Dawnbridge

TI-84 Plus CE field manual for IB Math

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24

Exponential regression

All courses

Fit y=a⋅bx to paired data and read the fitted parameters.

Goal

Fit an exponential model to ​(0,5),  ​(1,8),  ​(2,11),  ​(3,20),  ​(4,31).

1

Turn diagnostics on so the calculator shows ​r: press to open the catalogue, choose DiagnosticOn, and press .

2

Open the list editor with → 1: Edit. Enter the x-values 0, 1, 2, 3, 4 in L1 and the y-values 5, 8, 11, 20, 31 in L2.

NORMALFLOATAUTOREALRADIANMP
L1L2L3L4L505------------------18211320431------------
3

Run exponential regression: press , move right to CALC, then press for 0:ExpReg. Set Xlist = L1 (type L1 with ) and Ylist = L2 (type L2 with ); leave FreqList and Store RegEQ blank, clearing them with if anything is there. Then choose Calculate.

NORMALFLOATAUTOREALRADIANMP
ExpReg
a=4.904832668
b=1.578600873
r²=0.9932588275
r=0.9966237141
Result

The calculator uses the form ​y=a⋅bx, so the model is ​y≈4.90(1.58)x, with ​r≈0.997.

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    Fit an exponential model ​y=a⋅bx​ to ​(0,4),  ​(1,6),  ​(2,10),  ​(3,15).

  2. 2

    Fit an exponential model to the (noisy) data ​(0,3.1),  ​(1,4.1),  ​(2,6.0),  ​(3,8.1).

  3. 3

    Fit an exponential model to ​(0,80),  ​(1,63),  ​(2,52),  ​(3,41),  ​(4,33).