8. Two Variable Data Analysis

Worksheet

1

Describe the correlation between the following pairs of variables as positive, negative or none:

a

The age of a child and their clothing size

b

The age of a person and how funny they are

c

Temperature and the number of heaters sold

2

Determine whether the following statements are true or false:

a

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.

b

There is a causal relationship between the amount of weight training a person does and their strength.

3

A study found a strong positive association between the temperature and the number of beach drownings.

a

Does this mean that the temperature causes people to drown? Explain your answer.

b

Is the strong correlation found a coincidence? Explain your answer.

4

A study found a strong correlation between the approximate number of pirates out at sea and the average world temperature.

a

Does this mean that the number of pirates out at sea has an impact on world temperature?

b

Is the strong correlation found a coincidence? Explain your answer.

c

If there is correlation between two variables, is there causation?

5

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 |

a

Is there a causal relationship between the variables?

b

Consider the correlation coefficient, r, for temperature and number of fans sold. Is the value of r positive or negative?

6

Describe in words the meaning of the following correlation coefficients:

a

1

b

0

c

- 1

7

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?

8

Consider the following graph:

a

Explain why it would it be suitable to calculate the correlation coefficient for this set of data.

b

Describe the relationship between the variables in terms of strength and direction.

9

Consider the following graph:

Explain why it would not be appropriate to calculate the correlation coefficient for this data set.

10

For each of the following graphs, write down an appropriate correlation coefficient:

a

b

c

d

11

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.

12

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.

13

Describe the relationship between the variables in the following studies:

a

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.

b

A study found that the correlation coefficient between population of a city and number of speeding fines recorded was found to be 0.83.

c

A study found that the correlation coefficient between length of hair and length of fingernails was found to be 0.07.

d

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.

14

For each of the following sets of data:

i

Use technology to calculate the correlation coefficient. Round your answer to two decimal places.

ii

Describe the correlation between the the two variables in terms of strength, direction and form.

a

x | 3 | 6 | 9 | 12 | 15 | 18 | 21 |
---|---|---|---|---|---|---|---|

y | -7 | -7.35 | -7.77 | -7.56 | -7.63 | -8.05 | -7.28 |

b

x | 9 | 11 | 13 | 15 | 17 | 19 | 21 |
---|---|---|---|---|---|---|---|

y | -4 | -4.5 | -4.55 | -4.6 | -4.65 | -4.7 | -4.75 |

c

x | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|

y | 7 | 7.4 | 7.88 | 7.64 | 7.72 | 8.2 | 7.32 |

d

x | 2 | 6 | 7 | 14 | 17 | 22 |
---|---|---|---|---|---|---|

y | -0.2 | -0.9 | -0.6 | -2.0 | -2.4 | -2.0 |

e

x | 4 | 5 | 9 | 13 | 17 | 21 |
---|---|---|---|---|---|---|

y | -0.2 | -0.7 | -0.4 | -1.9 | -2.4 | -0.9 |

f

x | 3 | 6 | 9 | 14 | 14 | 22 |
---|---|---|---|---|---|---|

y | 0 | 1.64 | 1.25 | 3.74 | 3.82 | 0.22 |

15

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 |

a

Construct a scatterplot for the data.

b

Use technology to calculate the correlation coefficient. Round your answer to two decimal places.

c

Hence, describe what happens to the sales of coffee as the temperature increases.

Sign up to access Worksheet

Get full access to our content with a Mathspace account

Pose and solve problems involving rates, percentages, and proportions in various contexts, including contexts connected to real-life applications of data, measurement, geometry, linear relations, and financial literacy.

Create a scatter plot to represent the relationship between two variables, determine the correlation between these variables by testing different regression models using technology, and use a model to make predictions when appropriate.