Correlation & Causation

Identifying Correlation & Causation

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Positive Correlation

Recall if the dependent variable (the y) increases as the independent variable (the x) increases, we say we have a positive correlation.

Negative Correlation

if the dependent variable (the y) decreases as the independent variable increases (the x), we say there is a negative correlation.

Correlation

So if one thing increases or decreases as another thing increases, we say there is a correlation.

Multiple Choice

Students who had less sleep did not tend to burn more or fewer calories during class.

Is this showing a correlation?

• Yes

• No

Explanation

There is no suggestion of correlation here. The phrase "did not tend" indicates that there is NO correlation.

Multiple Choice

A teacher noticed that students' ages increased as their needs for blankies decreased.

Is this showing a correlation?

• Yes

• No

Explanation

As one thing increased (ages), another thing decreased (needs for blankies).

This is the essence of negative correlation. There IS correlation.

Multiple Choice

A banker noticed that the cost of the car his clients drove did not really indicate the size of their bank accounts.

Is this showing a correlation?

• Yes

• No

Explanation

The phrase "did not really indicate" tells us that there is NO correlation.

He is kind of saying that he has seen men with big bank accounts driving old beaters and he has seen men with small bank accounts driving brand new expensive cars.

Multiple Choice

A yoga instructor collected student data. He found that students who had less sleep did not tend to burn more or fewer calories during class. What can he conclude?

• There is no correlation between amount of sleep and number of calories burned.

• There is a correlation between amount of sleep and number of calories burned. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between amount of sleep and number of calories burned. There is probably also causation. This is because there is likely an increase in the number of calories burned with an increase in the amount of sleep.

Explanation

We see from the following that amount of sleep and number of calories burned tend not to vary together.

"students who had less sleep did not tend to burn more or fewer calories during class"

Thus, there is no correlation between amount of sleep and number of calories burned.

Multiple Choice

A yoga instructor collected student data. He found that students who had less sleep did not tend to burn more or fewer calories during class.

Which of these answers could never be right based on the given information?

• There is no correlation between amount of sleep and number of calories burned.

• There is a correlation between amount of sleep and number of calories burned. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between amount of sleep and number of calories burned. There is probably also causation. This is because there is likely an increase in the number of calories burned with an increase in the amount of sleep.

Important Tip!

• There is no correlation between amount of sleep and number of calories burned.

• There is a correlation between amount of sleep and number of calories burned. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between amount of sleep and number of calories burned. There is probably also causation. This is because there is likely an increase in the number of calories burned with an increase in the amount of sleep.

Multiple Choice

A traffic study determined that a larger city population indicates a longer commute time for drivers. What can we say from this information?

• There is no correlation between commute time and city population.

• There is a correlation between commute time and city population. However, there is no causation. This is because there is an increase in the commute time with an increase in the city population.

• There is a correlation between commute time and city population. There may or may not be causation. Further studies would have to be done to determine this.

Explanation

We see from the following that commute time and city population tend to vary together.

"a larger city population indicates a longer commute time for drivers"

Thus, there is a correlation between commute time and city population.

However, we cannot be sure there is causation without further studies.

Multiple Choice

A company found that employees who start work earlier do not necessarily drink more or less coffee. Which statement is most likely true?

• There is no correlation between start time and amount of coffee consumed.

• There is a correlation between start time and amount of coffee consumed. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between start time and amount of coffee consumed. However, there is no causation. This is because there is probably an increase in the amount of coffee consumed with an earlier start time.

Explanation

We see from the following that start time and amount of coffee consumed tend not to vary together.

"employees who start work earlier do not necessarily drink more or less coffee"

Thus, there is no correlation between start time and amount of coffee consumed.

Multiple Choice

A company found that employees who start work earlier do not necessarily drink more or less coffee.

Which statement cannot be a correct answer given that we are just working with data?

• There is no correlation between start time and amount of coffee consumed.

• There is a correlation between start time and amount of coffee consumed. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between start time and amount of coffee consumed. However, there is no causation. This is because there is probably an increase in the amount of coffee consumed with an earlier start time.

• There is no correlation between start time and amount of coffee consumed.

• There is a correlation between start time and amount of coffee consumed. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between start time and amount of coffee consumed. However, there is no causation. This is because there is probably an increase in the amount of coffee consumed with an earlier start time.

