Positive Correlation

Correlation & Causation

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Types of Correlation

• The first picture shows positive correlation - as the independent variable increases, the dependent variable increases

• The second picture shows a negative correlation - as the independent variable increases, the dependent variable decreases.

• As you can see in the third picture there is sometimes NO correlation - no relationship between the variables.

Strength of Correlation

• The closer the data points are to the line of best fit, the stronger the correlation.

• The further the data points are to the line of best fit, the weaker the correlation.

Correlation Coefficient (r value)

• We can measure the strength of a correlation with a number called the correlation coefficient.

• Strong positive correlations are close to positive one.

• Strong negative correlations are close to negative one.

• Weak correlations are close to zero.

Multiple Choice

What type of correlation is being demonstrated in this graph?

• Postive

• Negative

• No Correlation

Answer Explained

If you added the line of best fit to this data, it would have a negative slope. That means that this is a negative correlation.

Multiple Choice

What type of correlation is being demonstrated in this graph?

• Postive

• Negative

• No Correlation

Answer Explained

If you add a line of best fit to this graph, the slope of the line would be positive. So that means we have a positive correlation.

Multiple Choice

What type of correlation is being demonstrated in this graph?

• Postive

• Negative

• No Correlation

Answer Explained

There is no way to determine the line of best fit. The data is too scattered. This means that there is no correlation.

Main Idea

There is either correlation or no correlation. Most students find that part pretty clear.

When there is correlation, there is NOTHING that we can say about causation. Further studies (like a randomized experiment) need to be completed before we can know anything at all about causation.

So, for this topic, any statements about causation will be incorrect. You are looking for the answer that says further studies need to be completed.

Multiple Choice

A researcher measured the shoe size and reading ability of a large group of children. He found that, as shoe size increases, so does reading ability. What does his analysis show?

• There is no correlation between shoe size and reading ability.

• There is a correlation between shoe size and reading ability. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between shoe size and reading ability. There is probably also causation. This is because there is an increase in reading ability with an increase in shoe size.

Answer Explained

We see from the following that shoe size and reading ability tend to vary together.

"as shoe size increases, so does reading ability"

Thus, there is a correlation between shoe size and reading ability.

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

• There is no correlation between shoe size and reading ability.

• There is a correlation between shoe size and reading ability. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between shoe size and reading ability. There is probably also causation. This is because there is an increase in reading ability with an increase in shoe size.

Multiple Choice

A grocery store conducted a survey. It showed that when customers buy less cereal, it does not indicate a change in the amount of milk they purchase. What can we conclude?

• There is no correlation between amount of cereal bought and amount of milk purchased.

• There is a correlation between amount of cereal bought and amount of milk purchased. However, there is no causation. This is because there is likely a decrease in the amount of milk purchased with a decrease in the amount of cereal bought.

• There is a correlation between amount of cereal bought and amount of milk purchased. There may or may not be causation. Further studies would have to be done to determine this.

Answer Explained

We see from the following that amount of cereal bought and amount of milk purchased tend not to vary together.

"when customers buy less cereal, it does not indicate a change in the amount of milk they purchase"

Thus, there is no correlation between amount of cereal bought and amount of milk purchased.

Multiple Choice

Reuben compared the player statistics from team's basketball season. He determined that being taller does not imply that a player scores more or fewer points. What is likely true?

• There is no correlation between height and number of points scored.

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

• There is a correlation between height and number of points scored. However, there is no causation. This is because there is probably an increase in the number points scored with an increase in height.

Answer Explained

We see from the following that height and number of points scored tend not to vary together.

"being taller does not imply that a player scores more or fewer points"

Thus, there is no correlation between height and number of points scored.

Multiple Choice

A computer manufacturer conducted a survey. It showed that a younger customer will not necessarily purchase a lower or higher priced computer. What is likely true?

• There is no correlation between age and purchase price.

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

• There is a correlation between age and purchase price. There is probably also causation. This is because there is likely a decrease in the purchase price with a decrease in age.

Answer Explained

We see from the following that age and purchase price tend not to vary together.

"a younger customer will not necessarily purchase a lower or higher priced computer"

Thus, there is no correlation between age and purchase price.

Multiple Choice

A hospital found that a lower outside temperature indicates a higher number of patient visits. What can we determine from this information?

• There is no correlation between outside temperature and number of patient visits.

• There is a correlation between outside temperature and number of patient visits. However, there is no causation. This is because there is an increase in the number of patient visits with a decrease in the temperature outside.

• There is a correlation between outside temperature and number of patient visits. There may or may not be causation. Further studies would have to be done to determine this.

