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)