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