Answer Explained

We see from the following that outside temperature and number of patient visits tend to vary together.

"a lower outside temperature indicates a higher number of patient visits"

Thus, there is a correlation between outside temperature and number of patient visits.

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

• There is no correlation between outside temperature and number of patient visits.

• There is a correlation between outside temperature and number of patient visits. However, there is no causation. This is because there is an increase in the number of patient visits with a decrease in the temperature outside.

• There is a correlation between outside temperature and number of patient visits. There may or may not be causation. Further studies would have to be done to determine this.

Multiple Choice

Mr. Long studied his students' history test scores and sleeping habits. He found that students who slept less tended to earn lower scores on the test. What conclusion should he make?

• There is no correlation between test score and amount of sleep.

• There is a correlation between test score and amount of sleep. There is probably also causation. This is because there is a decrease in a student's test score with a decrease in the amount of sleep.

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

Answer Explained

We see from the following that test score and amount of sleep tend to vary together.

"students who slept less tended to earn lower scores on the test"

Thus, there is a correlation between test score and amount of sleep.

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

Important Tip!

• There is no correlation between test score and amount of sleep.

• There is a correlation between test score and amount of sleep. There is probably also causation. This is because there is a decrease in a student's test score with a decrease in the amount of sleep.

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

Multiple Choice

A financial magazine conducted a survey. It showed that a person with more years of education tends to have a higher salary. What is likely true?

• There is no correlation between years of education and salary.

• There is a correlation between years of education and salary. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between years of education and salary. There is probably also causation. This is because there is an increase in salary with an increase in the years of education.

Answer Explained

We see from the following that years of education and salary tend to vary together.

"a person with more years of education tends to have a higher salary"

Thus, there is a correlation between years of education and salary.

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

Important Tip!

• There is a correlation between years of education and salary. There may or may not be causation. Further studies would have to be done to determine this.

• There is a correlation between years of education and salary. There is probably also causation. This is because there is an increase in salary with an increase in the years of education.

Multiple Choice

Mr. Wright studied his students' math test scores and TV habits. He found that students who watched less TV tended to earn higher scores on the test. What conclusion should he make?

• There is no correlation between test score and amount of TV watched.

• There is a correlation between test score and amount of TV watched. There is probably also causation. This is because there is an increase in a student's test score with a decrease in the amount of TV watched.

• There is a correlation between test score and amount of TV watched. There may or may not be causation. Further studies would have to be done to determine this.

Answer Explained

We see from the following that test score and amount of TV watched tend to vary together.

"students who watched less TV tended to earn higher scores on the test"

Thus, there is a correlation between test score and amount of TV watched.

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

Same Important Tip!

• There is a correlation between test score and amount of TV watched. There is probably also causation. This is because there is an increase in a student's test score with a decrease in the amount of TV watched.

• There is a correlation between test score and amount of TV watched. There may or may not be causation. Further studies would have to be done to determine this.

Multiple Choice

A car dealership conducted a survey. It showed that a younger customer tended to purchase a lower priced car. What is likely true?

• There is no correlation between age and purchase price.

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

• There is a correlation between age and purchase price. There is probably also causation. This is because there is a decrease in the purchase price with a decrease in age.

Answer Explained

We see from the following that age and purchase price tend to vary together.

"a younger customer tended to purchase a lower priced car"

Thus, there is a correlation between age and purchase price.

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

Same Important Tip

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

• There is a correlation between age and purchase price. There is probably also causation. This is because there is a decrease in the purchase price with a decrease in age.

Multiple Choice

A doctor's office found that a lower outside temperature did not indicate a change in the number of appointments made. What can we determine from this information?

• There is no correlation between outside temperature and number of appointments made.

• There is a correlation between outside temperature and number of appointments made. However, there is no causation. This is because there is likely an increase in the number of appointments made with a decrease in the temperature outside.

• There is a correlation between outside temperature and number of appointments made. There may or may not be causation. Further studies would have to be done to determine this.

Answer Explained

We see from the following that outside temperature and number of appointments made tend not to vary together.

"a lower outside temperature did not indicate a change in the number of appointments made"

Thus, there is no correlation between outside temperature and number of appointments made.

Poll

How ready do you feel to learn this topic in ALEKs?

• I still have no idea how to do these kinds of problems.

• I kind of get it, but I really could use some more practice.

• I'm pretty sure that I could go to ALEKs right now and show that I've learned this topic.

• I have already learned this topic.

Open Ended

What advice would you offer a classmate about this topic?