Answer to Question #287913 in Statistics and Probability for Leyman

Question

A group of researchers conduct a research about fertility among Malaysian citizens. Data obtained from the research are as followed:

A = number of siblings that a married couple has

B = number of children that a married couple has

Table 1

A

3

4

4

6

7

9

B

2

5

5

6

4

4

Determine the statistics analysis method if you want to find the relationship between A and B.

Is there exists a relationship between A and B?

Plot a scatter diagram for Table 1. Draw the regression line on the diagram.

Answer 1

The statistical analysis method used to determine whether a relationship exist between the independent variable $A$ and the dependent variable $B$ is correlation. Correlation involves determining the correlation coefficient $r$ which measures the strength and direction of relationship between two variables.

To determine whether a relationship exist between $A$ and $B$, we find the value of the correlation coefficient $r$ as follows.

$r={n\sum ab-\sum a\sum b\over \sqrt{(n\sum a^2-(\sum a)^2)(n\sum b^2-(\sum b)^2)}}$

From the data above,

$n=6\\ \sum a=33\\\sum b=26\\\sum ab=146\\\sum a^2 =207\\\sum b^2=122$

Therefore, the correlation coefficient is given as,

$r={6(146)-(33\times 26)\over\sqrt{(6(207)-33^2(6(122-26^2)}}\\ r={18\over\sqrt{153\times56}}={18\over92.5635}=0.19(2dp)$

Therefore, a weak positive relationship exist between the number of siblings that a married couple has (A) and the number of children that a married couple has (B).

Entering the following commands in $R,$ produces the scatter diagram below.

>A=c(3,4,4,6,7,9)

>B=c(2,5,5,6,4,4)

>plot(A,B, main="A scatter diagram of B against A")

To draw a regression line on the scatter diagram, we enter the following commands

>A=c(3,4,4,6,7,9)

>B=c(2,5,5,6,4,4)

>abline(lm(B~A), color="blue")

These commands draws the required regression line which is blue in color on the scatter plot.