Question

for the following pair of variables, state the units that might be used to measure each variable. then state whether you believe that they are correlated. if you believe they are correlated, state whether the correlation is positive or negative. explain your reasoning.

latitude and the average high temperature in june

to measure latitude, the unit degrees of latitude might be used.
to measure temperature, the unit degrees fahrenheit might be used.

what correlation, if any, is there between the variables?

a. there is a positive correlation because the average high temperature in june tends to increase when latitude increases.
b. there is a negative correlation because the average high temperature in june tends to increase when latitude decreases.
c. the variables are not correlated.

Explanation:

Identify the variables and their units

Using the Latitude Measurement knowledge point

• Latitude measures distance north or south of the equator in degrees of latitude.
• Average high temperature in June is measured in degrees Fahrenheit (or degrees Celsius).

Analyze the relationship between latitude and temperature

Using the Correlation Analysis knowledge point

• As latitude increases (moving further away from the equator toward the poles), the average high temperature in June tends to decrease.
• Conversely, as latitude decreases (moving closer to the equator), the average high temperature in June tends to increase.
• Since the variables move in opposite directions, this represents a negative correlation.

Evaluate the multiple-choice options

Using the Correlation Analysis knowledge point

• Option A states there is a positive correlation, which is incorrect because temperature decreases as latitude increases.
• Option B states there is a negative correlation because temperature tends to increase when latitude decreases (or decrease when latitude increases). This correctly describes the inverse relationship.
• Option C states there is no correlation, which is incorrect.

Answer:

• (A) There is a positive correlation because the average high temperature in June tends to increase when latitude increases.
• (B) There is a negative correlation because the average high temperature in June tends to increase when latitude decreases. (Correct answer)
• (C) The variables are not correlated.