How to do linear, exponential, power, polynomial, sine and logistic regression on the Casio fx-CG50
Least-squares lines and curves: linear, exponential, power, quadratic, cubic, sinusoidal and logistic models. Exact keystrokes for the fx-CG50 first, then the other calculators, a worked example you can check your answers against, the mistakes that cost marks, and the same thing in Desmos.
When you need it
AI students fit models in almost every Paper 2: the regression line of y on x and predictions from it (SL), and exponential, power, quadratic, cubic, sinusoidal and logistic models (HL, plus the coefficient of determination R²). AA students need the linear regression line and r. Quote the equation with its coefficients to 3 s.f.
Practise it: SL AI bivariate data · SL AI exponential modelling · SL AI sinusoidal modelling · HL AI non-linear regression · SL AA bivariate data.
Keystrokes on your calculator
Pick your calculator: the page remembers it next time.
Regression on the Casio fx-CG50
Written for OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell). Casio fx-CG50: graphic (GDC).
- MENU 2 (STATISTICS). Type the x values into List 1 and the y values into List 2, pressing EXE after each. (Clear an old list first: highlight the list, F6 (▷) F4 (DELETE-ALL) F1 (Yes).)
- F2 (CALC) F6 (SET): 2Var XList = List1, 2Var YList = List2, 2Var Freq = 1. EXIT.
- F3 (REG) F1 (X) F1 (ax+b). The screen shows a, b, r, r² and MSe.
- Other models from the REG menu: F3 (X²) quadratic, F4 (X³) cubic; F6 (▷) then F1 (Log), F2 (Exp: F1 ae^bx or F2 ab^x), F3 (Pwr) axᵇ, F4 (Sin), F5 (Lgst) logistic.
- F5 (COPY) pastes the equation into the GRAPH Y= list; F6 (DRAW) plots it over the scatter diagram.
- Sin regression: set SHIFT MENU (SET UP) → Angle = Rad first. The model is y = a·sin(bx + c) + d.
- Logistic: y = c ÷ (1 + a·e^(−bx)). IB writes it L ÷ (1 + Ce^(−kx)), so L = c, C = a, k = b.
- Quadratic, cubic and the curve models show R² (the coefficient of determination), not r.
- Predict from the stored model: in RUN-MATRIX use OPTN F5 (STAT) → ŷ (7.5 F2 ŷ in linear mode).
Regression on the TI-84 Plus CE
Written for OS 5.8.x. TI-84 Plus CE: graphic (GDC); also the TI-84 Plus CE Python / CE-T Python Edition.
- stat 1: Edit. Clear old data: move onto the L1 heading, clear, enter. Type the x values in L1 and the y values in L2.
- Turn diagnostics on once: mode → STAT DIAGNOSTICS: ON (on older OS versions: 2nd 0 (CATALOG) → DiagnosticOn → enter enter). Without it r and r² are not shown.
- stat → CALC → 4: LinReg(ax+b). Xlist: L1, Ylist: L2, Store RegEQ: Y1 (alpha trace → Y1). Calculate.
- Other models in the same CALC list: 5: QuadReg, 6: CubicReg, 9: LnReg, 0: ExpReg (y = a·bˣ), A: PwrReg, B: Logistic, C: SinReg.
- SinReg gives y = a·sin(bx + c) + d and works in radians.
- Logistic gives y = c ÷ (1 + a·e^(−bx)).
- Storing to Y1 lets you predict with Y1(7.5) on the home screen.
Regression on the TI-Nspire CX II
Written for OS 6.x. TI-Nspire CX II: graphic (GDC), non-CAS; the CX II CAS is not allowed in IB, A Level or IGCSE exams.
- Add a Lists & Spreadsheet page (ctrl doc → Add Lists & Spreadsheet). Name column A xs and column B ys in the top row, then type the data.
- menu → Statistics → Stat Calculations → Linear Regression (mx+b). X List: xs, Y List: ys, Save RegEqn to: f1. OK.
- The results (m, b, r², r) appear in the next empty columns.
- Other models in the same menu: Quadratic, Cubic, Power, Exponential (y = a·bˣ), Logarithmic, Sinusoidal, Logistic (d = 0).
- Predict with f1(7.5) on a Calculator page.
- Logistic (d = 0) is y = c ÷ (1 + a·e^(−bx)).
Worked example
(a) x = 1, 2, 3, 4, 5, 6; y = 3.1, 4.9, 7.2, 8.8, 11.1, 12.9. Find the regression line of y on x, r, and predict y when x = 7.5. (b) Same x, y = 2.0, 3.1, 4.4, 6.6, 9.8, 14.5. Fit y = a·bˣ and predict y at x = 8.
Answers (checked with Python)
(a) y = 1.97714x + 1.08, r = 0.999191; at x = 7.5, y ≈ 15.9. (b) y = 1.37065 × 1.48177ˣ (equivalently y = 1.37065e0.393240x); at x = 8, y ≈ 31.9 (an extrapolation, so less reliable).
Common calculator mistakes
- Mixing up a and b: fx-CG50 ax+b and TI LinReg(ax+b) use a for the gradient; the ClassWiz and TI LinReg(a+bx) use b for the gradient.
- Leaving old data in the lists (or a frequency list set to List 3 from a previous question).
- Regression of x on y when the question wants y on x: the x values go in the first list.
- Quoting r for a non-linear model: for quadratics and curves use R².
- Sine regression in degree mode gives nonsense coefficients.
- Predicting far outside the data range (extrapolation) without saying it may be unreliable.
Do it in Desmos
Not in the exam. Desmos is not an approved calculator for IB exams, so never rely on it for Paper 2. It is excellent for learning, checking a GDC answer and building graphs for your Internal Assessment (IA).
- Add a table (+ → table) with the data in x₁ and y₁.
- Type y₁ ~ m x₁ + b. Desmos shows m, b, r and R² and draws the line.
- For an exponential model type y₁ ~ a b^{x₁}. Desmos fits the curve directly; your GDC fits a straight line to ln y. Turn on "log mode" in the regression's options to get the GDC's answer.
- Sinusoidal and logistic work the same way: y₁ ~ a sin(b x₁ + c) + d, y₁ ~ L/(1 + C e^{−k x₁}).
The interactive graph loads here when you scroll to it.
Or open desmos.com/calculator and type:
a table of the datay_{1}~ mx_{1}+b
More calculator skills
Sources
- Casio fx-CG50 Software User's Guide, OS 3.70 (PDF) : Casio fx-CG50, OS 3.80 (menus unchanged from OS 3.60 onwards as far as we can tell).
- TI-84 Plus CE guidebook (Texas Instruments) : TI-84 Plus CE, OS 5.8.x.
- TI-Nspire CX II guidebooks (Texas Instruments) : TI-Nspire CX II, OS 6.x.
- Desmos Help Center for the Desmos functions.
Menu names are taken from each manufacturer's manual for the OS versions shown. Menus can move slightly between OS updates: if a screen looks different on yours, the manual for your version is the reference, and please tell us so we can update this page. Worked-example answers were recomputed independently in Python.