Question

the table shows a companys profit based on the number of pounds of food produced.
profit

pounds of food produced	profit ($)
250	0
500	10,300
650	11,500
800	9,075

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

Explanation:

Step1: Set up quadratic regression

Let the quadratic regression equation be $y = ax^{2}+bx + c$, where $x$ is pounds of food produced and $y$ is profit. Use statistical software or calculator with regression - function to find $a$, $b$, and $c$ based on the data points $(100,- 11000),(250,0),(500,10300),(650,11500),(800,9075)$.

Step2: Obtain regression equation

After performing quadratic regression, we get an equation (the actual values of $a$, $b$, $c$ are calculated from the data).

Step3: Substitute $x = 350$

Substitute $x = 350$ into the quadratic regression equation $y=a(350)^{2}+b(350)+c$. After calculation, we find that the value of $y$ is closest to $\$5300$.

Answer:

$5,300$