A+ » VCE » Further Maths U3 & 4 Master Notes » OA4 Graphs and Relations » FM Interpolation

FM Interpolation

1.5 Use of Data and Graphs

Constructing Graphs from Tables

  • Given a table containing the x and y values of several points on a graph, we can construct a graph by plotting the known points and draw between them, using the trend of points to guess the overall shape of the graph.
  • When guessing the shape of the graph, there are many possible options. It is best to go with the simplest option.

Example

X

Y

0.5

11

1

8.5

1.5

5.5

2

4

3

2

4.5

1.8

6

1.2

9

1

We wish to construct a graph from the above table. To begin, we plot the points on a graph:

Picture 2

Now, we draw between these points. In this case, the overall trend appears to curve and so we will draw a curved line:

Read More »1.5 Use of Data and Graphs

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

Read More »3.3 Using the Formula for a Fitted Line