Dawnbridge

TI-Nspire CX II field manual for IB Math

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21

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

Open a Lists & Spreadsheet page, name the first column x, and enter 0, 1, 2, 3, 4. Name the second column y, and enter 5, 8, 11, 20, 31.

*Document
RAD
AxByCD=10.5.21.8.32.11.43.20.54.31.A1
2

Run the regression: press → 4: Statistics → 1: Stat Calculations → A: Exponential Regression. Set X List = x and Y List = y, moving between fields with .

*Document
RAD
AxByCD=10.5.21.8.32.11.43.20.54.31.A1
Exponential Regression
X List:x[]▶
Y List:y[]▶
Frequency List:1▶
Category List:▶
1st Result Column:c[]▶
OKCancel
3

Set 1st Result Column to an empty column, such as c[], so the Nspire writes the regression equation and coefficients into the spreadsheet. Press to calculate.

*Document
RAD
ByCDE==ExpReg15.TitleExponent...28.RegEqna*b^x311.a4.905420.b1.579531.r²0.9933B1
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).