SITE-A teams: Lesson 2

 

Framers believe that there is a linear relationship between the average amount of rainfall during the growing season of carrots and the average weight of a carrot produced. Scientists have set up an experiment in a controlled environment and gathered the data below:

Average        Average

Rainfall        Weight

(cm)            (kg)

15                 87

18                 89

20                 93

22                 101

23                 102

25                 108

 

Is there a linear relationship between the average amount of rainfall and the average weight?

Let x be the average amount of rainfall, and let y be the average weight of a carrot produced. Let’s do a scatterplot of these data.

Turn on the CASIO fx7400G.

image2a.gif (1706 bytes)

Use your cursor arrows to highlight the STAT menu and press image1e.gif (1717 bytes)

or just press image2b.gif (1675 bytes) when at the main menu screen.

 

Use your cursor arrows to move to the first cell in List1 and enter the average amount of rainfall. After entering an amount make sure to press image1e.gif (1717 bytes) to go down to the next cell.

 

Use your cursor arrows to move to the first cell in List2 and enter the respective average weight of a carrot produced. After entering an amount make sure to press image1e.gif (1717 bytes) to go down to the next cell.

 

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

Press image2c.gif (1809 bytes) (V-Window).

Set up the viewing window as follows: Xmin: 0 Ymin: 80.5

                                                                    max: 39 max: 115

                                                                    s c l: 5 s c l:         10

Press image1c.gif (1733 bytes)

Press image1j.gif (1688 bytes) (GRPH)

Press image1b.gif (1704 bytes)(Green more key)

Press image1f.gif (1692 bytes) (SET)

Scroll down and set the parameters as follows:

StatGraph1

G-Type: Scat                  Press image1j.gif (1688 bytes) if necessary.

XList: List1                  Press image1j.gif (1688 bytes) if necessary.

YList: List2                  Press image2d.gif (1695 bytes) if necessary.

Freq: 1                  Press image1j.gif (1688 bytes) if necessary.

M-Type: x                  This is your choice.

Press image1c.gif (1733 bytes)

Press image1j.gif (1688 bytes) (GRPH)

Press image1j.gif (1688 bytes) (GPH1)

Scatterplot will appear.

There might be a linear relationship between the average amount of rainfall and the average weight of a carrot produced.

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

Press image1j.gif (1688 bytes) ( X )

What appears is: LinearReg

                                a = 2.21374

                                b = 51.2849

                                r = 0.96974

y = a x + b

Copy this equation into the grapher.

Press image2e.gif (1693 bytes) ( COPY )

Use your down cursor arrow to move to an empty slot and press image1e.gif (1717 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 image1f.gif (1692 bytes)

(DRAW).

Go to the GRAPH menu and trace along the line itself so as to make some projections about the average amount of rainfall that will produce average carrot weights of 85.6 kg and 118.8 kg.

Press image1h.gif (1733 bytes)

Use your cursor arrows to highlight the GRAPH menu and press image1e.gif (1717 bytes)

or just press image1i.gif (1676 bytes) when at the main menu screen.

Press image1f.gif (1692 bytes) (DRAW)

Press shftf1.gif (1808 bytes) (Trace).

Use your right cursor arrow to move to where y = 85.6 and y = 118.8.

My answers are (15.5, 85.597) and (30.5, 118.8).

This is to say that an average amount of rainfall of

15.5 cm during the growing season of carrots

would produce a crop of carrots where the

average weight of a carrot is approximately

85.6 kg. Similarly, an average amount of

rainfall of 30.5 cm during the growing

season of carrots would produce a crop of

carrots where the average weight of a carrot

is approximately 118.8 kg.

Press image1c.gif (1733 bytes)

Press image1j.gif (1688 bytes) (SEL) This will de-select the equation.

 

Press image1h.gif (1733 bytes)

Turn off the CASIO fx7400G.

image1k.gif (1829 bytes) (OFF)