Press the Y= key and clear any equations.
Press the STAT key, use the arrow keys to select EDIT, and enter this data:
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These data points represent the cooling of a cup of chocolate over time. The numbers under the L1 heading are times in minutes. The numbers under the L2 heading are temperatures in degrees Fahrenheit.
Press the STAT key, select CALC, and choose option number 10: ExpReg. This will bring you back to the home screen, with ExpReg showing. Type "L1, L2" by pressing 2nd and 1, then comma, then 2nd and 2. Type "Y1" by pressing VARS, moving across to Y-VARS, choosing Function, and choosing option number 1. Your home screen should show:
ExpReg L1, L2, Y1
Now press ENTER. You will see something like:
y = a * b ^ x
a = 135.9519732
b = .9882916719
The variables a and b are the coefficients for the exponential equation that best fits the data you entered.
Press the StatPlot key (2nd and Y=). Choose Plot1 and press ENTER. Set the options as follows:
On
Type
Scatter
(the first icon)
XList
L1
YList
L2
Mark
Box
(the first icon)
Press the WINDOW key and enter the following:
Xmin
0
Xmax
50
Xscl
10
Ymin
50
Ymax
150
Yscl
10
These numbers will tell the graphing calculator what part of the graph it should display. When you do a stat plot, you need to look at your data and choose values that will include your data. You can let the calculator choose these values for you by pressing the ZOOM key and choosing option number 9: ZOOMSTAT.
Press the GRAPH key. The graph will show the individual data points as well as the best fit equation. Press the TRACE key and use the arrow keys to predict the future.
When will this cup of chocolate reach room temperature of 72 degrees?
When will it reach 32 degrees? What is wrong with this model?
To see exactly how closely your equation fits your data, press the VARS key and choose option number 5: Statistics. Move across to EQ and choose option number 7: r. This will display r on your home screen. Press ENTER to see the value of r.
r-.992267713
The variable r is the regression coefficient. It is a measure of how well the best fit line fits the data. It is always between 1 and -1. The closer it is to either 1 or -1, the better the fit.