Chapter 2 Section 4

1
Chapter 2 Section 4

• Cautions about Regression and Correlation

2
Residuals

• A residual is the difference between an observed
  value of the response variable and the value
  predicted by the regression line.
• residual observed y predicted y
• Ex 2.16
• The mean of the least-squares residuals is always
  zero.

3

• A residual plot is a scatterplot of the
  regression residuals against the explanatory
  variable.
• The residual plot helps show if the regression is
  good. If there is not pattern in the residual,
  then the regression is good.
• See figure 2.19.

4
Lurking variables

• A lurking variable is a variable that has an
  important effect on the relationship among the
  variables in a study but is not included among
  the variables studied.
• Plot both the response variable and the
  regression residuals against the time order of
  the observations, this will help you find lurking
  variables.
• Ex 2.17

5
Outliers and influential observations

• Ex 2.18
• An outlier is an observation that lies outside
  the overall pattern of the other observations
• An observation is influential for a statistical
  calculation if removing it would markedly change
  the result of the calculation.

6
Beware the lurking variableand running with
scissors

• Correlation measures only linear association.
• Extrapolation can produce unreliable predictions
• Correlation and least-squares regression are not
  resistant
• Lurking variables can make correlation or
  regression misleading

7

• Ex 2.21
• Association does not imply causation
• Ex 2.22
• Beware correlations based on averaged data. A
  correlation based on averages over many
  individuals is usually higher that the
  correlation between the same variables based on
  data for individuals.
• The restricted-range problem, Ex 2.23

8
Daily Work, pp 169-179

• 54, 56, 60, 64, 68