Question

If the linear model applies the function f(x) = 1.3x + 9.2, what is the predicted value and residual

when the tree is 3 years old with a height of 14?

A) Predicted value: 13.1
Residual: 0.9
B) Predicted value: 11.8 Residual: 0.2
C) Predicted value: 15.7 Residual: 1.3
D) Predicted value: 18.3 Residual: 0.7

Answer 1

A) Predicted value: 13.1 Residual: 0.9

Explanation:

By definition:

residual = observed - predicted

The linear model is:

f(x) = 1.3x + 9.2

where f(x) is the height and x is the age of the tree.

Replacing with x = 3:

f(x) = 1.3(3) + 9.2 = 13.1 ft

which is the predicted value. The observed value is 14 ft, then:

residual = 14 - 13.1 = 0.9 ft