Question

Your Economics instructor assigns your class to investigate factors associated with the gross domestic product (GDP) of nations. Each student examines a different factor (such as life expectancy, literacy rate, etc.) for a few countries and reports to the class. Apparently some of your classmates do not understand Statistics very well because you know several of their conclusions are incorrect. Explain the mistakes in their statements below: a) "My correlation of -0.772 shows that there is almost no association between GDP and infant mortality rate." b) "There was a correlation of 0.44 between GDP and continent." c) "There was a very strong correlation of 1.22 between life expectancy and GDP." d) "The correlation between literacy rate and GDP was 0.83. This shows that countries wanting to increase their standard of living should invest heavily in education." e) "The correlation of 0.90 means that as GDP goes up, imports drop by 90%."

Answer 1

Answer:

The Correlation analysis “R” is measured to compute the strength of relationship among variables. Moreover, the value of correlation is calculated among -1 to +1. Which implies that if the computed value is near to -1 then there will be strong but negative relation and if near to +1 then it is strong but relation among the variable. However zero is consider as neutral point.  

A. The computed value of correlation is - 0.772. The value identifies that that there is a strong but negative association among the variables (GDP and infant mortality rate).

B. The correlation analysis cannot computed among the variables continent and GDP because "continent" is a categorical variable not quantitative.  

C. The computed value of correlation is higher than 1. Thus, the statement implies that there is a very strong relationship among life expectancy and GDP which is incorrect. As the association cannot be higher than 1.  

D. There is a strong relationship among literacy rate and GDP as the relationship is nearer to 1. Furthermore, the association among literacy rate and GDP doesn’t suggest the causation.

E. The computed correlation among the variables is 0.90. Which indicated that the variables goes up. That is, when the GDP goes down the import is also decrease and when GDP increases the import increases Thus, the there is a positive correlation.