Describing scatterplots (form, direction, strength, outliers) (article) | Khan Academy
Scatterplots. Perhaps the most important step in examining the relationship between two variables is to create a scatterplot. A scatterplot is simply a graph which. A scatter plot (also known as a scatter diagram) shows the relationship between two quantitative (numerical) variables. These variables may be positively related . Purpose: Check for Relationship, A scatter plot (Chambers ) reveals relationships or association between two variables. Such relationships manifest.
So something that seems to kind of correlate in a positive direction might have a value of 0. An example of a situation where you might find a perfect positive correlation, as we have in the graph on the left above, would be when you compare the total amount of money spent on tickets at the movie theater with the number of people who go.
This means that every time that "x" number of people go, "y" amount of money is spent on tickets without variation.
An example of a situation where you might find a perfect negative correlation, as in the graph on the right above, would be if you were comparing the amount of time it takes to reach a destination with the distance of a car traveling at constant speed from that destination. On the other hand, a situation where you might find a strong but not perfect positive correlation would be if you examined the number of hours students spent studying for an exam versus the grade received.
This won't be a perfect correlation because two people could spend the same amount of time studying and get different grades.
- Describing scatterplots (form, direction, strength, outliers)
- Scatterplots and correlation review
- Scatter Plots
But in general the rule will hold true that as the amount of time studying increases so does the grade received. Let's take a look at some examples. The graphs that were shown above each had a perfect correlation, so their values were 1 and The graphs below obviously do not have perfect correlations. Which graph would have a correlation of 0? Click on Answers when you think that you have them all matched up. In this case you will say that the variables are closely related to each other.
As discussed earlier, you can also divide the scatter diagram according to the slope, or trend, of the data points: Scatter Diagram with Strong Positive Correlation Scatter Diagram with Weak Positive Correlation Scatter Diagram with Strong Negative Correlation Scatter Diagram with Weak Negative Correlation Scatter Diagram with Weakest or no Correlation Strong positive correlation means there is a clearly visible upward trend from left to right; a strong negative correlation means there is a clearly visible downward trend from left to right.
A weak correlation means the trend, up of down, is less clear. A flat line from left to right is the weakest correlation, as it is neither positive nor negative and indicates the independent variable does not affect the dependent variable. In positive slant, the correlation will be positive, i.
You can say that the slope of straight line drawn along the data points will go up. The pattern will resemble the straight line.
For example, if the temperature goes up, cold drink sales will also go up. Scatter Diagram with Weak Positive Correlation Here as the value of x increases the value of y will also tend to increase, but the pattern will not closely resemble a straight line.
In negative slant, the correlation will be negative, i. The slope of a straight line drawn along the data points will go down. For example, if the temperature goes up, sales of winter coats goes down. Scatter Diagram with Weak Negative Correlation Here as the value of x increases the value of y will tend to decrease, but the pattern will not be as well defined.
Scatter Diagram with no Correlation In this type of chart, you are not able to see any kind of relationship between the two variables.
Plotting Relationships: Scatterplots
In either case, the independent variable has no effect on the second variable it is not dependent. Limitations of a Scatter Diagram The following are a few limitations of a scatter diagram: Scatter diagrams are unable to give you the exact extent of correlation.
Scatter diagram does not show you the quantitative measure of the relationship between the variable. It only shows the quantitative expression of the quantitative change. This chart does not show you the relationship for more than two variables. Benefits of a Scatter Diagram The following are a few advantages of a scatter diagram: It shows the relationship between two variables.
It is the best method to show you a non-linear pattern. The range of data flow, i. Observation and reading is straightforward. Plotting the diagram is relatively simple. Summary Scatter diagrams are very useful to determine the relation between two variables. Usually the first variable is independent and the second is dependent on the first variable.
What is a Scatter Diagram (Correlation Chart)?
To analyze the pattern of the relationship, you make changes to the independent variable and monitor the changes in the dependent variable. Please keep in mind that the scatter diagram is different than the Ishikawa diagram. The Ishikawa diagram shows you only the variables; it does not show you the relationship between these variables.
However, the Ishikawa diagram can help you draw the scatter diagram; for example, you can find the two variables cause and effectand then draw the scatter diagram to analyze the relationship between them.