The table shows the number of fans sold at a store during days of various temperatures:
| \text{Temperature (\degree C)} | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
|---|---|---|---|---|---|---|---|---|
| \text{Number of fans sold} | 12 | 13 | 14 | 17 | 18 | 19 | 21 | 23 |
Is there a causal relationship between the variables? Explain your answer.
Determine whether the following are examples of variables with no correlation:
The age of a child and their shoe size.
The age of a child and their height.
The age of a child and the number of pets owned.
The age of a child and the amount of adjectives learned.
Determine whether the following describe a relationship that is correlated but not causal:
The sales of ice cream and increase in temperature.
The number of hours worked and how much money is made for a given person.
The amount of showers had in a day and the amount of the water bill.
The amount of rainfall received, and level of water in a lake.
The larger the dimensions of a rectangular verandah, the more area.
The season of the year and the number of water related injuries.
Increase in temperature, and the level of mercury in a thermometer.
The number of students shouting in class and the number of detentions received.
Determine whether the following describe a causal relationship and not just a correlation:
An individual's decision to work in construction and his diagnosis of skin cancer.
The number of minutes spent exercising and the amount of calories burned.
A decrease in temperature and the increase in attendance at an ice skating rink.
As a child's weight increases, so does her vocabulary.
Determine if following statements are true or false:
There is a causal relationship between the number of times a coin lands on heads and the likelihood that it lands on heads on the next flip.
There is a causal relationship between the amount of weight training a person does and their strength.
A study found a strong positive association between the temperature and the number of beach drownings.
Does this mean that the temperature causes people to drown? Explain your answer.
Is the strong correlation found a coincidence? Explain your answer.
A study found a strong correlation between the approximate number of pirates out at sea and the average world temperature.
Does this mean that the number of pirates out at sea has an impact on world temperature?
Is the strong correlation found a coincidence? Explain your answer.
If there is correlation between two variables, is there causation?
It is discovered that the number of crimes recorded in a city in a given week correlates with the percentage of a city’s population that is homeless. The correlation is strong and positive.
Is there a causal relationship between the two variables? Explain your answer.
The scatterplot shows the relationship between the height of water \left(H\right) in a lake measured after an amount of rainfall \left(R\right) in the area:
Describe the correlation between the variables.
Is there a causal relationship between the variables? Explain your answer.
The following table shows the concentration of H+ ions in a chemical solution and the pH of the solution:
| Concentration | 0.0001 | 0.0005 | 0.001 | 0.005 | 0.01 | 0.05 |
|---|---|---|---|---|---|---|
| pH | 4 | 3.3 | 3 | 2.3 | 2 | 1.3 |
Describe the correlation between the variables.
Given that the pH is calculated using the concentration of H+ ions, state whether there is a causal non-linear relationship between these two variables.
The following graph and table show the number of people who drowned in a swimming pool and the corresponding number of movies that Nicolas Cage starred in each year:
Describe the correlation between the two variables.
Is there are causal relationship between the two variables?
| Number of drownings | Number of films Nicolas Cage appeared in | |
|---|---|---|
| 1999 | 109 | 2 |
| 2000 | 102 | 2 |
| 2001 | 102 | 2 |
| 2002 | 98 | 3 |
| 2003 | 85 | 1 |
| 2004 | 95 | 1 |
| 2005 | 96 | 2 |
| 2006 | 98 | 3 |
| 2007 | 123 | 4 |
| 2008 | 94 | 1 |
| 2009 | 102 | 4 |
The following table shows the amount of mozzarella cheese consumed per capita in the US and the corresponding number of civil engineering degrees awarded in the US each year:
Describe the correlation between the two variables.
Is there are causal relationship between the two variables?
| Per capita consumption of mozzarella cheese (US) | Civil engineering doctorates awarded (US) | |
|---|---|---|
| 2000 | 9.3 | 480 |
| 2001 | 9.7 | 501 |
| 2002 | 9.7 | 540 |
| 2003 | 9.7 | 552 |
| 2004 | 9.9 | 547 |
| 2005 | 10.2 | 622 |
| 2006 | 10.5 | 655 |
| 2007 | 11 | 701 |
| 2008 | 10.6 | 712 |
| 2009 | 10.6 | 708 |
The following table of values describes the number of divorces occurring in the US state of Alabama (per 1000 people) and the corresponding cost of bananas in the US each year:
Describe the correlation between the two variables.
Is there are causal relationship between the two variables?
| \text{Divorces} \\ \text{per 1000 people} \\ \text{in Alabama} | \text{Cost of bananas} \\ \text{(dollars} \\ \text{per pound)} | |
|---|---|---|
| 1999 | 5.7 | 0.5 |
| 2000 | 5.5 | 0.47 |
| 2001 | 5.4 | 0.48 |
| 2002 | 5.4 | 0.5 |
| 2003 | 5.2 | 0.53 |
| 2004 | 4.9 | 0.62 |
| 2005 | 4.9 | 0.57 |
| 2006 | 4.9 | 0.59 |