Yes, a symmetrical distribution can have nonzero kurtosis. Kurtosis is a measure of the weight in the tails, or the extreme values, which can occur in both directions, thus not affecting the symmetry. For example, a normal distribution is symmetric and has a kurtosis greater than zero.

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.

The standard error of a statistic is a measure of the statistical accuracy of an estimate, equal to the standard deviation of the theoretical distribution of a large population of such estimates. It is used to test hypotheses on the grounds of a set of data. For sample means, the standard error tells us how the mean varies from one sample to another.

Changing the units of measurement will change the scale of the data, and hence will affect the values of standard deviation and variance. If the data is scaled up, both measures will increase, and if the data is scaled down, they will decrease. However, the relative dispersion, as measured by the coefficient of variation, will remain the same.

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.