Predictions can be made through substituting any given x-value into the trendline equation.

• Interpolation is a prediction within the dataset

• Extrapoation is a prediction outside of the dataset

Note: As a trendline often cannot go on forever neither can predictions. Just because you can substitute an x-value into a trendline equation does not mean the predicted y-value is going to be relevant.

Validity of predictions

Interpolation is going to be fairly accurate if the raw data at the given value is closely scattered to the trendline. The more widely scattered the data is the more approximate a prediction becomes.

Extrapolation and its accuracy depends on what is happening to data throughout the graph.

We need to consider:

• the strength of relationship

• the direction in which the data is going at the beginning and end of the graph compared to the trendline

• what values it is actually possible to predict over given the context of the problem eg human height has a maximum.

We can also use the coefficient of determination R². This is given on excel.

This tells us the % of variation in the y-variable that can be explained by the trendline.

It could be thought of as indicating goodness of fit. A value of 1 indicates very reliable predictions. A value of 0.0 indicates a model that is no good for predictions.