SAJC 2022 Correlation and Linear Regression Lecture Notes (Teacher)

SAJC 2022 JC 2 H1 Mathematics Correlation and Linear Regression Page 1 of 59 Chapter 7 (Statistics) Correlation and Linear Regression Objectives At the end of the chapter, students should be able to: (a) Understand that bivariate data consists of the values of two variables (independent and dependent variables) obtained from the same sample expressed in ordered pairs; (b) Use the graphic calculator to plot the scatter diagram for a set of bivariate data to determine if there is a linear relationship between the two variables; (c) Understand that the cor relation coefficient is a measure of the fit of a scatter diagram to a linear model; (d) Calculate the product moment correlation coefficient for a set of bivariate data using a graphic calculator, and relate the value (in particular, values close to -1, 0 and 1) to the appearance of the scatter diagram; [Note: zero correlation does not necessarily imply ‘no relationship’, but rather ‘no linear relationship’.] (e) Understand that a high correlation between two variables does not necessarily imply one directly causes the other; (f) Understand the concepts of linear regression and ‘least squares’ with reference to the scatter diagram; (g) Use a graphic calculator to find the equation of the least squares regression line, and interpret its slope and intercept; [Note: A differ ent line will be obtained if we interchange the independent and dependent variables.] (h) Understand the concepts of extrapolation and interpolation of data, and use the appropriate regression line to make prediction or estimate a value in practical situations.

SAJC 2022 JC 2 H1 Mathematics Correlation and Linear Regression Page 2 of 59 Contents 7.1 Introduction 7.1.1 Bivariate Data 7.1.2 Independent vs Dependent Variables 7.2. Scatter Diagrams 7.2.1 Drawing Scatter Diagrams 7.2.2 Interpreting Scatter Diagrams 7.3 Product Moment Correlation Coefficient, r 7.3.1 What is Product Moment Correlation Coefficient, r? 7.3.2 Calculation of Product Moment Correlation Coefficient, r using Formula 7.3.3 Calculation of Product Moment Correlation Coefficient, r using Graphic Calculator 7.3.4 Properties of Product Moment Correlation Coefficient, r 7.3.5 Limitations of Product Moment Correlation Coefficient, r 7.3.6 The Effects of Transformation on Product Moment Correlation Coefficient, r 7.4 Linear Regression 7.4.1 Types of Regression Lines 7.4.2 Using Graphic Calculator to find Equations of Regression Lines 7.4.3 Least Squares Regression Lines of y on x 7.4.4 Least Squares Regression Lines of x on y 7.4.5 Properties of Regression Lines 7.5 Interpolation and Extrapolation 7.6 Self-Reading Examples Resources 1. A Concise Course in A Level Statistics with Worked Examples By J. Crawshaw and J. Chambers 2. A Comprehension Guide: H2 Mathematics for “A” Level, Volume 2 By Frederick Ho, David Khor