A confidence interval is calculated using the sample mean plus and minus the standard error. Specifically, it is calculated by taking the point estimate and adding/subtracting the margin of error (which is the standard error multiplied by the relevant Z-value or T-value).

In a uniform distribution, all outcomes are equally likely. This distribution is characterized by two parameters, a and b, which are the minimum and maximum values, respectively. The probability of any outcome is constant and equal across the entire range of the distribution.

A sample might not accurately represent the population when the sampling method is biased. In this case, the sample may not be diverse enough or inclusive of all relevant aspects of the population. This can lead to skewed results and inaccurate inferences about the population. Hence, it's essential to choose an unbiased sampling method.

In cluster analysis, a cluster is a group of similar data points. The goal of cluster analysis is to group, or cluster, observations that are similar to each other.

The range is the simplest measure of dispersion, calculated as the difference between the maximum and minimum values in a dataset. It gives us an idea of how spread out the values are, but it doesn't take into account how the values are distributed within this range.

Model selection refers to the process of choosing the most appropriate regression model for the data among a set of potential models.

A Pearson correlation coefficient of +1 indicates a perfect positive correlation. This means that every time the value of the first variable increases, the value of the second variable also increases.

Non-parametric statistical methods are most useful when the data does not meet the assumptions for parametric methods. For example, if the data does not follow a normal distribution, or if there are concerns about outliers or skewness, non-parametric methods may be appropriate.

Overfitting in polynomial regression can be addressed by using regularization techniques, such as Ridge or Lasso, which add a penalty term to the loss function to constrain the magnitude of the coefficients, resulting in a simpler model. Other strategies can include reducing the degree of the polynomial or using cross-validation to tune the complexity of the model.

The F-statistic in the context of a multiple linear regression model is used to test the overall significance of the model. The null hypothesis is that all of the regression coefficients are equal to zero, against the alternative that at least one does not.

The Variance Inflation Factor (VIF) assumes a linear relationship between the predictor variables. This is because VIF is derived from the R-squared value of the regression of one predictor on all the others.

The null hypothesis is the status quo or the statement of no effect or no difference, which is assumed to be true until evidence suggests otherwise.