We say we have ____________________ when a regression equation is used to make a prediction for a value of x that is outside the range of the values of x that were used to construct the regression equation.

Question

BlackTom AI · Accepted Answer

The question asks about the term used when a regression equation is employed to predict a value of x that lies outside the range of x-values used to fit the model.
Option 1: interpolation. Interpolation refers to predicting within the range of observed data, not beyond it. Since the scenario describes using the model to predict outside the observed x-range, this is not interpolation.
Option 2: correlation. Correlation describes the strength and direction of a linear relationship between two variables, not the act of making predictions outside the data range. It does not capture the extrapolation process.
Option 3: determination. Very commonly used in statistics as the coefficient of determination (R-squared), which measures the proportion of variance explained by the model. It is related to model fit, not to the act of predicting beyond observed x-values, so this option mischaracterizes the concept here.
Option 4: extrapolation. Extrapolation is exactly the process of using a regression equation to predict outcomes for x-values outside the range of the data used to create the model. This captures the described scenario where predictions are made beyond the observed domain.
Option 5: standardization. Standardization (or z-scoring) involves rescaling variables to have a standard mean and variance, not about making predictions outside the original data range. It does not address the extrapolation concept.
Thus, the option that aligns with predicting beyond the observed x-range is the one that describes extrapolation, which matches the scenario described in the question.

We say we have ____________________ when a regression equation is used to make a prediction for a value of x that is outside the range of the values of x that were used to construct the regression equation.

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We say we have ____________________ when a regression equation is used to make a prediction for a value of x that is outside the range of the values of x that were used to construct the regression equation.

View Explanation

Log in for full answers

Similar Questions

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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Would we use the regression line to predict growth in per capita income for cities where 70% of residents have at least 4 years of college?

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