1. Choose the Best Regression Equation
Notes Day 6.5
Choose the Best Regression Equation
Volume of a Box cubic Application Problems

2. Complete a regression equation to find the best model.
Go to “catalog” on the calculator and turn “diagnostics on.” x Y -5
-842 -1 -6 8 2 12 4
184 5
408
Quadratic:
R2=
.9304
Y = x x –
Cubic:
R2= 1
Y = 5x3 – 9x2 – (2.4• 10-11)x + 8
Quartic:
R2=
1 but not really quartic
Y = (5.57• 10-12)x4 + 5x3 – 9x2 + 8
Cubic Regression is best

3. Cuts of 1.811 inches will maximize volume to 96.771 cubic inches
An open box is to be made from a 10-in. by 12-in. piece of cardboard by cutting x-inch squares in each corner and then folding up the sides. Write a function giving the volume of the box in terms of x. Approximate the value of x that produces the greatest volume.
A. Label the side lengths in terms of x
12 – 2x
Write an equation in factored form for the volume as if the box were closed. x x
V(x)=(12 – 2x)(10 – 2x)(x)
10 – 2x
C. Find the roots and plot on the graph.
X = {6,5,0}
Write the volume equation in standard form
and plot the end behavior on the graph.
V(x)=(120 – 44x + 4x2)(x)
V(x)=4x3 – 44x x 90
E. Find the relative min/max on the calculator. Plot.
(1.811 , )
Min(5.523 , )
F. Explain what this ordered pair represents? 5
Cuts of inches will maximize
volume to cubic inches
Why isn’t volume greatest as x approaches infinity?
Some dimensions would be negative.
G. What are the dimensions of the box?
8.378 in. by in. by in.