the table shows a companys profit based on the number of pounds of food produced.\nprofit\n| pounds of food…

the table shows a companys profit based on the number of pounds of food produced.\nprofit\n| pounds of food produced | profit ($) |\n| ---- | ---- |\n| 100 | -11,000 |\n| 250 | 0 |\n| 500 | 10,300 |\n| 650 | 11,500 |\n| 800 | 9,075 |\nusing the quadratic regression model, which is the best estimate of the profit when 350 pounds of food are produced?\n$5,150\n$5,300\n$10,150\n$11,000

the table shows a companys profit based on the number of pounds of food produced.\nprofit\n| pounds of food produced | profit ($) |\n| ---- | ---- |\n| 100 | -11,000 |\n| 250 | 0 |\n| 500 | 10,300 |\n| 650 | 11,500 |\n| 800 | 9,075 |\nusing the quadratic regression model, which is the best estimate of the profit when 350 pounds of food are produced?\n$5,150\n$5,300\n$10,150\n$11,000

Answer

Answer:

$5,300$

Explanation:

Step1: Recall quadratic regression formula

The general quadratic regression equation is $y = ax^{2}+bx + c$. Using a calculator or software (e.g., TI - 84 Plus: Stat, Edit to enter data, then Stat, Calc, 5: QuadReg), with $x$ as pounds of food produced and $y$ as profit.

Step2: Input data points

Input the points $(100,- 11000),(250,0),(500,10300),(650,11500),(800,9075)$ into the regression tool.

Step3: Get the regression equation

After running the quadratic regression, we get an equation (approximate). Let's assume the equation is $y=ax^{2}+bx + c$.

Step4: Substitute $x = 350$

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