Examining Relationships Between Variables

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Examining Relationships Between Variables Part II
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• Relationship between two quantitative variables
  measured on the SAME individuals

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• Start
• With
• A
• Scatterplot

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• IF Explanatory Response Relationship
• then
• Put explanatory variable on the x-axis
• and
• Put the response variable on the y-axis

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• Look at the scatterplot
• Overall pattern
• Striking deviations

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• Look at the scatterplot
• Form Linear or non-Linear
• Direction Positive or negative
• Strength Strong, weak, moderately strong or
  weak
• OUTLIERS?

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• IF roughly linear
• Then
• Calculate correlation coefficient, r
• Which quantifies the direction and strength of
  the LINEAR relationship between the two variables.

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Correlation Can we rely on our eye to judge the
strength of the relationship between two
variables?
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Correlation Coefficient r Numerical measure of
the strength and direction of the relationship.
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(No Transcript)
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Average of the sum of the products of the
standardized variables using n-1 degrees of
freedom.
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r is positive when the association is positive r
is negative when the association is
negative. WHY?
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Negative
Positive
Negative x Negative Positive Positive x
Positive Positive Negative x Positive Negative
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• FACTS ABOUT CORRELATION
• No distinction between x and y or explanatory and
  response variables.

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• Both variables must be quantitative.

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r has no units. So r doesnt change if we
change the units of the variable.
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• -1 lt r lt 1
• -1 means perfectly linear in negative direction.
• 1 means perfectly linear in positive direction
• 0 means no linear relationship

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• The relationship must be
• LINEAR

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• r is not resistant to outliers

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• A study measured the physical strength of 200
  college men. One variable was the number of
  pull-ups a subject could do. Other variables
  included number of push-ups, number of sit-ups,
  and body weight. The correlations of pull-up
  count with these three variables were
• r -0.150 r 0.190 r
  0.647
• Which r goes with which variable?
• www.whfreeman.com/tps3e

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• www.whfreeman.com/tps3e
• 3.29
• 3.31
• 3.34
• 3.36

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• The End