Fit a linear function to data when a scatter plot suggests a linear association.
Use a linear model to extrapolate cautiously
Problem
Evaluate \(y=3x+2\) at \(x=15\) after fitting the model on \(1\le~x\le~8\). Calculate \(y\), classify the use as interpolation or extrapolation, and state the reliability limitation.
Extending a fitted line is a mathematical calculation and an evidence question at the same time. Measure how far the requested input lies beyond the observed range, then describe the result as an extrapolated prediction whose uncertainty grows because the relationship may change outside the data.
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