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.

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.

Simple random sampling is a basic type of sampling method where each individual in the population has an equal chance of being selected. This ensures that the sample will be representative of the population, making it easier to make accurate inferences about the whole population.

In a 95% confidence interval, if the true population parameter lies outside of the interval, it is considered a Type I error. This is when the null hypothesis is true, but is incorrectly rejected.

PCA reduces the dimensionality of a dataset by creating new uncorrelated variables that successively maximize variance. These new variables or "principal components" can replace the original variables, thus reducing the data's dimensionality.

The Central Limit Theorem (CLT) states that, given certain conditions, the mean of a sufficiently large number of independent random variables will be approximately normally distributed, regardless of the shape of the original distribution. This underpins many statistical methods, including hypothesis tests and confidence intervals, which may assume normality of the sampling distribution.

Box plots are particularly useful for identifying outliers in a dataset. The box plot displays a summary of the data distribution including minimum, first quartile, median, third quartile, and maximum. Outliers are typically represented as individual points that are far from the 'box' and 'whiskers'.

A sample in statistics is a subset of individuals or observations from a larger population. Sampling is a key concept in statistics and data science because it allows us to collect and analyze a manageable amount of data that represents a larger group.