Question

Explain what the following correlation tell you about two sets of data

Answer 1

Part a)

Solution;

A correlation coefficient of 0.4 implies a relatively weak positive association between two sets of data. There is a notable small increment in one data set as the other increases.

Part b)

Solution;

A correlation coefficient of -0.96 implies a strong negative association between two sets of data. An increase in the values of one data set amounts to a decrease in the values of the other data set by approximately the same magnitude.

Part c)

Solution;

A correlation coefficient of -0.02 implies a weak negative association between two sets of data. An increase in the values of one data set amounts to a negligible decrease in the values of the other data set.

Part d)

Solution;

A correlation coefficient of 1.0 implies a perfect positive association between two sets of data. An increase in the values of one data set amounts to an increase in the values of the other data set by exactly the same magnitude. A scatter plot would reveal that the line y =x fits the data well.

Part e)

Solution;

A correlation coefficient of 0.86 implies a strong positive association between two sets of data. An increase in the values of one data set amounts to an increase in the values of the other data set by approximately the same magnitude.

Explanation:

Correlation coefficient measures the degree of association between two variables or data sets. Correlation coefficients can be positive or negative and may imply weak or strong association between two data sets.

A correlation coefficient of less than 5 is implies a weak association while a value greater than or equal to 5 implies a strong association. Finally, a correlation of 1.0 implies perfect association.

Answer 2

a. r = 0.4. The correlation is positive. It's a weak association

b. r = -0.96 The correlation is negative. It is a very strong association

c. r = -0.02 The correlation is negative. It is a very weak association

d. r = 1. The correlation is positive. It's a perfect association

e. r = 0.86. The correlation is positive. It is a very strong association

Explanation:

r is known as Pearson's linear correlation coefficient measures how strong the correlation between two variables is.

`0 <r \leq 1` It is a positive correlation

A positive correlation means that when the variable x increases the variable y also increases.

`-1\leq r <0` It is a negative correlation

A positive correlation means that when the variable x increases the variable y decreases.

`r = 0` means there is no correlation between the variables.

a. r = 0.4. The correlation is positive. It's a weak association

b. r = -0.96 The correlation is negative. It is a very strong association

c. r = -0.02 The correlation is negative. It is a very weak association

d. r = 1. The correlation is positive. It's a perfect association

e. r = 0.86. The correlation is positive. It is a very strong association