3.7 Least Squares Regression for Transformed Data

Note: if you cannot remember how to interpret least squares regression lines, revise notes for 3.3 Using the Formula for a Fitted Line.

Guideline to Analyse Least Squares Linear Regression Relationships for Transformed Data

  • Analysing a least squares linear fit for transformed data is similar to the process for non-transformed data, however you must keep in mind the association is not between the explanatory variable and response variable, it is between the transformed variable and the non-transformed variable (which will be either the explanatory or response variable).
  • When interpreting the meaning of the coefficient of determination, it gives an indication of what percentage of variation in the transformed variable is explained by variation of the non-transformed variable, or visa-versa (e.g. for an explanatory variable squared transformation, the coefficient indicates what percentage of variation in y can be explained by variation in x^2).
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3.3 Using the Formula for a Fitted Line

Interpolation

  • After fitting a model to a dataset (through linear regression), we can use that model to estimate values we don’t have data points for.
  • When estimating values that lie within the range of available raw data points, we refer to it as interpolating.
  • Interpolation is considered accurate if the fit has high strength and sufficient data points were used.

Example: if a linear fit is creating using data points ranging in value from 1 to 10, estimating the value of the response variable when the explanatory variable has a value of 2 would be considered interpolation.

Extrapolation

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