When two variables increase and decrease together, they are said to have a positive correlation. This is indicated by a positive Pearson's Correlation Coefficient.

This is known as multicollinearity. In regression analysis, multicollinearity refers to a situation where two or more independent variables are highly correlated. This can make it difficult to determine the effect of each individual variable on the dependent variable and can lead to unstable and unreliable estimates.

Multiple linear regression is a statistical technique used to predict the outcome of a response variable based on the value of two or more explanatory variables.

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'.

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).

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.

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.

In probability theory, an "outcome" is a possible result of an experiment or trial. For example, if you toss a coin, the possible outcomes are heads or tails. Each outcome of an experiment corresponds to a unique event.

When adding polynomial terms or interaction effects to a regression model, the assumption of linearity might be violated. The linearity assumption in regression analysis states that the relationship between the independent and dependent variables is linear, i.e., a change in the independent variable will result in a constant change in the dependent variable. When adding polynomial terms or interaction effects, we are essentially modeling a non-linear relationship.

A bimodal distribution is one that has two different modes, or peaks. This can often be identified in a histogram, where two separate areas of the data have higher frequencies. This might indicate that the data is drawn from two different populations.