Multiple Choice

A phone company determined that a higher income indicates that a customer has a more expensive calling plan. What does the analysis show?

• There is no correlation between income and calling plan price.

• There is a correlation between income and calling plan price. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between income and calling plan price. There is probably also causation. This is because there is an increase in the calling plan price with an increase in income.

Explanation

We see from the following that income and calling plan price tend to vary together.

"a higher income indicates that a customer has a more expensive calling plan"

Thus, there is a correlation between income and calling plan price.

However, we cannot be sure there is causation without further studies.

Multiple Choice

A wine store conducted a study. It showed that a customer does not tend to buy more or fewer bottles when more samples are offered. What can we conclude?

• There is no correlation between number of bottles bought and number of samples offered.

• There is a correlation between number of bottles bought and number of samples offered. However, there is no causation. This is because there is probably an increase in the number of bottles bought with an increase in the number of samples offered.

• There is a correlation between number of bottles bought and number of samples offered. There may or may not be causation. Further studies would have to be done to determine this.

Explanation

We see from the following that number of bottles bought and number of samples offered tend not to vary together.

"a customer does not tend to buy more or fewer bottles when more samples are offered"

Thus, there is no correlation between number of bottles bought and number of samples offered.

Multiple Choice

Felipe compared the player statistics from his team's soccer season. He determined that having less playing time implies that a player scores fewer goals. What should he say based on his findings?

• There is no correlation between playing time and number of goals.

• There is a correlation between playing time and number of goals. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between playing time and number of goals. However, there is no causation. This is because there is a decrease in the number of goals with a decrease in playing time.

Explanation

We see from the following that playing time and number of goals tend to vary together.

"having less playing time implies that a player scores fewer goals"

Thus, there is a correlation between playing time and number of goals.

However, we cannot be sure there is causation without further studies.

Multiple Choice

Diane compared the player statistics from her team's soccer season. She determined that having less playing time implies that a player scores fewer goals. What should she say based on her findings?

• There is no correlation between playing time and number of goals.

• There is a correlation between playing time and number of goals. However, there is no causation. This is because there is a decrease in the number of goals with a decrease in playing time.

• There is a correlation between playing time and number of goals. There may or may not be causation. Further studies would have to be done to determine this.

Explanation

We see from the following that playing time and number of goals tend to vary together.

"having less playing time implies that a player scores fewer goals"

Thus, there is a correlation between playing time and number of goals.

However, we cannot be sure there is causation without further studies.

Multiple Choice

An environmental study was conducted. It reported that, for a park, having more visitors indicates having a larger number of trees. What can be determined?

• There is no correlation between number of visitors and number of trees.

• There is a correlation between number of visitors and number of trees. However, there is no causation. This is because there is an increase in the number of trees with an increase in the number of visitors.

• There is a correlation between number of visitors and number of trees. There may or may not be causation. Further studies would have to be done to determine this.

Explanation

We see from the following that number of visitors and number of trees tend to vary together.

"for a park, having more visitors indicates having a larger number of trees"

Thus, there is a correlation between number of visitors and number of trees.

However, we cannot be sure there is causation without further studies.

Multiple Choice

A flute instructor examined student progress. He found that playing a longer song does not necessarily mean that a student will have more or fewer wrong notes. What can he conclude?

• There is no correlation between song length and number of wrong notes.

• There is a correlation between song length and number of wrong notes. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between song length and number of wrong notes. There is probably also causation. This is because there is likely an increase in the number of wrong notes with an increase in the song length.

Explanation

We see from the following that song length and number of wrong notes tend not to vary together.

"playing a longer song does not necessarily mean that a student will have more or fewer wrong notes"

Thus, there is no correlation between song length and number of wrong notes.

Multiple Choice

Data was collected at a tennis court. It showed that being older implies that a player will stay for a shorter length of time. What is likely true?

• There is no correlation between age and length of stay.

• There is a correlation between age and length of stay. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between age and length of stay. However, there is no causation. This is because there is a decrease in the length of stay with an increase in age.

Explanation

We see from the following that age and length of stay tend to vary together.

"being older implies that a player will stay for a shorter length of time"

Thus, there is a correlation between age and length of stay.

However, we cannot be sure there is causation without further studies.