Look at the effects of growth hormone (gibberellic acid)
on plant height with a 0.1 molar solution:
Acid Plant height in one week
20 ml 18.5 cm
30 ml 20.7 cm
40 ml 45.2 cm
50 ml 62.3 cm
60 ml 10.6 cm
What is the estimated plant height at 10 ml of acid?
What is the estimated plant height at 25 ml of acid?
With your TI-83 or 84 graphing calculator,
First, make sure the Diagnostics are on. To make sure,
PRESS 2nd 0 to get CATALOG
Press and hold the down arrow key till pointer gets to
DiagnosticOn
(If you go too far use the up arrow to get the pointer
back to it)
Press ENTER ENTER
You should read
DiagnosticOn
Done
Press CLEAR
---------------------------
Make sure Plot1 is on.
Press Y= to get STAT PLOT then up arrow to highlight
Plot1 then ENTER
Press 2nd MODE to get Quit (to go back to main screen)
---------------------------
Make sure TABLE SETUP is on ASK for the independent
variable
Press 2nd WINDOW to get TBLSET
Press down arrow twice and right arrow once to
highlight Ask
Press 2nd MODE to get Quit (to go back to main screen)
-------------------------
Press STAT ENTER
Enter the values 20, 30, ..., 60 in L1
Enter the values 18.5, 20.7, .... 10.6 in L2
Press STAT, then right arrow to highlight CALC
Scroll with down arrow to highlight LinReg(ax+b) and
press ENTER
Press VARS, then right arrow to highlght Y-VARS, then
press ENTER ENTER
Read
LinReg
y=ax+b
a=.258
b=21.14
r²=.0358107396
r=.1892372573
That value or r² is not near 1, so CLEAR.
-------------------------------------------
Press STAT again, then right arrow to highlight
CALC
Scroll with down arrow this time to highlight
QuadReg and press ENTER
Press VARS, then right arrow to highlight Y-VARS,
then press ENTER ENTER
You should read
QuadReg
y=ax²+bx+c
a=-.0822857143
b=6.840857143
c=-94.06
r²=.5457879872
That value or r² is also not near 1, so CLEAR.
-----------------------------------------------
Press STAT again, then right arrow to highlight
CALC
Scroll with down arrow this time to highlight
CubicReg and press ENTER
Press VARS, then right arrow to highlight Y-VARS,
then press ENTER ENTER ENTER
Read
CubicReg
y=ax³+bx²+cx+d
a=-.0075916667
b=.8287142857
c=-27.01797619
d=288.56
r²=.9922768519
Now that value of r² is very near 1 so we have found a
good regression function for the data. However, let's
try the quartic regression to see if its r² value is
even closer to 1. If it's not closer then we'll come
back to this one.
-----------------------------------------------
Press STAT again, then right arrow to highlight
CALC
Scroll with down arrow this time to highlight
QuartReg and press ENTER
Press VARS, then right arrow to highlight Y-VARS,
then press ENTER ENTER ENTER
Read
QuartReg
y=ax4+bx³+cx²+dx+e
a=-1.320833E-4
b=.0135416667
c=-.3807916667
d=2.115633333
|e=41.3
Press the down arrow to read
R²=1
Now that value of R² is exactly 1, so we have found
the best possible standard regression function for
the data.
To see the data points plotted and watch the graph go
through them, press ZOOM, then scroll down to highlight
ZoomStat
Then press ENTER
---------------------------
Now to get the answer you want, press 2nd GRAPH to
get TABLE
Enter 10 under the X column, press ENTER,
read 36.6 under Y1 column
Enter 25 under the X column, press ENTER,
read 16.195 under the Y1 column
Edwin
