Data analytics primarily deals with the exploration, interpretation, and presentation of data to uncover insights and support decision-making. It involves gathering data, cleaning it, and then analysing it to identify trends, patterns, and correlations. Data analytics typically relies on statistical analysis and visualisation techniques to communicate findings to stakeholders.

On the other hand, data science encompasses a broader range of activities, including data analytics, but also involves the development of algorithms, machine learning models, and other computational methods to extract deeper insights and predictions from data. Data scientists not only analyze data but also design and implement algorithms to automate processes, make predictions, and optimize outcomes.

Sampling techniques, such as simple random sampling, stratified sampling, cluster sampling, systematic sampling, and convenience sampling, are essential tools in research methodology. They allow researchers to gather data efficiently by selecting a representative subset of individuals or items from a larger population. This process saves time and resources while still providing valuable insights into the characteristics and trends of the entire population.

The main advantage of sampling lies in its ability to provide accurate and reliable information while minimizing costs and efforts. By studying a carefully selected sample, researchers can make inferences about the population as a whole, making sampling a practical and effective method for data collection and analysis. Additionally, sampling helps reduce biases and errors that may arise when attempting to study an entire population, ensuring that research findings are more accurate and applicable.

Overfitting: When a machine learning model learns the training data too well, capturing noise or random fluctuations instead of the underlying pattern, leading to poor generalization to new, unseen data.

Underfitting: When a machine learning model is too simplistic to capture the underlying structure of the data, resulting in poor performance on both the training and test datasets.

In essence, the long format prioritizes flexibility and ease of analysis by structuring data vertically, allowing for straightforward manipulation and interpretation of each observation's attributes. This format is particularly beneficial when dealing with datasets containing repeated measures or hierarchical data, as it enables efficient handling of varying levels of granularity within the same dataset.

Conversely, the wide format emphasizes simplicity and comprehensibility by organizing data horizontally, with each variable occupying its own column. This format is advantageous for quickly comprehending the overall structure of the data, especially when dealing with datasets featuring numerous variables.

Eigenvectors are special vectors that don't change their direction when a linear transformation is applied to them. They might only get scaled (stretched or compressed) by a scalar factor. In simpler terms, they are like arrows that might change in length but keep pointing in the same direction after a transformation. Eigenvalues are the scalars that represent how much the corresponding eigenvectors are scaled during a linear transformation. They tell us how the eigenvectors are stretched or compressed. In essence, eigenvalues quantify the extent of stretching or compression of eigenvectors under a given transformation.

In statistical analysis, the p-value indicates the probability of obtaining results as extreme as the observed ones, assuming the null hypothesis is true. A high p-value, typically above 0.05, suggests weak evidence against the null hypothesis, indicating that the observed data is likely consistent with the null hypothesis. On the other hand, a low p-value, usually below 0.05, implies strong evidence against the null hypothesis, suggesting that the observed data is unlikely to have occurred if the null hypothesis were true, leading to its rejection in favour of an alternative hypothesis.

Resampling is typically performed in data analysis when there's a need to adjust the frequency or duration of data points, often to match a desired timeframe or to reduce noise. It's a fundamental technique in statistics and signal processing, aiding in making data more manageable or representative without infringing on copyright concerns.