19. The following table gives the number of motor vehicle thefts (in thousands) in the U.S. for the
years 1983 – 1993. x = 1 represents 1983. Use the regression capabilities of your calculator to
fit a cubic model to this data. Round to three decimal places. Use your model to predict the
number of motor vehicle thefts in 1995.
Year
(x)
1234567891011
Thefts
(y)
1008
1032
1103
1224
1289
1433
1565
1636
1662
1611
1561
20. The table below shows the per capita consumption of beef in the United States in recent years.
What is the equation of the regression line which best fits this data? What is the correlation
coefficient for this regression line? How close a fit is the regression line? Use the regression line
to predict the per capita consumption of beef in 2001.
Year x
Per capita consumption of beef, in lbs
1990 0
64.0
1991 1
63.1
1992 2
62.8
1993 3
61.5
3
Fall 2003 – O’Brien
21. The table below shows the total annual amount of advertising expenses (in billions of dollars) in
the United States in recent years. What is the equation of the regression line which best fits this
data? What is the correlation coefficient for this regression line? How close a fit is the regression
line? Use the regression line to predict the annual amount of advertising expenses in 2003.
x = 1 corresponds to 1991. Round all numbers to three decimal places.
Year (x)
123456
Expenses (y)
$126.4
$131.3
$138.1
$150.0
$160.9
$173.2
Miscellaneous Problems
Directions: Solve the following problems. Show all of your support work.
22. In 1990, around 115 billion dollars was invested globally in telecommunications infrastructure.
In 1994, around 145 billion was spent. Assuming that global investment in telecom
infrastructure is growing at a constant rate, write a linear model which gives investment (I) in
billions of dollars as a function of t, the number of years since 1990. Use your model to predict
global telecom investment in 2003.
23. Zeno’s Cabs purchased a taxi for $24,600 in 1994. After 8 years, the cab must be replaced. It’s
salvage value is $2,200. Write a linear equation (in slope-intercept form) giving the value of the
cab during its 8 years of use. What was the value of the cab 3 years after it was purchased? Show all of your support work.
24.