It’s important to stop and think about our predictions.

• Sometimes, the numbers just don’t make sense.
• Other times it’s harder to tell something’s wrong!

Extrapolation is applying a model estimate for values outside of the data’s range for \(x\).

• Our linear model is only an approximation.
  • We don’t know anything about the relationship outside of the scope of our data.

The best fit line is \[\hat{y} = 2.69 + 0.179x\]

• The correlation is \(R=0.877\).
• So the coefficient of determination is \(R^2 = 0.767\).
  • (think: a C grade)

Now suppose we wanted to predict the value of \(y\) when \(x=0.1\): \[\hat{y} = 2.66 + 0.181\times0.1 = 2.67\]

• Seems reasonable… but the true (population) best-fit model looks like this: