food are produced?

$5,150
$5,300
$10,150
$11,000

Answer 1

$5,300

Explanation:

i promise you i did the test on e2020

Answer 2

$5,300

Explanation:

Formulae used,

`a=\frac{(\sum x^2y\sum xx)-(\sum xy\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}`

`b=\frac{(\sum xy\sum x^2x^2)-(\sum x^2y\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}`

`c=(\sum y)/(n)-b(\sum x)/(n)-a(\sum x^2)/(n)`

Where,

`\sum xx=\sum x^2-((\sum x)^2)/(n)`

`\sum xy=\sum xy-(\sum x\sum y)/(n)`

`\sum xx^2=\sum x^3-(\sum x\sum x^2)/(n)`

`\sum x^2y=\sum x^2y-(\sum x^2\sum y)/(n)`

`\sum x^2x^2=\sum x^4-((\sum x^2)^2)/(n)`

Putting the values from the table, we get the best fit line as,

`y= -0.0817x^2 + 102.24x - 20421`

As we want to calculate the profit at 350 pounds, so putting x=350, we get

`y= -0.0817(350)^2 + 102.24(350) - 20421=\$5354.75`