Examining Bivariate Relationships

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Examining Bivariate Relationships

• In this chapter we will focus on relationships
  between several variables for the same group of
  individuals.
• When examining new data always ask your self
  What individuals do the data describe, what are
  the variables, are the variable quantitative or
  categorical.

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• Response variable is the dependent variable it
  depends on the explanatory variable. It measure
  an outcome of study.
• Explanatory variable is the independent variable.
  It attempts to explain the observed outcomes.
• We will always use the words Explanatory and
  Response because independent and dependent have
  many other meanings.

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• Example 3.1 ( Alcohol and Body Temp)
• Example 3.2 (Median SAT Verbal and Math Scores)
• There may not always be an explanatory and
  response variable. Sometimes whether there are
  or not depends on how you will use the data.

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• Scatterplots!
• The most effective way to display the relation
  between two variables is a scatterplot.
• Example 3.3
• Data on pg. 70 Table 1.15
• We think that percent taking the test will help
  explain average score so which variable is the
  response and which is the explanatory?

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• Explanatory variable is always plotted on the x
  axis (horizontal)
• Response variable always plotted on the y axis
  (vertical)
• If there is no explanatory/response variable then
  the data can go on either axis

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• Interpreting Scatterplots
• Always look for the following
• The overall pattern and striking deviations from
  the pattern.
• Describe the overall pattern by the form,
  direction, and strength.
• Look for outliers they are important deviations
  from the overall pattern

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• Analyze 3.3 graph.
• What does the overall graph look like?
• Is there a clear direction?
• What do think about the datas strength?

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• Positive associations (direction) occurs when the
  graph rises to right, or the values of both
  variables get bigger together.
• Negative associations (direction) occurs when
  the graph falls to the right or as one variable
  gets large the other gets small.

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• The strength of the relationship is determined by
  how closely the points follow a clear form.
• Example 3.4
• What is the response variable and explanatory
  variable.

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• When adding categorical data into the mix you may
  want to change the symbol or colors of that data.
• On your calculator you can just change the way
  the points look in the stat-plot feature.

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• Example 3.5 is the South Different

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• Example 3.6 Do solar panels reduce gas usage?