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Scatter Plotting Variable Pairs

Tutorial Navigation

Getting Started	General Instructions \| Introduction to Your Study
Descriptive Statistics	Histograms \| Scatter Plots \| Central Tendency \| Standard Deviation \| Confidence Intervals
Relating Variables	Correlation
Important Concepts	The Normal Distribution \| Z Scores \| Probability Distributions
Levels	You are currently on Scatter Plots at level 3. Level 1 \| Level 2 \| Level 3
Next Topic	Probability Distributions

Explanation

Understanding Scatter Plots
The shape formed by the points on a scatter plot quickly tell you something about the relationship between the two variables that you have plotted. For this reason, people talk about the 'shape' of the relationship between two variables. This refers to the shape they make on the scatter plot. We will be looking for one type of relationship in this study, one called 'linear'.

Two variables have a linear relationship if the points on their scatter plot lie on a straight line
There will often be errors or noise in a measurement, meaning that data do not all lie on a perfect straight line, but are scattered about a straight line a little. These data still have a linear relationship, but one that is noisy.
Remembering that the lower left hand corner of the scatter plot indicates the lowest value either variable can take:
- If the line formed by the scatter plot moves up as it moves right like this /, then there is a positive relationship between the two variables - as one gets higher, you would expect the other to get higher too.
- If the line formed by the scatter plot moves down as it moves right like this \, then there is a negative (or inverse) relationship between the two variables - as one gets higher, you would expect the other to lower.
If a line curves or changes direction, the relationship is not linear.
If the data forms a cloud with no clear direction, perhaps oval or rectangular in shape, then there is probably no relationship between the two variables being plotted.

By looking at a scatter plot, it is possible to learn the following things about the two plotted variables:

Whether or not there is a linear relationship between the two variables;
How much noise, error, or deviation from a perfect linear relationship there is;
The direction of the relationship if there is one (positive or negative);
The shape of the relationship if it is not linear.

Exploration

Here are four scatter plots, each with one or more types of relationship. Look at the relationships listed below and say which plot displays each type of relationship.

Which plot shows a perfect linear relationship?
Which plot shows a noisy, linear relationship?
Which plot shows no relationship?
Which plot shows an negative relationship?
Which plot shows a relationship that is not linear?

Application

The data from your study is plotted below. Look at the shape the dots make and answer the questions below.

Do the variables have a perfect linear relationship?
Do the variables have a nearly linear relationship?
As age increases, does hr_admit increase or decrease?
Do the variables have a positive or a negative relationship?

Probability Distributions