Cubic Regression
Name:
1. The table below gives the number of children (in thousands) receiving social
security during the years 1988 through 1995.
a. Find the cubic regression equation.
b. Find the value for 𝑟 2 .
c. Determine the number of children for the year 1978.
d. Determine the number of children for the year 2005.
2. The table below shows the average price (in thousands of dollars) of a house in
the northeastern US for the years 1987 through 1995.
a. Find the cubic regression equation.
b. Determine the 𝑟 2 .
c. Determine the estimated cost for the year 1982.
d. Determine the estimated cost for the year 2000.
3. The table below shows the average speed (in knots) of the Trident motor yacht
for several different engine speeds (in hundreds of revs per min).
a. Find the cubic regression equation.
b. Find the value of 𝑟 2 .
c. Estimate the average speed of an engine of 2400 RPM’s (24 in chart).
d. What engine speed produces a boat speed of 14 knots?
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Cubic Regression
Name:
4. The table below shows the average monthly social security benefits (in dollars)
from 1940 through 2003.
Year
1940 1950 1960 1970
1980
1990
2000
2003
Amount 22.71 29.03 81.73 123.82 321.10 550.50 844.60 922.10
a. Determine the cubic regression equation.
b. Determine the value 𝑟 2 .
c. Determine the estimated average benefits for the year 1930.
d. Determine the average benefits for a retired worker in 2010.
5. The table below shows the gestation period (in days) of 5 animals and their
expected longevity (in years).
Animal
Rat
Gestation 21
Longevity 3
Squirrel Pig
44
115
9
10
Cow
280
12
Elephant
624
40
a. Determine the cubic regression equation.
b. Determine the value of 𝑟 2 .
c. Estimate the longevity of an animal with a gestation period of 151 days.
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