Final answer:
A linearized model might be used when data seem to have a potential relationship, due to its simplicity and interpretability. Outliers can dramatically affect the analysis, leading to an inaccurate interpretation. If the data show a non-linear or curvilinear relationship, a least-squares regression may not be optimal even though it provides a uniform approach to data analysis.
Step-by-step explanation:
Using a linearized model might be preferred for several reasons when analyzing data that could be potentially related. The key is in the simplicity and interpretability that linear models offer. Although your regression equation 13.5x + 42.9 has a high R-value of 0.977, suggesting a strong linear relationship, this doesn't imply that a linear model is always the best representation of the data.
In some cases, data may show a non-linear relationship, which can be misconstrued by the influence of outliers. When outliers are present, they can dramatically affect the slope and intercept of the least-squares regression line, as well as the R-value, leading to an inaccurate interpretation of the data. By removing such outliers, you may obtain a more representative R-value that reflects the true nature of the relationship between variables.
Moreover, when you mention that the relationship between X and Y variables does not seem clear or appears curvilinear, it might be because the underlying relationship is not linear, in which case a least-squares regression may not be the best method for analysis. Despite this, a linearized model provides a fundamental and straightforward way to start analyzing and predicting behavior of variables since residuals are minimized in a least-squares regression line, creating a uniform approach.