True or false? If a particular observation from the population is less than the population average, then the residual is positive.TrueFalse

Analysis of the Statement

1. Understanding Residuals:

   • A residual is defined as the difference between observed values and the values predicted by a model. In the context of a population average, if we consider the average as a predicted value, then the residual can be expressed as: $\text{Residual} = \text{Observed Value} - \text{Population Average}$

2. Interpreting the Statement:

   • The statement claims that if a particular observation is less than the population average, then the residual is positive:
   • Mathematically, if: $\text{Observed Value} < \text{Population Average}$
   • This leads to: $\text{Residual} = \text{Observed Value} - \text{Population Average} < 0$
   • This shows that the residual would actually be negative.

Conclusion

Given the explanation and mathematical representation:

Final Answer

False