In multiple linear regression, the F-statistic is used to test the overall significance of the model. This test checks the null hypothesis that all regression coefficients are zero against the alternative that at least one of them is not zero. If the F-statistic is significantly large and the corresponding p-value is small, we reject the null hypothesis, concluding that the regression model has some validity in predicting the outcome variable.

The least squares method is used to find the best-fitting line through the data points. This is done by minimizing the sum of the squares of the vertical distances of the points from the line.

A binomial distribution is appropriate when conducting an experiment where each trial has exactly two possible outcomes (often termed success and failure), the trials are independent, and the probability of success is constant across trials.

In simple linear regression, the dependent variable is the outcome we are trying to predict, and the independent variable is the predictor. The dependent variable is also known as the response or target variable, and the independent variable is also known as the explanatory or feature variable.

Discrete probability distributions are used when the outcomes are countable or discrete. Examples include the number of heads when flipping coins or the number of defective items in a batch. Continuous probability distributions are used when outcomes are uncountably infinite, typically involving measurements. Examples include the height of individuals or the time it takes to run a mile.

The Mann-Whitney U test is used for comparing independent distributions, particularly to determine whether two independent samples were drawn from a population with the same distribution.

A random variable in probability theory is a variable that can take on different values, each with an associated probability. It's not "random" in the everyday sense of the word, but its exact value is uncertain until it's observed.

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.

The standard deviation, a measure of dispersion or spread, determines the width of a normal distribution. A larger standard deviation results in a wider, flatter distribution, while a smaller standard deviation results in a narrower, steeper distribution.

Transformations, such as logarithmic or square root transformations, can help in reducing skewness by making the distribution more symmetric. The choice of transformation often depends on the degree and direction of skewness.

Multicollinearity is diagnosed in a multiple linear regression model by checking the correlation matrix and the Variance Inflation Factor (VIF). A high correlation between independent variables and a VIF greater than 5 or 10 suggests the presence of multicollinearity.

According to the empirical rule (also known as the 68-95-99.7 rule), in a normal distribution, about 68% of the data lies within one standard deviation of the mean, about 95% lies within two standard deviations, and about 99.7% lies within three standard deviations.