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IB Maths AI HL 4.13 Non-linear regression Question Bank

Practise IB Mathematics HL 4.13 by applying non-linear regression methods to exam-style questions.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation HL
Level
HL

Exam points

  • identify the mathematical structure, variable or representation
  • select and apply the correct theorem, formula or algorithm
  • check the result using units, domain, graph or logical reasoning

AHL 4.13 (HL)—Non-linear regression question 1

[Maximum number: 3]

Juliet is a sociologist who wants to investigate if income affects happiness amongst doctors. This question asks you to review Juliet's methods and conclusions.
Juliet obtained a list of email addresses of doctors who work in her city. She contacted them and asked them to fill in an anonymous questionnaire. Participants were asked to state their annual income and to respond to a set of questions. The responses were used to determine a happiness score out of 100 . Of the 415 doctors on the list, 11 replied.

Question (a)

(a)

Juliet wants to create a model to predict how changing annual income might affect happiness scores. To do this, she assumes that annual income in dollars, X, is the independent variable and the happiness score, Y, is the dependent variable.

She first considers a linear model of the form

Y=a X+b
[ 3 ]

Question (i)

(i)

Find the coefficient of determination for each of the two models she considers.

[ 2 ]

Question (ii)

(ii)

Hence compare the two models.

Juliet decides to use the coefficient of determination to choose between these two models.

[ 1 ]
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