Dawnbridge

TI-Nspire CX II field manual for IB Math

AI HL only · 39 of 45

39

Sinusoidal regression

AI HL

Enter periodic paired data, run sinusoidal regression, and read the fitted model y=asin(bx+c)+d.

Goal

Fit a sinusoidal model to ​(0,4.1),  ​(1,5.9),  ​(2,6.3),  ​(3,5.1),  ​(4,2.8),  ​(5,1.7),  ​(6,2.1),  ​(7,3.9), where ​x​ is in radians.

1

Sinusoidal regression only works in radians, so check the document setting is Radian (press → 7: Settings & Status → 2: Document Settings, or change it on the page's status bar).

2

Open a Lists & Spreadsheet page, name the first column x, and enter 0 through 7. Name the second column y and enter 4.1, 5.9, 6.3, 5.1, 2.8, 1.7, 2.1, 3.9.

*Document
RAD
AxByCD=10.4.121.5.932.6.343.5.154.2.8A1
3

Run the regression: press → 4: Statistics → 1: Stat Calculations → C: Sinusoidal Regression. Set X List = x, Y List = y, and 1st Result Column = c[], moving between fields with , then press .

*Document
RAD
ByCDE==SinReg14.1TitleSinusoid...25.9RegEqna*sin(b*x+c)+d36.3a2.4065345.1b0.88793552.8c0.0435259B1
Result

The calculator uses the form ​y=asin(bx+c)+d, so to three significant figures the model is ​y=2.41sin(0.888x+0.0435)+3.98.

Your turn

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

  1. 1

    Fit a sinusoidal model ​y=asin(bx+c)+d​ to ​(0,7.5),  ​(1,8.8),  ​(2,8.7),  ​(3,6.6),  ​(4,4.5),  ​(5,2.9),  ​(6,3.4),  ​(7,5.6), where ​x​ is in radians.

  2. 2

    Fit a sinusoidal model to ​(0,3.1),  ​(1,4.6),  ​(2,4.3),  ​(3,2.1),  ​(4,1.3),  ​(5,2.4),  ​(6,4.5),  ​(7,4.4), where ​x​ is in radians.

  3. 3

    Fit a sinusoidal model to ​(0,9.2),  ​(1,12.4),  ​(2,12.3),  ​(3,8.5),  ​(4,5.1),  ​(5,6.3),  ​(6,10.1),  ​(7,13.1), where ​x​ is in radians.