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

Answer:

$5,300

Step-by-step explanation:

Formulae used,

$a=\dfrac{(\sum x^2y\sum xx)-(\sum xy\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}$

$b=\dfrac{(\sum xy\sum x^2x^2)-(\sum x^2y\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}$

$c=\dfrac{\sum y}{n}-b\frac{\sum x}{n}-a\frac{\sum x^2}{n}$

Where,

$\sum xx=\sum x^2-\dfrac{(\sum x)^2}{n}$

$\sum xy=\sum xy-\dfrac{\sum x\sum y}{n}$

$\sum xx^2=\sum x^3-\dfrac{\sum x\sum x^2}{n}$

$\sum x^2y=\sum x^2y-\dfrac{\sum x^2\sum y}{n}$

$\sum x^2x^2=\sum x^4-\dfrac{(\sum x^2)^2}{n}$

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

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

Answer 2

Answer:

$5,300

Step-by-step explanation:

i promise you i did the test on e2020