Suppose a one-year-old child has a shoulder girth of 56 cm. Predicting the height of this child would require extrapolation. The data used to create the model is for people with approximately 90 to 130 cm shoulder girth. The linear model may no longer hold outside the range of the data.

Question

BlackTom AI · Accepted Answer

The prompt describes a scenario where a predictive model for height is built using data from individuals with shoulder girth roughly 90 to 130 cm, and asks about predicting the height for a child with a shoulder girth of 56 cm. This sets up a situation where the input value lies well outside the observed data range, which is a classic case of extrapolation.
Option 1: True. Extrapolation occurs when you use a model to make predictions beyond the range of the data used to fit it. Since 56 cm is far below the 90–130 cm range, the linear relationship established by the model may not hold there. Factors such as nonlinearity, changing growth patterns, or physiological constraints could cause predictions to be unreliable or biased outside the data’s domain. Therefore, asserting that predicting height in this case would require extrapolation and that the linear model may no longer be valid beyond the observed data supports the statement as true.
Option 2: False. If one claimed it is not extrapolation or that the linear model will remain valid outside the data range, this would ignore a fundamental principle of many statistical models: their validity is typically constrained to the domain of the training data. Prediction beyond 90–130 cm shoulder girth without evidence of the relationship holding in that region is precisely extrapolation, and assuming the model stays accurate would be incorrect.
Additional nuance: It’s also worth noting that even within the data range, linear models can be imperfect if the true relationship is nonlinear or if heteroscedasticity exists. However, the core issue here is that 56 cm lies outside the 90–130 cm data window, making extrapolation the appropriate classification, which aligns with the statement in the question.

FA25_QTM_100_3 8.24: Body measurements, Part III- Requires Respondus LockDown Browser

Suppose a one-year-old child has a shoulder girth of 56 cm. Predicting the height of this child would require extrapolation. The data used to create the model is for people with approximately 90 to 130 cm shoulder girth. The linear model may no longer hold outside the range of the data.

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FA25_QTM_100_3 8.24: Body measurements, Part III- Requires Respondus LockDown Browser

Suppose a one-year-old child has a shoulder girth of 56 cm. Predicting the height of this child would require extrapolation. The data used to create the model is for people with approximately 90 to 130 cm shoulder girth. The linear model may no longer hold outside the range of the data.

View Explanation

Log in for full answers

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Consider the estimated regression model Y_hat = 0.5 + 1.2X1. This model was estimated on a data set where X1 has a range of values between 8 and 34. Should we use the model to predict Y_hat=2.9 = 0.5 + 1.22 for X1=2?