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 plac

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.