RI 2025 H2 S6 Corr and Reg Lecture Notes

RAFFLES INSTITUTION H2 Mathematics 9758 Year 6 2025 ________________________________ Chapter S6: Correlation and Regression Page 1 of 26 Chapter S6: Correlation and Regression Syllabus will include • Use of scatter diagram to judge if there is a plausible linear relationship between the two variables • Correlation coefficient as a measure of the fit of a linear model to the scatter diagram • Interpreting the product moment correlation coefficient (in particular, values close to −1, 0 and 1) • Concepts of linear regression and method of least squares to find the equation of the regression line • Concepts of interpolation and extrapolation • Use of the appropriate regression line to make prediction or estimate a value in practical situations, including explaining how well the situation is modelled by the linear regression model • Use of a square, reciprocal or logarithmic transformation to achieve linearity CONTENT 1 Terminology 1.1 Describing Variables 1.2 Scatter Diagram 1.2.1 Producing a Scatter Diagram using the Graphing calculator 1.2.2 Interpreting Scatter Diagrams 2 Product Moment Correlation Coefficient 2.1 Calculating the Value of the Product Moment Correlation Coefficient 2.2 Properties of the Product Moment Correlation Coefficient 2.3 Interpreting Correlation 2.3.1 Importance of Scatter Diagram 2.3.2 Correlation does not imply Causation 3 Linear Regression 3.1 Least Squares Regression Line of y on x 3.2 Least Squares Regression Line of x on y 3.3 Calculating the Least Squares Regression Lines and Product Moment Correlation Coefficient using the Graphing calculator 4 Application and Interpretation 5 Linearisation of Data Appendix: Equivalence of the 2 Formulae for the Product Moment Correlation Coefficient

Raffles Institution H2 Mathematics 2025 Year 6 __________________________________________________________________________________________ ________________________________ Chapter S6: Correlation and Regression Page 2 of 26 INTRODUCTION Suppose that you are helping a proud mother to keep track of the weight of her newborn. After monitoring the infant’s weight ( y kg) for a period of time ( t days), you obtain the following data: t 7 32 71 97 188 273 409 y 4.43 4.88 6.31 7.18 10.63 13.60 17.95 Can you then tell the mother how much her baby will weigh by the next month? What about the next year? How certain would you be of your prediction? Can you further use your data to check if the infant’s growth is normal? In this chapter, we will deal with the skills required to answer the above questions. Statistical inference entails the study of correlation between variables and regression analysis, the art and science of finding these relationships between variables. Empirical data rarely corroborate exactly with theoretical mathematical models, hence the need for statistical analysis to accommodate such deviations. 1 TERM