Regression Line And Correlation Coefficient

EVALUATION

Use the least square method to fit a regression line of y on x for the following data

X	1	4	5	7	8	10	12	16	19	20
Y	2	3	4	5	7	8	10	15	20	18

 Use the line obtained to find the value of y when x = 9

CORRELATION COEFFICIENT

DEFINITION:

The correlation coefficient determines the amount or degree of linear relationship between two variables. The correlation coefficient is represented by r

The characteristics of r are as follows:

1. The value of r is the same irrespective of the variable labelled x or y.
2. the value of r satisfies the inequality   -1< x < + 1
3. if r is close to +1, the variables are highly positively correlated. If r is close to -1 then, x and y are highly negatively correlated. If r is close to zero, the correlation between x and y is very low. There is no correlation between x and y when r = 0

 There are two methods of obtaining the correlation coefficient.

1. Pearson’s  coefficient of correlation or product moment correlation coefficient
2. Rank correlation coefficient.

GENERAL EVALUATION/REVISIONAL QUESTIONS

1. If Cos A = 24/25 and Sin B= 3/5, where A is acute and B is obtuse, find without using tables, the values of (a) Sin 2A (b) Cos 2B (c) Sin (A-B)
2. Use the addition formula to find the values of the following

(a)Sin 75⁰ (b) cos 75⁰ (c) tan 45⁰

• Calculate the Product moment correlation coefficient and the Spearman’s rank correlation coefficient.

X	50	45	43	30	30	43	23	43	25
Y	12	13.5	14	11	12	15	13.5	12	14

READING ASSIGNMENT: Read correlation and regression.Page313–320. Further Mathematics project 2.

WEEKEND ASSIGNMENT

Use the table below to answer questions 1 and 2.

Height	160	161	162	163	164	165
No of students	4	6	3	7	8	2

1. The mean of the distribution is

(a)  4875.1 cm ( b)  4001.2   (c) 3571.0cm  (d) 162.2 cm (e)  129.2cm

2.         The median of the distribution is

            (a)    160    (b)   162    (c)  163  (d)  164   (e)  165

3.         Calculate the standard deviation of 3,4, 5,6,7,8,9

             (a)   2      (b)     2.4     (c)     3.6    (d)   4.0        (e)    4.2

4.         Calculate the mean deviation of 6 ,  8 , 4  , 0  ,  4

            (a)  4 .0   (b) 3.6   (c)   3.0   (d)  2. 8   (e)  2 . 1

5.         The table below shows the rank Rx and Ry of marks scored by 10 candidates in an oral and

written tests respectively. Calculate the spearman’s rank correlation  coefficient   of   the   data.

Rx	1	2	3	4	5	6	7	8	9	10
Ry	2	3	4	1	6	5	8	7	10	9

(a)51/55    b) 6/55  c)49/55   d)54/55  e) 61/55

THEORY

1          The distribution of marks scored in statistics and mathematics by ten students is given in the table below:

Maths(x	11	20	23	42	48	50	57	64	80	90
Stat(y)	26	23	35	46	44	50	50	58	68	70

1. Plot a scatter diagram for the distribution
2. Draw an eye- fitted line of  best fit
3. Use your line to estimate the students marks in statistics  if  his mark in maths is  40

2.         The table below gives the marks obtained by members of  a class in maths and                                           physics examination

STUDENTS	A	B	C	D	E	F	G	H	I	J
Maths	85	75	59	43	74	69	62	80	54	63
Physic	92	72	62	48	85	73	46	74	58	50

1. Calculate the product moment correlation coefficient.
2. Comment on your result.