Question

a) assuming the relation is linear, a correlation of - 0.772 shows a weak relation in a positive direction. b) assuming the relation is linear, a correlation of - 0.772 shows a weak relation in a negative direction. c) assuming the relation is linear, a correlation of - 0.772 shows a strong relation in a positive direction. d) there was a correlation of 0.44 between gdp and continent. choose the correct answer below. a. correlation cannot be less than one. b. correlation cannot be greater than zero. c. continent is a quantitative variable. correlation does not apply. d. continent is a categorical variable. correlation does not apply.

Explanation:

Step1: Recall correlation properties

The correlation coefficient $r$ ranges from - 1 to 1, i.e., $-1\leq r\leq1$. Also, correlation is calculated between two quantitative variables.

Step2: Analyze part (a)

A correlation coefficient can be between - 1 and 1, so it can be less than one and greater than zero. Option A is wrong.

Step3: Analyze continent variable

Continent is a categorical variable (e.g., Africa, Asia, etc.). Correlation is not applicable for categorical variables. Options B and C are wrong as they wrongly assume continent is quantitative.

Step4: Analyze part (b)

A correlation of - 0.772 shows a strong negative linear relationship (since $|r| = 0.772$ is close to 1 and the sign is negative). The statement in part (b) mis - interprets the sign and strength of the correlation.

Answer:

a) D. Continent is a categorical variable. Correlation does not apply.
b) The statement is wrong because a correlation of - 0.772 shows a strong negative linear relationship, not a weak relationship in a positive direction.