SITE-A teams: Lesson 3

The cost of operating the Internal Revenue Service (IRS) increased steadily from 1980 to 1990. The table below depicts the approximate cost in billions of dollars per year:

Year    Cost

(billions)

1988    2.3

1981    2.5

1982    2.6

1983    2.9

1984    3.1

1985    3.6

1986    3.7

1987    4.2

1988    5.0

1989    5.1

1990    5.5

Is there a linear growth pattern in this data?

Let x be the year, and let y be the cost in billions of dollars of operating the IRS. Let’s do a scatterplot of these data.

Turn on the CASIO fx7400G.

or just press 2 when at the main menu screen.

Use your cursor arrows to move to the first cell in List1 and enter the years. After entering each year make sure to press to go down to the next cell.

Use your cursor arrows to move to the first cell in List2 and enter the cost in billions of dollar of operating the IRS for the respective year. After entering an amount make sure to press

to go down to the next cell.

Now we have to set the viewing window for our scatterplot.

Press (V-Window).

Set up the viewing window as follows: Xmin: 1969.5 Ymin: 0

&nb sp;                       max: 2008.5 max: 6.9

&nb sp;                       s c l: 2        s c l: 1

Press

Press (GRPH)

Press (Green more key)

Press (SET)

Scroll down and set the parameters as follows:

StatGraph1

G-Type:             Scat         Press if necessary.

XList:             List1         Press if necessary.

YList:             List2         Press if necessary.

Freq:             1                 Press if necessary.

M-Type:          x              This is your choice.

Press

Press (GRPH)

Press (GPH1)

Scatterplot will appear.

There might be a linear relationship between time in years and the cost of operating the IRS.

Use linear regression to find the "least-squares" line through the data.

Press ( X )

What appears is:

LinearReg

a = 0.33454

b = - 660.39

r = 0.98239

y = a x + b

Copy this equation into the grapher.

Press ( COPY )

Use your down cursor arrow to move to an empty slot and press

This stores the linear equation into the grapher and marks it as selected for graphing.

Now we are back in the STAT and we can draw the line among the data points by pressing

(DRAW).

Go to the GRAPH menu and trace along the line itself so as to make some projections about the cost of operating the IRS in 1997 and 2000.

Press

or just press 4 when at the main menu screen.

Press (DRAW)

Press (Trace).

Use your right cursor arrow to move to where x = 1997 and x = 2000.

My answers are (1997, 7.6863) and (2000, 8.69).

This means that in 1997 we expect the cost of

running the IRS to be about \$7.6 billion and

\$8.69 billion in 2000.

Press

User your down cursor arrow to move to the equation that was just drawn.

Press (SEL) This will de-select the equation.

Press

Turn off the CASIO fx7400G.

(OFF)