Question

Find the value of pearson coefficient r.give your conclusion about the variables of the studies.

1.the diameter of the longest lichens growing on gravestones were measured. Data gathered show the following:

Age of gravestone x(years)=9,18,20,31,44,52,61,63,63

Diameter of lichen=2,3,4,20,22,41,35,22,28,32

2.In a biology experiment a number of cultures were grown in the laboratory. The numbers of bacteria,in millions,and their ages,In days ,are given below.

Age x(days)=1,2,3,4,5,6,7,8

No. Of bacteria Y(mil)=34,106,135,181,192,231,268,300

Answer 1

For the first part, there are 9 values for x variable and 10 for y variable. Since the number of values should be equal, I have assumed the last value to be 65.

$r = \frac{ \sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y}) }{ \sqrt{\sum_{i=1}^{n}(x_i-\bar{x})^2}\sqrt{\sum_{i=1}^{n}(y_i-\bar{y})^2}}$

From the table above,

$r=\frac{2311.2}{\sqrt{4141.4\times 1721.6}}=0.865$

The correlation coefficient is closer to one (positive). Thus, there is a strong positive association between Age of gravestone and diameter of lichen.

2.

From the table,

$r=\frac{1485.5}{\sqrt{42\times 53700.875}}=0.989$

The correlation coefficint is positive and close to one. Thus, these is a strong positive association between age in days and number of bacteria.