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

Accepted Solution

Answer:$5,300Step-by-step explanation:Formulae used,[tex]a=\dfrac{(\sum x^2y\sum xx)-(\sum xy\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex][tex]b=\dfrac{(\sum xy\sum x^2x^2)-(\sum x^2y\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex][tex]c=\dfrac{\sum y}{n}-b\frac{\sum x}{n}-a\frac{\sum x^2}{n}[/tex]Where,[tex]\sum xx=\sum x^2-\dfrac{(\sum x)^2}{n}[/tex][tex]\sum xy=\sum xy-\dfrac{\sum x\sum y}{n}[/tex][tex]\sum xx^2=\sum x^3-\dfrac{\sum x\sum x^2}{n}[/tex][tex]\sum x^2y=\sum x^2y-\dfrac{\sum x^2\sum y}{n}[/tex][tex]\sum x^2x^2=\sum x^4-\dfrac{(\sum x^2)^2}{n}[/tex]Putting the values from the table, we get the best fit line as,[tex]y= -0.0817x^2 + 102.24x - 20421[/tex]As we want to calculate the profit at 350 pounds, so putting x=350, we get[tex]y= -0.0817(350)^2 + 102.24(350) - 20421=\$5354.75[/tex]