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Casio TEAMS Grant Algebra Lessons II

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'a do a scatterplot of these data.

  1. Turn on the CASIO FX7400G.
  2. Use your cursor arrows to highlight the STAT menu and press  
    or just press 2 when at the main menu screen.
  3. 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 to go down to the next cell.
  4. 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 to go down to the next cell.

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

  1. Press Shift Ò F3 (V-Window).

    Set up the viewing window as follows:
      
       Xmin: 0    Ymin: 80.5
       max : 39   max : 115
       scl : 5    scl : 10
     
  2. Press  
  3. Press (GRPH)
  4. Press (Green more key)
  5. 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.
  1. Press
  2. Press (GRPH)
  3. Press (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.

  1. Press ( X )

    What appears is: LinearReg
    a = 2.21374
    b = 51.2849
    r = 0.96974

    y = a x + b
  2. Copy this equation into the grapher.
  3. Press ( COPY )
  4. Find 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 average amount of rainfall that will produce average carrot weights of 85.6 kg and 118.8 kg.

  1. Press
  2. Use your cursor arrows to highlight the GRAPH menu and press or just press when at the main menu screen.
  3. Press (DRAW)
  4. Press (Trace).
  5. 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  
Press (SEL) This will de-select the equation.
Press

Turn off the CASIO FX7400G
 (OFF)