Correlation Coefficient

Correlation Coefficient

Correlation tests for a relationship between two variables. However, seeing two variables moving together does not necessarily mean we know whether one variable causes the other to occur. This is why we commonly say “correlation does not imply causation.”

Study Time and Grades

As study hours increase, grades increase. There is a positive correlation between hours and grades.

So....Do hours spent studying cause higher grades?

Ice Cream Sales and Shark Attacks

As ice cream sales increase, shark attacks increase. As ice cream sales decrease, shark attacks decrease.

So....ice cream sales cause shark attacks?

5G and COVID cases

There is a correlation between areas with 5G and high COVID cases.

So......Does 5G cause COVID?

Multiple Choice

This implies that one variable has a direct affect on the other variable.

• Correlation

• Causation

Multiple Choice

A correlation shows that two things

• Are Related

• Cause Each Other to Happen

• Are Unrelated

Multiple Choice

Correlation or Causation?

The number of times you come to tutoring and your test scores improving

• Correlation

• Causation

Multiple Choice

Correlation or Causation?

The inches of snowfall and the number of heart attacks

• Correlation

• Causation

Multiple Choice

Correlation or Causation?

The speed you drive and the amount of fuel you use

• Correlation

• Causation

Multiple Choice

What is the type of correlation?

• Negative 
• no correlation
• positive 

Multiple Choice

What type of association does this graph have?

• positive
• negative
• none
• all of the above

Multiple Choice

What type of association does this graph have?

• positive 
• negative
• none
• all of the above

Multiple Choice

Which scatter plot shows a linear relationship between x and y?

• Graph A

• Graph B

• Graph C

• Graph D

Correlation coefficient (r) formulas are used to find how strong a relationship is between data. The formulas return a value between -1 and 1, where:

• 1 indicates a strong positive relationship.

• -1 indicates a strong negative relationship.

• A result of zero indicates no relationship at all.

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = 1.2

• B) r = 0.89

• C)r = 0

• D) r = -0.89

Multiple Choice

Describe the correlation in the graph shown.

• A) Strong Negative

• B) Strong Positive

• C) Weak Negative

• D) No Correlation

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = -0.9

• B) r = 1

• C) r = 0.9

• D) r = -1

Multiple Choice

Average time spent listening to music per day and average time spent watching TV per day.  $r=-.17$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Score on science exam and number of words written on the essay question.  $r=.28$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Car weight and distance traveled using a full tank of gas.  $r=-.86$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Number of steps taken per day and number of kilometers walked per day.  $r=.92$  

• strong positive

• strong negative

• weak positive

• weak negative

Formula for Correlation Coefficient (r)

Luckily we can use our calculator!!

Find the correlation coefficient of the data.

Strong or weak?

Positive or negative?