Variance and the square of the standard deviation are the same. The variance is calculated as the mean of the squared deviations from the mean, and the standard deviation is the square root of this variance. Hence, squaring the standard deviation gives us the variance.

Polynomial regression allows modeling of non-linear relationships. Unlike linear regression that models relationships between variables as a straight line, polynomial regression models relationships as curves, better capturing relationships that change in direction at different levels of the independent variables.

The maximum value that a probability can take is 1. This signifies that an event is certain to occur. In probability theory, probabilities range from 0 (implying the event is impossible) to 1 (implying the event is certain).

A Bernoulli distribution is a discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q=1-p. It models a single trial with two possible outcomes, often labelled 'success' and 'failure'.

In multiple regression, model selection aims to choose the most parsimonious model that best predicts the response variable. A parsimonious model is a model that accomplishes the desired level of explanation or prediction with as few predictor variables as possible.

If the Chi-square test for goodness of fit is statistically significant, this means that the observed data differs significantly from what we would expect if the data followed the theoretical distribution.

Pearson's Correlation Coefficient is highly sensitive to outliers. This is because it involves a mean and standard deviation calculation, and these values can be greatly influenced by outliers. Even a single outlier can significantly skew the result of the correlation.

In statistics, a population is the entire group of individuals or observations that we want to understand or draw conclusions about. It's the total set of observations that can be made. For example, if you want to know the average height of an adult male in the US, the population would be all adult males in the US.

The first Principal Component is the direction (or vector) in the multidimensional space along which the data varies the most, so it captures the most variance in the data.

The whiskers of a box plot are used to indicate the variability of the data outside the upper and lower quartiles. They often extend to the maximum and minimum data values (excluding outliers), or 1.5 times the interquartile range.

One common feature of non-parametric methods is the use of ranks rather than raw data points, which makes them more robust to outliers and does not require the assumption of a specific distribution.

The p-value is the probability of obtaining a result as extreme as, or more extreme than, the result actually obtained, assuming the null hypothesis is true. If the p-value is smaller than the significance level (alpha), we reject the null hypothesis.