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.

Ac_on.gif (1767 bytes)

Use your cursor arrows to highlight the STAT menu and press exe.gif (1747 bytes)

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 exe.gif (1747 bytes) 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 exe.gif (1747 bytes)

to go down to the next cell.

 

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

Press shiftf3.gif (1888 bytes) (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 quit.gif (1764 bytes)

Press f1.gif (1719 bytes) (GRPH)

Press flag.gif (1724 bytes) (Green more key)

Press f4.gif (1732 bytes) (SET)

Scroll down and set the parameters as follows:

StatGraph1

G-Type:             Scat         Press f1.gif (1719 bytes) if necessary.

XList:             List1         Press f1.gif (1719 bytes) if necessary.

YList:             List2         Press f2.gif (1726 bytes) if necessary.

Freq:             1                 Press f1.gif (1719 bytes) if necessary.

M-Type:          x              This is your choice.

Press quit.gif (1764 bytes)

Press f1.gif (1719 bytes) (GRPH)

Press f1.gif (1719 bytes) (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 f1.gif (1719 bytes) ( 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 f3.gif (1726 bytes) ( COPY )

Use your down cursor arrow to move to an empty slot and press exe.gif (1747 bytes)

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 f4.gif (1732 bytes)

(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 menu.gif (1772 bytes)

Use your cursor arrows to highlight the GRAPH menu and press exe.gif (1747 bytes)

or just press 4 when at the main menu screen.

Press f4.gif (1732 bytes) (DRAW)

Press shftf1.gif (1808 bytes) (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 quit.gif (1764 bytes)

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

Press f1.gif (1719 bytes) (SEL) This will de-select the equation.

 

Press menu.gif (1772 bytes)

Turn off the CASIO fx7400G.

shiftac.gif (1924 bytes) (OFF)