The principle of equally likely outcomes is a basic assumption in the classical definition of probability. It states that if an experiment has n outcomes, and there's no reason to believe that any one outcome is more likely than any other, then each outcome is assumed to have an equal probability of 1/n. For example, in tossing a fair coin, heads and tails are equally likely.

DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based clustering method that can find arbitrary shaped clusters and is less affected by outliers. It works based on the density of points in a region, growing clusters according to the density estimate.

The standard deviation measures the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.

If the p-value from a Mann-Whitney U test is less than the significance level (often 0.05), you would reject the null hypothesis, suggesting there is a significant difference between the groups.

The Law of Large Numbers states that as a sample size grows, its mean gets closer to the average of the whole population. In other words, as the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes.

A Residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis. If the points in a residual plot are randomly dispersed around the horizontal axis, a linear regression model is appropriate for the data; otherwise, a non-linear model is more appropriate.

The Mann-Whitney U test does not provide information about the shape of the distributions. It is a non-parametric test that does not make any assumptions about the distribution of the data.

Multiple linear regression analysis is used to understand the relationship between several independent (explanatory) variables and a dependent (response) variable. It can also be used for predicting the mean value of the dependent variable given the values of the independent variables.

A larger sample size decreases the spread of the sampling distribution of the mean. This is because as the sample size increases, the standard error (a measure of the spread of the distribution of sample means) decreases, which means that the sampling distribution becomes more concentrated around the true population mean.

The eigenvalue of a component in PCA is directly proportional to the variance of that component. In other words, a larger eigenvalue corresponds to a larger amount of variance explained by that principal component.