Question

The weight, y, in pounds, of kittens was tracked for the first 8 weeks after birth, where t represents the number of weeks after birth. The linear model representing this relationship is y hat equals 1.7 plus 1.48 times t. David wanted to predict the weight of a kitten at 12 weeks.

What is this an example of, and is this method a best practice for prediction? Explain your reasoning.

This is an example of extrapolation. Extrapolation is a best practice for prediction, as the prediction is accurate even though 12 weeks is outside the given interval of 8 weeks.
This is an example of extrapolation. Extrapolation is not a best practice for prediction, as the prediction is not accurate because 12 weeks is outside the given interval of 8 weeks.
This is an example of linear modeling. Linear modeling is a best practice for prediction, as the prediction is accurate even though 12 weeks is outside the given interval of 8 weeks.
This is an example of linear modeling. Linear modeling is not a best practice for prediction, as the prediction is not accurate because 12 weeks is outside the given interval of 8 weeks.

Answer 1

B) This is an example of extrapolation. Extrapolation is not a best practice for prediction, as the prediction may not be accurate because 12 weeks is outside the given interval of 8 weeks.

Explanation:

Extrapolation

When we use independent values outside the range of the original data to predict corresponding dependent values, it is called "extrapolation". These predictions can be unreliable because there is no evidence that the relationship described by the linear model is true for all independent values.

In this case, the linear model is based on tracking the weight of kittens for the first 8 weeks after birth, and David wants to predict the weight at 12 weeks. Using a linear model for predictions beyond the observed data introduces uncertainty, as the model may not accurately capture the behavior of the data outside the original range. Therefore, while the linear model may provide a prediction, it may not be as reliable when applied to time points beyond the initial 8 weeks.