CHAPTER 3.1 AP STAT
By Chris Raiola
Emily Passalaqua
Lauren Kelly
OVERVIEW
• What is a scatterplot?
• How to describe a scatterplot
• How to create a scatterplot
• What is correlation?
• How is correlation calculated?
• Important facts about correlation
SCATTERPLOTS
• Scatterplot- a graph in which the values of two variables are plotted along
two axes, the pattern of the resulting points revealing any correlation
present.
• Explanatory variable: x-axis (input variable)
• Response variable: y-axis (output variable)
• The mnemonic used for describing a scatterplot is DOFS
•
•
•
•
Direction- Positive or negative direction
Outliers- any outlying/unusual points on the scatterplot
Form- Linear or Nonlinear
Strength- Weak, moderate, or strong (based on how close the points are to each
other)
SCATTERPLOTS CONT.
• Examples (which are explanatory and which are response?)
• Amount of rain and flower growth
• Resting pulse rate and amount of daily exercise
• Dallas Cowboys winning percentage and attendance at
games
• Height and weight
WHAT A SCATTERPLOT LOOKS LIKE
D: positive
O: none
F: Linear
S: moderately
strong
HOW TO SET UP A SCATTERPLOT
1. Collect all the data necessary for the graph
2. Make a title for the scatterplot
3. Decide which variable goes on each axis
4. Label and scale the x-axis and y-axis appropriately
5. Plot individual data values
CORRELATION
• Correlation- measures the strength of the linear relationship between two
quantitative variables (the symbol is “r”)
• r is always a number between -1 and 1
• An r greater than 0 indicates positive association, while r less than zero
indicates a negative association
• The closer it is to 0, the weaker the linear relationship
• The extreme values r = -1 and r = 1 occur only in cases of perfect linear
relationships
CORRELATION FORMULA
IMPORTANT FACTS ABOUT
CORRELATION
• The correlation “r” itself has no unit of measurement
• Correlation makes no distinction between explanatory and response
variables
• “r” does not change when we change the units of measurement of x,y, or
both
• Correlation requires that both variables be quantitative
• Correlation does NOT describe curved relationships between variables, no
matter how strong the relationship is
• Correlation is not resistant. “r” is strongly affected by outliers
• Correlation is not a complete summary of two-variable data
• Correlation does not describe causation
EXAMPLES
STUDY TIPS
• There are many mnemonic devices that we use in Stat to remember things,
and DOFS should be an important one to remember when referring to
scatterplots
• Be sure to know the difference between explanatory and response
variables, because they are easy to mix up
• Study the facts of correlation, and make sure you know how to use the
formula as well as the application on your calculator (i.e. using the “STAT”
button to use the different functions)