QUIZ: Applications of Cubic Functions Part 2
The data in the table give the average speed y (in knots) of the Trident motor yacht for several different engine speeds x (in hundreds of
revolutions per minute, or RPMs)
Engine Speed, x Boat Speed, y
9
11
13
15
6.43
7.61
8.82
9.86
17
19
21.5
10.88
12.36
15.24
Create a scatterplot (Boat Speed vs. Engine Speed) of the data in Excel and paste your graph below. Be sure to include a TITLE for your graph and
LABEL THE X AND Y AXES.
Find a quadratic regression model ( y
 ax 2  bx
 c
) for the data and
report the model below. What is the value of r-squared for this model?

Find a cubic regression model ( y
 ax 3  bx 2  cx
 d
) for the data and
report the model below. What is the value of r-squared for this model?

Which model is a better fit for the data? How do you know?
Estimate the average boat speed of the Trident for an engine speed of
2400 RPMs. (Hint: 2400 RPMs would equal an x value of 24 since the
equation denotes engine speed in hundreds of revolutions per minute.)