Dawnbridge

Casio fx-CG50 field manual for IB Math

AI HL only · 38 of 44

38

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

From the MAIN MENU, open Statistics. The fitted model is expressed with radian arguments, so first press (SET UP), set Angle = Rad, and press to return to the list editor.

2

Enter the ​x​-values 0 through 7 in List 1 and the ​y​-values 4.1, 5.9, 6.3, 5.1, 2.8, 1.7, 2.1, 3.9 in List 2, pressing after each entry.

RadNorm2
d/cReal
List 1List 2List 3List 4SUB104.1215.9326.3435.1542.8651.7762.1873.9
GRAPHCALCTESTINTRDIST▷
3

Press (CALC), then (SET) and set 2Var XList = List1, 2Var YList = List2, 2Var Freq = 1, then . Press (REG), then (▶) to reach the second strip, then (Sin).

RadNorm2
d/cReal
SinReg
a=2.40653
b=0.887935
c=0.0435259
d=3.98479
MSe=5.4397×10-03
y=a·sin(bx+c)+d
COPY
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.