IBDP Mathematics Applications & Interpretations SL Chapter 6 Notes
Modelling relationships: linear correlation of bivariate data
STUDY NOTES FOR MATHEMATICS – CHAPTER 6 – Modelling relationships: linear correlation of bivariate data
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All DP mathematics courses serve to accommodate the diverse range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. The aims of these courses are to enable students to: develop mathematical knowledge, concepts, principles, logical, critical and creative thinking, employ and refine their powers of abstraction and generalization. Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives.
In this chapter we consider bivariate data, which means data has two variables recorded for each individual. In most real-world situations, there will not be an exact relationship between the two variables. Our goal is to find which model best fits the data and measure how strong the relationship between the variables is. We delve into topics such as correlation when using scatter plots by drawing the line of best fit to classify the strength between variables. However, as this method is subjective, we use Pearson’s product moment correlation coefficient r as it is a more precise measure of strength. In order to find the equation of the line which best fits the data, we use a method known as linear regression. This method minimises the distance between the line and the data points, known as a residual.
- Chapter 1 Measuring space: accuracy and 2D geometry
- Chapter 2 Representing space : non right angled trigonometry and volumes
- Chapter 3 Representing and describing data: descriptive statistics
- Chapter 4 Dividing up space : coordinate geometry , lines , Voronoi diagrams
- Chapter 5 Modelling constant rate of change: linear function
- Chapter 6 Modelling relationships: linear correlation of bivariate data
- Chapter 7 Quantifying uncertainty: probability, binomial and normal distributions
- Chapter 8 – Testing for validity: Spearman’s hypothesis testing and x^2 test for independence
- Chapter 9 Modelling relationships with functions: power f unctions
- Chapter 10 Modelling Rates of change: Exponential and logarithmic functions
- Chapter 11 Modelling Periodic Phenomena: Trigonometric Functions
- Chapter 12 Analyzing Rates of Change: Differential Calculus
- Chapter 13 Approximating Irregular Spaces: Integration