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Abstract-In statistics and data analysis, we often need to establish a relationship between the various parameters in a data set. This relationship is important for prediction and analysis. Regression Analysis is such a technique. This work mainly focuses on the different Regression Analysis models used nowadays and how they are used in context of different data sets. Picking the right model for analysis is often the most difficult task and therefore, these models are looked upon closely in this research. While a Linear Regression Analysis model is used to fit linear data, a Polynomial Regression Analysis model focuses on a data set representing polynomial relationship between data parameters. Logistic Regression model is used in a scenario where we need a binary type of prediction. When the data set becomes complex, these models may suffer from issues like Underfitting and Overfitting. Ridge and Lasso Regression are considered the best models to deal with this type of situation. Ridge regression is used when data suffers from multicollinearity, that is independent variables are highly correlated. Lasso regression differs from ridge regression in a way that it uses absolute values in the penalty function, instead of squares. Using these models in the right way and with right data set, Data Analysis and Prediction can produce the most accurate results.

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During last few years, many soft computing techniques have been employed for image watermarking. These are more into delving the issue of optimization of visual quality of signed images and robustness of the embedding algorithm. The used techniques either operate in adaptive or learning mode, especially those using Artificial Neural Networks or in non adaptive analytical mode such as ones based on Fuzzy logic. Several researchers have also worked on this problem using hybrid and evolutionary algorithms. This research survey especially deals with the image watermarking techniques which rely on adaptive soft computing techniques. The results of gradient descent based Back propagation Network (BPN algorithm, Radial Basis Function Neural Network (RBFNN algorithm and a newly developed Single Layer Feed forward Neural Network (SLFN algorithm commonly known as Extreme Learning Machine (ELM) used to carry out watermarking in uncompressed grayscale images are compared. These techniques are compared for different images and the comparison is based on the visual quality of signed images, the watermark detector response coefficients such as similarity correlation and normalized correlation parameters and the robustness studies. Time complexity issue is also examined to establish the use of watermarking process on a real time scale. It is concluded that the ELM algorithm gives a reasonable generalized behavior in terms of computation of these parameters as compared to its other counterparts. It's fast training in milliseconds and subsequent embedding and extraction makes it suitable for developing watermarking application on a real time scale.