Non-parametric tests are also known as distribution-free tests because they make fewer assumptions about the data, specifically, they do not require the data to follow a specific distribution.

To test the assumption of independence in a Chi-square test for goodness of fit, you can conduct a separate Chi-square test of independence. This test compares the observed frequencies in each category with what we would expect if the variables were independent.

Skewness affects the relationship between the mean, median, and mode. In a positively skewed distribution, the mean is usually greater than the median, which is greater than the mode. In a negatively skewed distribution, the mode is usually greater than the median, which is greater than the mean.

The Central Limit Theorem holds true when the sample size is sufficiently large (usually n > 30), regardless of the shape of the population distribution. This theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

In the field of statistics, a parameter is a numerical characteristic of a population, whereas a statistic is a numerical characteristic of a sample. Parameters are often unknown because we cannot examine the entire population. We use statistics, which we compute from sample data, to estimate parameters.

Adding more predictors to a model may increase the R-squared value, making it appear that the model is improving. However, if these additional predictors are not truly associated with the response variable, it may result in overfitting, making the model perform poorly on new, unseen data.

Ridge regression introduces a regularization term (penalty term) into the loss function which helps to shrink the coefficients towards zero and mitigate the effect of multicollinearity.

PCA relies heavily on the concepts of Eigenvalues and Eigenvectors. These allow it to determine the axes along which the data has the most variance, which are used to form the new variables (principal components).

Homoscedasticity is the condition in which the variance of the errors or residuals is constant across all levels of the explanatory variables. It is one of the key assumptions of linear regression.

In probability, two events are independent if the occurrence of one event does not affect the occurrence of the other. This means that the probability of both events occurring is the product of their individual probabilities.