The theorem combines our prior knowledge (the prior probability) and evidence (the likelihood) to provide a new, updated probability of an event (the posterior probability).

A confidence interval is composed of three parts: a point estimate (the sample mean), a margin of error (which depends on the standard error and the Z-value or T-value), and the level of confidence (which indicates the probability that the interval estimate contains the population parameter).

Techniques like forward selection, backward elimination, and stepwise regression are commonly used for model selection in multiple regression.

The presence of a pattern in the residuals of a multiple linear regression model can indicate a violation of the independence assumption. This assumption requires that the residuals, which are the differences between the observed and predicted values of the dependent variable, are independent of each other. If a pattern is observed in the residuals, it may indicate that the residuals are not independent, and the model may not provide valid results.

Quantitative data can be further classified as discrete and continuous. Discrete data is countable and has a finite number of possible values, such as the number of students in a class. Continuous data can take any value within a given range, such as the weight of a person.

Outliers can have a big impact on the skewness of a dataset. If the outlier is greater than the rest of the data, it will pull the skewness positive, and if it is less than the rest of the data, it will pull the skewness negative.

The Sign Test ignores the magnitude of the differences between paired observations, and only considers the sign of the differences.

Larger sample sizes reduce the standard error and thus, the width of the confidence interval becomes narrower. This means that with larger samples, our estimates are more precise.

The Kaiser-Meyer-Olkin (KMO) measure is a measure of how suitable the data is for factor analysis. It determines the adequacy for each observed variable and for the complete model. KMO estimates vary between 0 and 1. A value of 0 indicates that the sum of partial correlations is large relative to the sum correlations, implying diffusion in the pattern of correlations (hence, factor analysis will be likely inappropriate).

K-means clustering is a commonly used technique for clustering data in a database. It is an unsupervised learning algorithm that partitions data into k clusters based on their attributes' similarity. K-means clustering is widely used for data analysis and segmentation tasks.