Describe the type of correlation the following correlation coefficients indicate:
A pair of data sets have a correlation coefficient of \dfrac{1}{10} while a second pair of data sets have a correlation coefficient of \dfrac{3}{5}. Which pair of data sets have the stronger correlation?
Describe the relationship between the variables in the following studies:
A study found that the correlation coefficient between heights of women and probability of being turned down for a promotion was found to be - 0.90.
A study found that the correlation coefficient between population of a city and number of speeding fines recorded was found to be 0.83.
A study found that the correlation coefficient between length of hair and length of fingernails was found to be 0.07.
A study found that the correlation coefficient between number of bylaws a council has about dog breeding and number of dogs available for adoption at the local shelter was found to be 0.55.
For each of the following graphs, write down an appropriate value for the correlation coefficient:
The scatter diagram shows data of the height of a ball kicked into the air as a function of time:
Which type of model is appropriate for the data, Linear or Non-linear?
Write down a possible value of Pearson’s correlation coefficient, r, for this set of data.
The scatter diagram shows data of a person's level of happiness as a function of their age:
Which type of model is appropriate for the data, linear or non-linear?
Write down a possible value of Pearson’s correlation coefficient, r, for this set of data.
The scatter diagram shows data of the height of an object after it is pushed off a rooftop as a function of time:
Which type of model is appropriate for the data, linear or quadratic?
Write down a possible value of Pearson’s correlation coefficient, r, for this set of data.
Explain whether or not the following statements are true or false.
If there is correlation between two variables, there must be causation.
If there is causation between two variables, there must be correlation.
Explain the difference between coincidence, causation, and a confounding factor.
For each of the following data examples, determine if there is a causal relationship between the variables:
The number of times a coin lands on heads and the likelihood that it lands on heads on the next flip.
The amount of weight training a person does and their strength.
Many trees lose their leaves in winter. Does this mean that cold temperatures cause the leaves to fall?
A geography teacher observes that many of the students who are involved in the music programme do better at tests. Does this mean that learning music makes students better at geography?
The table shows the number of fans sold at a store during days of various temperatures:
| \text{Temperature } (\degree\text{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?
Without calculating, consider the correlation coefficient, r, for temperature and number of fans sold. Is the value of r positive or negative?
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?
A survey was run to collect data on the number of hats being worn at school each day, compared to the temperature of that day. The r-value for the resulting scatterplot was 0.72, including any outliers.
State a conclusion that can be drawn from this data.
One of the surveyors suggests that both the temperature and number of hats being worn on a day are higher when it is sunnier. Explain what this suggestion implies.
For each of the following correlations, state whether you think it is coincidence, correlation, or a confounding factor. If you think there is a confounding factor, state it.
The marriage rate in New York correlates with the number of blunt object murders.
The battery life of a phone correlates with how many years the phone has been in use.
The number of jumpers being worn at school correlates with the number of heaters that are turned on that day.
The number of broken umbrellas on the street correlates with the number of shop signs that have fallen over.
The money spent on movie tickets in the US correlates with the average daily precipitation in Pennsylvania.
The global mean temperature correlates with the size of the polar icecaps.
The high tide of a lake correlates with the day of the week.