A Paired t-test is used to compare two related samples or repeated measurements on a single sample. It's often used in before-and-after scenarios where the same individuals are measured twice.

By definition, the probability of an impossible event is 0. This is because the measure of probability assigns 0 to events that cannot occur and 1 to events that are certain to occur.

Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay. In the context of a regression analysis, it refers to the condition when the error term (residuals) in a regression model is correlated with itself.

In an ANOVA test, the F-statistic is calculated as the ratio of the between-group variance (mean sum of squares between groups) to the within-group variance (mean sum of squares within groups). A larger F-statistic implies a greater degree of difference between the group means.

The difference between kurtosis and excess kurtosis comes down to a constant. Excess kurtosis is simply kurtosis minus 3. The "3" comes from the kurtosis of a normal distribution which is 3. Hence, excess kurtosis refers to kurtosis in relation to a normal distribution.

The 'R-squared' value, also known as the coefficient of determination, in a multiple linear regression model represents the proportion of variance in the dependent variable that can be predicted from the independent variables. It ranges from 0 to 1, where a higher value indicates a better fit of the model.

The support of a random variable is the set of values in the range of the variable that have non-zero probability. For a continuous random variable, it's the set of values over which the probability density function is non-zero.

In the Sign Test, the test statistic is computed by counting the number of positive and negative signs of the differences between paired observations.

The 'box' in a box plot represents the interquartile range (IQR) of the data. This is the range within which the middle 50% of the data falls, calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

According to the Central Limit Theorem, the distribution of the sample mean will approach a normal distribution as the sample size increases. Regardless of the shape of the population, the distribution of sample means taken with large enough sample size can be approximated by a normal distribution.