The Chi-square test for goodness of fit is used to test whether the observed data fits a specific distribution. It compares the observed data with the values that would be expected under the theoretical distribution.

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.

The skewness of a distribution can be determined using a box plot by looking at the position of the median in the box. If the median is not in the center of the box (i.e., the quartiles are not equidistant from the median), the data is skewed. If the median is closer to the bottom of the box, the data is positively skewed, and if it's closer to the top, the data is negatively skewed.

The silhouette score is a measure of how close each point in one cluster is to the points in the neighboring clusters. It ranges from -1 (incorrect clustering) to +1 (highly dense clustering). 0 indicates overlapping clusters.

Non-parametric tests can be used with nominal, ordinal, interval, and ratio scales of measurement. This is one of the reasons why non-parametric tests are sometimes chosen over parametric ones, as they can handle data that are not interval or ratio (which are required for many parametric tests).

Homoscedasticity refers to the assumption in regression analysis that the variance of the residuals (or "errors") is constant across all levels of the independent variables.

Simple linear regression is a statistical method that allows us to summarize and study relationships between two continuous (quantitative) variables: One variable, denoted x, is regarded as the predictor, explanatory, or independent variable. The other variable, denoted y, is regarded as the response, outcome, or dependent variable.

The probability of an event cannot be a negative number. By definition, the probability of an event is a number between 0 and 1, inclusive.

The key characteristic of a symmetric distribution is that it has the same shape on the left and right when split vertically at the center (i.e., about the mean). This means that the frequencies of corresponding values on either side of the center are equal.