Multicollinearity is a problem that can occur in multiple linear regression when two or more predictor variables are highly correlated with each other. This can lead to unstable estimates of the regression coefficients and make it difficult to determine the individual effects of the predictor variables.

In the context of probability, an outcome refers to a possible result of a random experiment. For example, if the experiment is tossing a coin, the possible outcomes are 'Heads' or 'Tails'. Each outcome is considered mutually exclusive, meaning only one outcome can occur at a time.

The assumptions of factor analysis include normality (the variables used in the analysis should be normally distributed), linearity (the relationship between the factors and the variables should be linear), and homoscedasticity (the variances of the errors should be constant).

The Gaussian or normal distribution has several important properties and is widely used in statistics and natural sciences. It's significant because it is the distribution that maximizes entropy among all distributions with given mean and variance, making it the most "uninformative" and often serving as a good default choice in many scenarios. Also, according to the central limit theorem, the sum of many independent and identically distributed (i.i.d.) random variables tends toward a normal distribution.

Pearson's correlation coefficient measures linear relationships, while Spearman's Rank Correlation measures monotonic relationships. Monotonic relationships are ones where the variables tend to change together, but not necessarily at a constant rate. Pearson's Correlation is used when the data is normally distributed, whereas Spearman's Rank Correlation is used when the data does not assume normal distribution.

If the Chi-square statistic is significantly larger than the critical value, we reject the null hypothesis in favor of the alternative hypothesis. This suggests that there is a significant association between the variables.

Qualitative data has several limitations in data analysis. Firstly, it cannot be easily quantified for statistical analysis which limits its utility in certain research settings. Secondly, collecting and analyzing qualitative data often requires substantial resources and time, which can be a challenge for large-scale studies. Lastly, qualitative data may be influenced by researcher bias, particularly during data collection and interpretation.

The assumption of normality in residual analysis states that if we draw a large number of samples and create a distribution of the sample means, this distribution will be well approximated by a normal distribution. This is necessary to make inferences about the regression coefficients and to calculate prediction intervals.

In the Wilcoxon Signed Rank Test, zeros in the difference of paired observations are typically discarded.

The primary purpose of ANOVA (Analysis of Variance) is to test if there is any statistically significant difference between the means of three or more groups.