Question

Which relationships could have a negative correlation? Check all that apply.

Answer 1

The relationships that could have a negative correlation are as follows. 

1. number of hours on video games and test scores 
  - Obviously, if you spend too much time on video games your test scores will be affected negatively. 
2. speed of the car and minimum stopping distance 
   - If the car speeds up, it needs a maximum stopping distance. That's why there's a traffic law about speed limit so as to avoid accidents. 
3. outside temperature and amount of heating bill
- The amount of heating bill is greatly dependent on the outside temperature. If it's winter, probably you'll get a higher heating bill but if it's summer, surely you'll get otherwise. So, if you're living in California and Florida, well, you're lucky enough. But if you're on the other side of the USA, just face the reality. 

The remaining 2 options have a positive correlation.

- The average running speed and total race time have a positive correlation because the total race time is dependent on the runner's speed. Both the average speed and total time can be solved by simply using a formula derived from that same formula.  

  - There are some research studies that prove our head's circumference is particularly correlated with age. Findings show that the older you get, the greater your head circumference is, so the wiser you become. 

Answer 2

A) Number of hours on video games and test scores
If more number of hours are spent on the video games, then the test scores will be less. This indicate that these two are negatively correlated.

B) Speed of a car and minimum stopping distance
If the speed of a car is more, it will need a larger minimum stopping distance. This indicates that these two are positively correlated

C) Average running speed and total race time
If the total race time is more, the average running speed will be less. This indicates that these two are negatively correlated

D) Adult’s head circumference and age
Adult's head circumference do not change much with the age. So these two does not seem to be correlated

E) Outside temperature and amount of a heating bill
If outside temperature is lower, the amount of heating bill will be higher. So these two are negatively correlated.

Therefore, the correct options to this question are:
1) number of hours on video games and test scores
2) average running speed and total race time
3) outside temperature and amount of a heating bill