MATH 1107 Elementary Statistics

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MATH 1107Elementary Statistics

• Lecture 6
• Scatterplots, Association
• and Correlation

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MATH 1107 Scatterplot, Association and
Correlation

• Take a look at the data on the right.
• In the US, Is there a relationship between
• Household income and violent crime?
• Household income and Death rate?
• If there is a relationship, is it direct or
  inverse?
• If there is a significant relationship, can we
  use it to predict the likelihood of crime or
  death rate in a particular state?

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MATH 1107 Scatterplot, Association and
Correlation
Using scatterplots, we can evaluate the
direction, the form, and the strength of the
relationship
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MATH 1107 Scatterplot, Association and
Correlation
Evaluate the direction, the form, and the
strength of the relationship
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MATH 1107 Scatterplot, Association and
Correlation

• Specifically, here are the things to look for in
  a scatterplot
• Direction Does the direction of the data move
  NW to SE? This indicates a negative
  relationship. Does the data move from the SW to
  the NE? This is a positive relationship. Does
  the data look like a cloud? This indicates no
  relationship.
• Form Does the data demonstrate a linear
  pattern? A curved pattern?
• Strength Is the data really tight? This
  indicates a strong correlation. Is the data
  really spreadout? This indicates a weak
  correlation.
• Are there any outliers? Or groups of outliers?

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MATH 1107 Scatterplot, Association and
Correlation

• A few additional points about scatterplots
• The dependent variable typically the one that
  you want to better understand or predict is
  plotted on the y-axis and the independent
  variable is plotted on the x-axis.
• We typically only use scatterplots with
  quantitative data. Question why?
• Rescale the scatterplot to only include the
  scales necessary to see the relationships.
  However, if the axes do not start at zero, this
  should be noted at the bottom of the page.
  Question why?
• Changing the units of a scatterplot should not
  change the relationship (i.e., lbs to kg)

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MATH 1107 Scatterplot, Association and
Correlation

• Correlations can be measured as a number between
  0 and 1 (absolute value). Where, numbers closer
  to 0 indicate less correlation and numbers closer
  to 1 indicate more correlation.
• A basic interpretation of the correlation
  coefficient is x of the change in variables 1
  and two move together.
• Correlation coefficients are really not expressed
  in meaningful units.
• Andremember that correlation coefficients are
  related to LINEAR relationships!

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MATH 1107 Scatterplot, Association and
Correlation

• Lets examine some scatterplots and correlation
  coefficients in EXCEL. Go to the EXCEL datasets
  on the website.