SS3 First Term Further Mathematics Lesson Note – Correlation and Regression

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WEEK 6

TOPIC: CORRELATION AND REGRESSION

CONTENT:

• Concept of corellation as emasure of realtionship
• Scatter diagrams
• Rank correlation
• Tied rank

Subtopic 1:

Concept of correlation as measure of relationships

We have considered in our last discussions on finding measures of location and the spread. We call such data univariate data. In this discussion, we want to look at situation when two variables are observed on each unit of the variables. When considering marks of a student in physics and mathematics. This is called bivariate data. We can also consider the height and weight together.

When we consider the two sets of univariate data as one bivariate, Association is formed. When a student scored high mark in maths we want to see if he will score hgih in English or he will score low. Then we want to find out it the two marks can be considered. When we do that an association is formed, when we begin to find out how we can use the marks in mathematics to predict the mark in English then we are looking at correlation between them. When two variables x and y are related, then we say they are correlation.

Correlation coefficient is the measure of the degree of association between x and y. There are two things we shall consider:

• When both variables are quantitatively measured such as marks, height and age.
• When the variable values are put in ranks form 1^st, 2^nd, 3^rd …

Sub-Topic 2: Scatter Diagram

Suppose x and y are random variables with measured values of students marks in mathematics and chemistry. If the scores are recorded as (x₁, y₁), (x₂, y₂)­, … (x_2n, y_n)­, then, we

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