Question

Determine whether each pair of variables is likely to have a positive correlation, a negative correlation, or no correlation. Number of calories consumed and amount of weight gained: Years of heavy smoking and life expectancy: Suppose that a statistical study shows that the correlation between two variables, X and Y, is r = 0.01. What can you say about the relationship between X and Y?

Answer 1

1. Number of calories consumed and amount of weight gained:

A person who consumes a large number of calories is expected to gain a lot of weight.

The greater the number of calories consumed, the greater is the expected weight of the person.Hence, the quantities are likely to be positively correlated.

Positive correlation.

2. The more a person smokes, the greater is the likelihood of dying early.

Hence, life expectancy should decrease with an increase in the number of years of heavy smoking.

Negative correlation.

3. The value of the Pearson correlation index r is extremely small (0.01). The correlation is extremely weak. Hence, it may concluded that X and Y have no correlation.

No correlation.