~In many practical applications, models (equation types) are chosen to fit data points (either collected or given in the problem). Once the model equation is determined, it can be used for describing all possible data points from that problem and predicting or estimating these points. It will be up to you to determine which model seems to be appropriate for your data points.
~Plotting these points (scatter plot) will give you a good idea of the type of model to choose. The independent variable (x) is on the horizontal axis while the dependent variable (y) is on the vertical axis.
~Now, you will undertake the problem of finding the best model (equation type) that best fits your data.
~Once a model is chosen and a equation is determined, predictions can be made.
~The model used may or may not be appropriate for the data. Your knowledge of model types and the scatter plot is important to determine this result.
~Popular model types (equation forms) are as follows:
1) Linear: y=ax+b or y=a+bx, depending on which menu you choose on the TI-83.
2) Quadratic: y=ax2+bx+c
3) Cubic: y=ax3+bx2+cx+d
4) 4th Power (Quartic): y=ax4+bx3+cx2+dx+e
5) Natural log (ln): y=a+lnx
6) Exponential: y=a+bx
7) Logistic curve: y= c / (1+ae-bx)
8) Trig curve (sine curve): y=a sin(bx+c)
~Values of the constants a,b,c,d, & e are determined by the TI-83
~TI-83 Procedures~
1) Collect the data or data may be given.
2) Determine the dependent & independent variables.
3) Enter your data in lists using, STAT, edit, enter, move to L1, enter independent variable values (x), move to L2, enter dependent variable values (y).
4) Choose a friendly viewing window compatible with your data. Clear all equations from y= menu.
5) Get a scatter plot by pressing 2nd STAT PLOT, enter, ON, enter, move curser to top left plot, enter, move curser down, L1 for X List, L2 for Y List, pick type of mark for your plot, enter, press graph.
6) Make a decision on the type of equation model you will use.
7) Press STAT, move to CALC, move curser down to one of the menus 4 to end, enter, 2nd L1, 2nd L2, enter.
8) The TI-83 will give the values for the constants associated with the equation model chosen.
9) Substitute these values into the model equation.
10) This equation may now be used for describing your data set and for prediction purposes.
11) Many different models can be found for the same data set, but usually, one will be the best.