1.4 Analysing Non-Linear Graphs

Intercepts of Non-Linear Graphs

  • Non-linear graphs can have no intercepts, one intercept or multiple intercepts along either axis.

Example

Picture 2

Above is a graph showing the profits earned by a community theatre in the years before they changed management. In the context of this situation, we can say that the intercepts at t=-3, -2 and 1 years represent points at which the community theatre just broke even (i.e. no profit or loss). The intercept at P=$1000 represents the profits made in the year the new management took over.

Maximum/Minimum Points

  • It may interest us to know the highest, or lowest values that the y-variable has taken. For example, if we want to find the highest a tide has been in a year in order to know how high to build a support structure.
  • The maximum and minimum points of non-linear graphs will be points of 0 gradient or the endpoints of a section (i.e. where a graph ends or undergoes structural change).
  • There may be multiple minimum points and/or multiple maximum points.
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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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