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?
For each of the following graphs, write down an appropriate estimate for the correlation coefficient:
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.
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.
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.
| 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 | 2.0 | 2.4 | 2.0 | 0.6 | 0.9 | 0.2 |
| x | 1 | 4 | 7 | 10 | 13 | 16 | 19 |
|---|---|---|---|---|---|---|---|
| y | -1 | -1.7 | -1.77 | -1.84 | -1.91 | -1.98 | -2.05 |
| x | 4 | 6 | 8 | 13 | 17 | 21 |
|---|---|---|---|---|---|---|
| y | 0.4 | 0.9 | 0.6 | 1.7 | 2.4 | 1.7 |
| x | 4 | 5 | 9 | 13 | 17 | 21 |
|---|---|---|---|---|---|---|
| y | -0.2 | -0.7 | -0.4 | -1.9 | -2.4 | -0.9 |
| x | 2 | 6 | 9 | 12 | 15 | 22 |
|---|---|---|---|---|---|---|
| y | 0 | 1.5 | 1.2 | 2.9 | 3.7 | 0.2 |
| 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 |
Sean is a hotdog vendor. He records the maximum temperature of the day and the number of hotdog sold. The results are in the following table:
| \text{Maximum temperature (\degree C)} | 30 | 34 | 33 | 35 | 33 | 28 | 27 | 31 | 37 | 29 |
|---|---|---|---|---|---|---|---|---|---|---|
| \text{Number of hotdogs} | 18 | 38 | 26 | 40 | 24 | 8 | 20 | 35 | 43 | 38 |
Construct a scatter plot to represent the data in the table.
Calculate the correlation coefficient to two decimal places.
As the temperature increases, describe what happens to the sales.