Which method is most effective in identifying how preprocessing techniques affect a deep learning model's accuracy and training time?

Performing a multivariate regression analysis with preprocessing techniques as independent variables is particularly effective in identifying how different preprocessing methods impact both the accuracy of a deep learning model and its training time. This approach allows for a thorough analysis of multiple preprocessing techniques simultaneously, providing insight into their individual contributions to the model's performance metrics.

By treating the preprocessing methods as independent variables, researchers can quantify how variations in these methods correlate with changes in accuracy and training time, establishing a clear picture of their effects. The multivariate nature of the analysis also takes into account potential interactions among preprocessing techniques, allowing for a more comprehensive understanding of how they work together or compete in influencing model outcomes.

In contrast, conducting a t-test may compare just two sets of preprocessing techniques but lacks the depth of analysis required for multiple methods. Using a line chart to visualize training time, while informative, does not provide quantitative measures or causal relationships that help understand the impact of preprocessing methods on accuracy. A pie chart would only show the distribution of techniques used without imparting any underlying insights into their effects on model performance.

Thus, the multivariate regression approach stands out as the most effective method for capturing the complex relationships between preprocessing techniques and their influence on model metrics.