Final answer:
A linearized model might be used instead of a linear regression when the relationship between variables is curvilinear. Transforming the data can result in a linear relationship that is more suitable for regression analysis, and it helps in simplifying the interpretation of the data.
Step-by-step explanation:
The least squares regression equation given is 13.5x + 42.9, with an R-value of 0.977. This suggests a strong positive linear relationship between the X and Y variables.
However, there are instances, such as when the relationship is curvilinear rather than linear, where a linear regression model may not be the most appropriate. In such cases, using a linearized model can transform the curvilinear relationship into a linear form where linear regression techniques can then apply effectively.
Using a linearized model can also simplify complex relationships, making it easier to understand and interpret the data.
Additionally, if there are any significant outliers or influential points, as suggested in one example where the omission of an outlier resulted in a different slope and improved r-value, a linearized model might be better suited to capturing the true nature of the data set without being overly influenced by such points.