Sections 2.1 Relationships and 2.2 Scatterplots

Associations between Variables:

• Two variables measured on the same cases are associated if
  knowing the value of one of the variables tells you something
  that you would not otherwise know about the value of the other
  variable

Response / Dependent Variable:

• Measures an outcome of a study

Explanatory / Independent Variable:

• Explains or causes changes in the response variable

Key Characteristics of a Data Set:

• Cases: Identify the cases and how many there are in the data set

• Categorical or quantitative: Classify each variable as categorical or
  quantitative

• Values: Identify the possible values for each variable

• Explanatory or response: If appropriate, classify each variable as
  explanatory or response

• Label: Identify what is used as a label variable if one is present

Scatterplot:

• A scatterplot shows the relationship between two quantitative variables measured on the same cases

  • The values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis

  • Each case corresponds to one point on the graph

Interpreting Scatterplots:

• As in any graph of data, look for the overall pattern and for striking
  deviations from that pattern

• You can describe the overall pattern of a scatterplot by the form,
  direction, and strength of the relationship

• An important kind of departure is an outlier, an individual value that falls outside the overall pattern of the relationship
  

Positively Associated:

• Two variables are positively associated when above-average values of one tend to accompany above-average values of the other and when
  below-average values also tend to occur together

Negatively Associated:

• Two variables are negatively associated when above-average values
  of one tend to accompany below-average values of the other, and vice
  versa

The three ways to describe a graph:

• Strength

• Direction

• Form

Nonlinear Relationships:

• There are other forms of relationships besides linear. The scatterplot
  below is an example of a nonlinear form

• Note the curvature in the relationship between x and y

The Log Transformation:

• Sometimes, the pattern that best describes data in a scatterplot is a curve other than a line

• In this case, it is often useful to apply a transformation to the data that renders the relationship approximately linear

• It can be used only for variables whose values are positive

• The natural logarithm is what we use to perform this transformation