The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, 68% of the data fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations. This rule provides a quick estimate of the probability of a certain event within the distribution.

ANOVA stands for Analysis Of Variance. It's a statistical technique used to check if the means of two or more groups are significantly different from each other.

The Central Limit Theorem states that, given certain conditions, the arithmetic mean of a sufficiently large number of iterates of independent random variables, each with a well-defined (finite) expected value and finite variance, will be approximately normally distributed, regardless of the shape of the original distribution.

Polynomial regression models relationships as curves, not straight lines. This allows polynomial regression to capture non-linear relationships, where the relationship changes direction at different levels of the independent variables. On the other hand, linear regression models relationships as straight lines, assuming a constant rate of change.

Pearson's Correlation Coefficient assumes that the variables are normally distributed. It's one of the key assumptions made when calculating the coefficient, and it refers to the shape of the distribution of the values.

In factor analysis, eigenvalues represent the total variance explained by each factor. A larger eigenvalue indicates that more of the total variance is accounted for by that factor.

For Pearson's Correlation Coefficient to be valid and reliable, the following assumptions should be met: both variables should be continuous, they should be linearly related, and both variables should be approximately normally distributed. Independence of observations is also required.

Sampling in statistical analysis is primarily used to estimate population parameters. Since it's often impractical or impossible to gather data from every individual in a population, we use samples to make inferences about the population as a whole.

The null hypothesis of the Spearman's Rank Correlation test is that there is no monotonic relationship between the variables. That is, changes in one variable do not consistently correspond to changes in the other variable.

The probability of the intersection of two independent events is calculated as the product of their individual probabilities. So if A and B are independent, P(A ∩ B) = P(A) * P(B). This is a direct result of the Multiplication Rule for independent events.