Before you take a scored quiz for this lesson, try this set of practice questions. How well you score on this self-check will be similar to your scored quiz. If you do not score well on this self-check, please review this lesson and try again.
Studying for long periods of time has been shown to be related to better higher grades but it doesn’t necessarily cause better grades. What does this statement describe?
- causation
- correlation
- relationships
- coefficients
Studying more and getting higher grades are correlated, but studying more does not cause getting better grades.
You are correct!
Studying more and getting higher grades are correlated, but studying more does not cause getting better grades.
Studying more and getting higher grades are correlated, but studying more does not cause getting better grades.
What kind of a relationship does a correlation coefficient of -0.97 represent?
- a strong positive correlation
- a weak negative correlation
- a weak positive correlation
- a strong negative correlation
Correlation coefficients have values between -1 and 1. The closer the value is to -1 or 1, the stronger the correlation.
Correlation coefficients have values between -1 and 1. The closer the value is to -1 or 1, the stronger the correlation.
Correlation coefficients have values between -1 and 1. The closer the value is to -1 or 1, the stronger the correlation.
You are correct!
Calculate the correlation coefficient of the following data.
| x | y |
| 2 | 5 |
| 3 | 10 |
| 5 | 15 |
| 6 | 12 |
- -0.82
- 80
- -28
- 0.82
The correlation coefficient is 0.82
The correlation coefficient is 0.82
The correlation coefficient is 0.82
You are correct!
Describe the correlation of the following data:
- strong, positive
- strong, negative
- weak, positive
- weak, negative
This data has a strong negative correlation.
You are correct!
This data has a strong negative correlation.
This data has a strong negative correlation.
Summary
Questions answered correctly:
Questions answered incorrectly:
Causal Relation
A causal relation asks the question “does one event cause another?”
For instance, can you say that studying causes higher grades? It’s hard to make that blanket statement, right?
There might be a strong correlation (or association) between studying and getting high grades, but can we say that one definitely causes the other.
A causal relation between two events exists if the first event causes the other.
Correlation Coefficient
We can find out more about the correlation between two things by looking at the correlation coefficient. This number tells you how strong or weak two things are to each other.
Suppose we want to know how strong or weak the relationship between x and y are. We have even collected data on both in the following table.
| x | y |
| 2 | 5 |
| 3 | 10 |
| 5 | 15 |
| 6 | 12 |
Next, to compute the correlation coefficient for the data, you will need your graphing calculator. Follow the steps on the following helpsheet.
Question
What is the correlation coefficient for the data above? What does it mean?
A correlation coefficient of +0.82 represents a positive association between x and y. Meaning that as the x-values increase so do the y values. Also, 0.82 is close to 1 (perfect correlation) which indicates that the association is a strong one.
Identifying types of correlations
Scatter plots along with the correlation coefficient can help us identify the strength of the correlation that you may have – positive, negative, weak or strong.
Try the following exercise. Each slide shows the scatter plot and correlation coefficient for a set of data.
- First, determine if the correlation is positive or negative.
- Second, determine if the correlation is weak or strong.
Identifying types of correlations
Correlation Coefficient = 0.29
Question
Is this correlation coefficient positive or negative?
This correlation is positive meaning that as the values along the horizontal axis increase, so do the values along the vertical axis.
Question
Is this correlation strong or weak?
The correlation coefficient of 0.29 is not close to 1 (perfect correlation) so this is a weak correlation.
Identifying types of correlations
Correlation Coefficient = -0.79
Question
Is this correlation coefficient positive or negative?
This correlation is negative meaning that as the days of the months increase, the units produced decrease.
Question
Is this correlation strong or weak?
The correlation coefficient of -0.79 is close to 1 (perfect correlation) so this is a strong correlation.
Identifying types of correlations
Correlation Coefficient = 1
Question
Is this correlation coefficient positive or negative?
This correlation is positive meaning that as the years increase, Sarah’s salary also increases.
Question
Is this correlation strong or weak?
The correlation coefficient of 1 is a strong or perfect correlation.
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Now that you have had some more practice, you should be better prepared for your quiz. If you still do not feel confident about any topics, please contact your teacher for some additional help.
