I assume you know how to enter data in your calculator.
In Home folder run F6: NewProb to reset the configuration.
Press Apps, and select 6: data/Matrix editor. Select a new data set
Give it a name: here testing.
Press OK/ENTER, The data entry screen opens, enter your values.
When you finish press F2.PlotSetUp.
Press F1:define to configure Plot1. Choose Scatter, then choose a mark for the data point. I select 5:Dot. and press [ENTER
Select the data column X=c1, Y=c2
Press ENTER to save configuration. Press [CTRL] [GRAPH] On my TI92 the CTRL key is the [Diamond] key. On the following graph I changed the mark to a cross to see the data point better. I also played with the window dimension. You can also do that with ZoomStat. Th graph remind me of a parabola (I know I chose the exact values)
Now we have to find the equation that fits these data best.
You press APPS 6:Data/ Matrix editor but you select current to return to your data set. You are taken to the data entry editor (Figure 3 above). In that screen Press F5:Calc to edit the type of statistics you want
On first line select QuadReg quadratic regression, X is from column1, Y is from column 2. Store RegEQ The regression equation in say Y1(x)
Press ENTER to save to get the Regression Equatio. Here it is
As you can see I cheated: a perfect parabola. R^2 =1.
And here the best fit represented on same graph as the satistical data
Usually you have to try different regression models, until you find the one that fits best the experimental data.
As you can see I have gone a long way out of my way to show you all the steps.
I hope it helps you and others who wonder how to do regressions on a TI89. If someone does not understand these explanations, the blame does not rest with me.