Question

A company found that a strong positive linear relationship exists between Y, its sales, and X, advertising expense. Predicting Y for values of X outside the range of the sample data is risky for which of the following reasons?

a. Extrapolation may lead to inaccurate predictions.
b. Interpolation may lead to inaccurate predictions.
c. The sample data is unreliable.
d. The correlation is weak.

Answer 1

Extrapolation beyond the observed range of X values is risky because the linear relationship may not hold outside the sample range, potentially leading to inaccurate predictions of Y. The Correct Answer is Option.A.

Step-by-step explanation:

Predicting Y for values of X outside the range of the sample data is risky for the following reason: a. Extrapolation may lead to inaccurate predictions. When the X and Y variables have a strong positive linear relationship, they are good candidates for analysis with linear regression, but this model is most reliable within the domain of observed X values. Predicting values outside of this domain, a process known as extrapolation, can be problematic because the linear relationship may not hold outside the sample range; this can lead to significant errors in the prediction of Y.

For example, if a company has observed sales increase with advertising expenses and model this with a regression line, it can be tempting to predict future sales for much higher advertising costs. However, the actual relationship between sales and advertising might change at higher expense levels (e.g., reaching a point of diminishing returns), making extrapolated predictions unreliable.