Question

which relationships would most likely be causal? select two options.
□ a positive correlation between the number of homework assignments completed and the grade on the exam
□ a positive correlation between the temperature in a canyon in the early spring and the number of snakes seen by hikers
□ a positive correlation between a childs shoe size and reading speed
□ a negative correlation between the time a glass of ice water sits on the counter and its temperature
□ a positive correlation between the number of students attending football games and the number of games that are won

Explanation:

• For the positive correlation between the number of homework assignments completed and the grade on the exam: Completing more homework (cause) likely leads to better understanding and thus a higher exam grade (effect).
• For the negative correlation between the time a glass of ice - water sits on the counter and its temperature: As time (cause) passes, the ice - water absorbs heat from the environment, so its temperature (effect) increases (negative correlation as time goes up, temperature (in terms of being 'cold') goes down in a sense of the initial ice - water state).
• The positive correlation between the temperature in a canyon in the early spring and the number of snakes seen by hikers: While there is a correlation, it's more of an association (snakes come out as it gets warmer, but the temperature change is a natural factor and not a direct causal manipulation in an experimental sense like homework).
• The positive correlation between a child’s shoe size and reading speed: Shoe size is related to age (as children grow, their shoe size increases), and reading speed also increases with age. It's a spurious correlation due to a common factor (age) rather than a direct causal relationship.
• The positive correlation between the number of students attending football games and the number of games that are won: There is no direct causal link. More students may attend because the team is winning (reverse causation possibility) or other factors like school spirit, but not a direct cause - effect where student attendance makes the team win.

Answer:

a positive correlation between the number of homework assignments completed and the grade on the exam, a negative correlation between the time a glass of ice water sits on the counter and its temperature.