Describe the correlation between the following pairs of variables as positive, negative or none:
The age of a child and their clothing size
The age of a person and how funny they are
Temperature and the number of heaters sold
Determine whether the following statements are true or false:
There is a causal relationship between the number of times a coin has landed on heads previously, 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?
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?
Consider the correlation coefficient, r, for temperature and number of fans sold. Is the value of r positive or negative?
Describe in words the meaning of the following correlation coefficients:
1
0
- 1
Data set A has a correlation coefficient of \dfrac{1}{10} while data set B has a correlation coefficient of \dfrac{3}{5}. Which data set has the stronger correlation?
Consider the following graph:
Explain why it would it be suitable to calculate the correlation coefficient for this set of data.
Describe the relationship between the variables in terms of strength and direction.
Consider the following graph:
Explain why it would not be appropriate to calculate the correlation coefficient for this data set.
For each of the following graphs, write down an appropriate correlation coefficient:
A researcher plotted the life expectancy of a group of men against the number of cigarettes they smoke a day. The results were recorded and the correlation coefficient r was found to be - 0.88.
Describe the correlation between the life expectancy of a man and the number of cigarettes smoked per day.
A researcher was evaluating the relationship between the number of years in education a person completes and the number of pets they own. The results were recorded and correlation coefficient r was found to be - 0.3.
Describe the correlation between a person's years of education and the number of pets they own.
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 sets of data:
Use technology to calculate the correlation coefficient. Round your answer to two decimal places.
Describe the correlation between the the two variables in terms of strength, direction and form.
| x | 3 | 6 | 9 | 12 | 15 | 18 | 21 |
|---|---|---|---|---|---|---|---|
| y | -7 | -7.35 | -7.77 | -7.56 | -7.63 | -8.05 | -7.28 |
| x | 9 | 11 | 13 | 15 | 17 | 19 | 21 |
|---|---|---|---|---|---|---|---|
| y | -4 | -4.5 | -4.55 | -4.6 | -4.65 | -4.7 | -4.75 |
| x | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|
| y | 7 | 7.4 | 7.88 | 7.64 | 7.72 | 8.2 | 7.32 |
| x | 2 | 6 | 7 | 14 | 17 | 22 |
|---|---|---|---|---|---|---|
| y | -0.2 | -0.9 | -0.6 | -2.0 | -2.4 | -2.0 |
| x | 4 | 5 | 9 | 13 | 17 | 21 |
|---|---|---|---|---|---|---|
| y | -0.2 | -0.7 | -0.4 | -1.9 | -2.4 | -0.9 |
| x | 3 | 6 | 9 | 14 | 14 | 22 |
|---|---|---|---|---|---|---|
| y | 0 | 1.64 | 1.25 | 3.74 | 3.82 | 0.22 |
Noah is a coffee vendor. He records the maximum temperature of the day and the number of coffees sold. The results are recorded in the following table:
| \text{Maximum Temperature (\degree{C})} | 28 | 32 | 31 | 33 | 31 | 26 | 25 | 29 | 35 |
|---|---|---|---|---|---|---|---|---|---|
| \text{Number of coffees} | 17 | 37 | 25 | 39 | 23 | 7 | 19 | 34 | 42 |
Construct a scatterplot for the data.
Use technology to calculate the correlation coefficient. Round your answer to two decimal places.
Hence, describe what happens to the sales of coffee as the temperature increases.