Correlation and regression lesson 1

Introduction

What is this type of graph called?

A scatter diagramWhat is a line of best fit?

Correlation

Lines of best fit always go through the mean of both sets of data

Scatter diagramsScatter diagrams illustrate bivariate data that is when two variables are

compared.

On your whiteboard draw scatter diagrams to illustrate positive correlation, negative correlation and no correlation.

How well the variables fit to a straight line of best fit is the measure of correlation they exhibit.

The two types of correlation are positive and negative.

Drawing lines of best fit• Draw suitable axis and plot the given points• Calculate the mean for both variables• Draw the line of best fit (through the middle of the points and the mean

of both sets of data)• Use the line of best fit to make estimates

Time x 10 15 20 25 30

Weight y 5.1 4.2 3.5 3.1 2.8

Product Moment Correlation Coefficient (PMCC)

The product moment correlation coefficient r is a statistical measure of how well each data point lies on a straight line

It has a value between 1 (perfect positive correlation) and -1 (perfect negative correlation).

In the exam questions it is acceptable to use a calculator to find r.

Using a calculator to calculate PMCC (r)

x 1 3 5

y 3 7 11

Stats mode

Enter the data as two lists

GRPH F1 twice (should draw a scatter graph for the data)

CALC (F1

F2 which looks like a X, then F2 ( a + bx)

This should give the results a = 1, b = 2 and r = 1 the other results can be ignored

Matching activity

One for you to try