Linearity Assumptions

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Linearity Assumptions
2015-03-01 09:59:40
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  1. If the linear prediction rule is correct, what should be expected?
    • The error component should be entirely random 
    • There are no systematic components (biases) in data
  2. What are the different names given to residuals based on their position in residual plots?
    • Below the line: negative 
    • Above the line: positive
  3. How would a residual plot show that a straight line model was not appropriate?
    • If the residuals vary as across the plot, for instance being negative at the extremes and positive in the centre 
    • This would suggest the data is curvilinear
  4. When can residual plots be produced?
    When both DV and IV are random variables
  5. When can residual plots be used?
    • When there is no clear IV 
    • Simply select one variable as the IV
  6. What is the pure error (lack of fit) test divided into?
    • Pure error 
    • Lack of fit
  7. How do we obtain the pure error?
    Measure the residuals relative to the mean response value for each condition rather than relative to the predicted value on the regression line
  8. What can be inferred if the mean values coincide precisely with the predicted values?
    • The means all lie on the regression line
    • The residual error equals the pure error and the lack of fit SS is 0
    • It must be considered, however that due to sampling error it is highly unlikely that all of the means will be in the regression line
  9. What are replicates?
    Measurements of Y at a given value of X
  10. How can we guarantee the existence of replicates?
    • When participants are assigned to a given value of X
    • Replicates might not occur if the IV is random