Everything Maths Grade 12

11.4 CHAPTER 11. STATISTICS

(a) Draw a scatter plot of the data on graph paper.

(b) Identify and describe any trends shown in the scatter plot.

(c) Find the equation ofthe least squares line byusing algebraic methodsand draw the line on

your graph.

(d) Use your equation topredict the height of a student with footlength 21 , 6 cm.

(e) Use your equation topredict the footlength ofa student 176 cm tall.

3. Repeat the data in Question 2 and find the regression line using a calculator.

More practice video solutions or help at http://www.everythingmaths.co.za

(1.) 01b2 (2.) 01b3 (3.) 01b4

Correlation Coefficients EMCDA

Once we have appliedregression analysis to aset of data, we would like to have a number that tells
us exactly how well thedata fits the function. Acorrelation coefficient, r, is a tool that tells us towhat
degree there is a relationship between two setsof data. The correlationcoefficient r∈ [−1; 1] when
r =− 1 , there is a perfect negative correlation, when r = 0, there is no correlationand r = 1 is a
perfect positive correlation.

y

x

����

���

��

���

�

��

��

��

� ��

���

�������

��

��

��

��

�

�����

�

�����

�

���

���

�����

�

��

��

y

x

���

��

��

�� �

�

��

�

��

��

�

�

�

�

� �

� �

�

� �� �

�

�

�

�

� �

��

�

����

� ��

��

��

���

���

�

��� �

�

�

�

�

�� �

�

�

�

�

y

x

��

�

�

�

�

�

�

�

�

� �

�

�

�

�

�

�

�

� ��

�

� �

� �

� � �

� �

�

�

�

��

�

�

�

�

� ��

�� �

�

�

�

�

�

�

�

�

�

��

�� �

�

�

�

��

�

�

���

� �

y

x

�

� � � �

� �

� �

�� � �

�

� � �

� � �� �

� �

� � �

�

� �

� �

�

�

�

�

��

�

� ��

� �

�

�

�

�� �

�� �

y

x

�

��

��

��

��

�

�

����

��

��

��

��

��

���

��

��

� �

��

��

�

�

��

�

�

��

�

��� �

�

���

���

�

�

��

��

�

��

�

��

���

�

�

��

�

�

�

�

�

�

�

�

Positive, strong Positive, fairly strong Positive, weak Noassociation Negative, fairly strong

r≈ 0 , 9 r≈ 0 , 7 r≈ 0 , 4 r = 0 r≈− 0 , 7

We often use the correlation coefficient r^2 in order to examine thestrength of the correlation only.

In this case:

r^2 = 0 no correlation

0 < r^2 < 0 , 25 very weak

0 , 25 < r^2 < 0 , 5 weak

0 , 5 < r^2 < 0 , 75 moderate

0 , 75 < r^2 < 0 , 9 strong

0 , 9 < r^2 < 1 very strong

r^2 = 1 perfect correlation

The correlation coefficient r can be calculated usingthe formula

r =

1

n− 1

��x− ̄x

sx

��

y− ̄y

sy

