Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004 AND Mathematical Studies Standard Level Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman Oxford University Press, 2012

Pearson’s Product-Moment Correlation Coefficient This is a number that tells us the strength of the relationship between any two sets of data that are thought to be related. r

Pearson’s Product-Moment Correlation Coefficient Pearson’s Product-Moment Correlation Coefficient (r), can take all values between –1 and +1 inclusive. – When r = –1 there is a perfect negative correlation between the data sets. – When r = 0 there is no correlation. – When r = +1 there is a perfect positive correlation between the data sets. – A perfect correlation is one where all the plotted points lie on a straight line.

Pearson’s Product-Moment Correlation Coefficient Pearson’s Product-Moment Correlation Coefficient (r), can take all values between –1 and +1 inclusive. – When 0 < r < 0.25 the correlation is very weak. – When 0.25 < r < 0.50 the correlation is weak. – When 0.50 < r < 0.75 the correlation is a moderate. – When 0.75 < r < 1 the correlation is strong.

FORMULA Pearson’s Product-Moment Correlation Coefficient (r) IB Note: For the EXAM students will only be expected to use their GDC to find the value of r.

s y represents the standard deviation of the variable Y; s x represents the standard deviation of the variable X; s xy represents the covariance of the variables X and Y. Covariance is a measure of how much two variables change together. FORMULA Pearson’s Product-Moment Correlation Coefficient (r)

Average speed in the metropolitan area and age of drivers The r-value for this association is Describe the association. Practice No correlation to very very weak

Sue investigates how the volume of water in a pot affects how long it takes to boil on the stove. The results are given in the table. Find Pearson’s correlation coefficient between the two variables. Practice r = 0.988

In an experiment a vertical spring was fixed at its upper end. It was stretched by hanging different weights on its lower end. The length of the spring was then measured. The following readings were obtained. Load (kg) x Length (cm) y It is given that the covariance S xy is (v)Write down the correlation coefficient, r, for these readings. (vi) Comment on this result. (i) Write down the mean value of the load, (ii) Write down the standard deviation of the load. (iii) Write down the mean value of the length, (iv) Write down the standard deviation of the length. Practice

Correlation Coefficient on the TI 84 Turn on your Diagnostics – Press ‘Mode’ then scroll down to ‘STAT DIAGNOSTICS’ and set to ‘on’. Enter the data in L1 and L2 Go to ‘STAT’ and ‘CALC’ – 4:LinReg (ax + b) – Xlist as L1 and Ylist as L2 – Leave FreqList blank

At a father-son camp, the heights of the fathers and their sons were measured. On your GDC: a)Draw a scatter plot of the data. b)Calculate r c)Describe the correlation between the variables. Practice

The data given below for a first-division football league show the position of the team and the number of goals scored On your GDC: a)Draw a scatter plot of the data. b)Calculate r c)Describe the correlation between the variables. Practice Position Goals Position Goals

The heights and shoe sizes of the students at Learnwell Academy are given in the table below. On your GDC: a)Draw a scatter plot of the data. b)Calculate r c)Describe the correlation between the variables. Practice Height (x) cm Shoe Size