Question

Enter the coefficients of the regression equation: _______x^2+________x+_______ Using this equation, find the profit, to the nearest dollar, for a selling price of 16.75 dollars.​

Answer 1

I think it is the first ones

Answer 2

`y=\boxed{-14.380}\;x^2+\boxed{299.970}\;x+\boxed{-950.851}`

$39

Explanation:

Create 5 additional columns on the given table for x², x³, x⁴, xy, and x²y.

Calculate the values and add the sum of each column.

(See attachment 1).

Use the matrix equation for determining the parabolic curve, entering the sums from attachment 1:

`\displaystyle a \sum x{_i}^4+b \sum x{_i}^3+c \sum x{_i}^2=\sum x{_i}^2y_i`

`\implies 74446.015625a+6046.90625b+520.25c=248662.875`

`\displaystyle a \sum x{_i}^3+b \sum x{_i}^2+c \sum x{_i}=\sum x{_i}y_i`

`\implies 6046.90625a+520.25b+48.5c=22987.5`

`\displaystyle a \sum x{_i}^2+b \sum x{_i}+c n_i=\sum y_i`

`\implies 520.25a+48.5b+5c=2313`

Solve for a, b and c using a calculator:

• a = -14.38019324...
• b = 299.9701548...
• c = -950.8513949...

Insert these values (rounding to 3 decimal places) into the quadratic formula
`y=ax^2+bx+c` :

`\large\boxed{y=-14.380x^2+299.970x-950.851}`

To find the profit (y) for a selling price of 16.75, substitute x = 16.75 into the found quadratic equation:

`\implies y=-14.380(16.75)^2+299.970(16.75)-950.851`

`\implies y=39.157...`

Therefore, the profit is $39 to the nearest dollar.

Note: Attachment 2 is the two-variable regression analysis as calculated by an online graphing calculator, proving that the y-value is 39 (nearest whole number) when x=16.75.