Question

an economics instructor assigns a 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 the classmates do not understand statistics very well because several of their conclusions are incorrect. explain the mistakes in comments a and b below. a) explain the mistake in the following statement. “my very low correlation of - 0.772 shows that there is almost no association between gdp and infant mortality rate.” choose the correct answer below. a. assuming the relation is linear, a correlation of - 0.772 shows a strong relation in a negative direction. b. assuming the relation is linear, a correlation of - 0.772 shows a weak relation in a positive direction. c. assuming the relation is linear, a correlation of - 0.772 shows a weak relation in a negative direction. d. assuming the relation is linear, a correlation of - 0.772 shows a strong relation in a positive direction.

Explanation:

Step1: Understand correlation coefficient

The correlation coefficient ($r$) ranges from - 1 to 1. A value close to -1 indicates a strong negative linear relationship, a value close to 1 indicates a strong positive linear relationship, and a value close to 0 indicates a weak or no linear relationship.

Step2: Analyze - 0.772

The correlation coefficient of -0.772 is close to - 1. This implies a strong negative linear relationship. That is, as one variable (e.g., GDP) increases, the other variable (e.g., infant mortality rate) decreases.

Answer:

A. Assuming the relation is linear, a correlation of - 0.772 shows a strong relation in a negative direction.