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 method of least squares is commonly used to find the best fitting line in simple linear regression. It minimizes the sum of the squares of the residuals (the vertical distances between the observed and predicted values).

A Type II error occurs when the null hypothesis is false, but it is not rejected. It is also known as a "false negative" result.

The Chi-square statistic in a Chi-square test for independence represents the sum of the squared differences between observed and expected frequencies, divided by the expected frequencies. This statistic measures the degree to which the observed frequencies deviate from the frequencies that would be expected under the null hypothesis of independence.

In a Chi-square test, the expected frequency for each cell in the contingency table is calculated by multiplying the row total and column total and then dividing by the total number of observations.

The Pearson Correlation Coefficient measures the linear relationship between two variables and can range from -1 to 1. A value of -1 means there is a perfect negative correlation, while a value of 1 means there is a perfect positive correlation.

Nominal and ordinal data are both types of categorical data. The key difference between the two is that while nominal data cannot be ordered or ranked, ordinal data can. Nominal data represents simple categories or groups with no order or priority. Examples include colors or city names. Ordinal data, on the other hand, represents categories that can be ranked or ordered. Examples include Likert scale data (e.g., a five-point scale from "strongly disagree" through "strongly agree"), educational level (high school, BA, MA, PhD), etc.

A residual plot in multiple linear regression is used to check various assumptions of the model. It can help visualize if the residuals are randomly scattered (checking for independence), whether they have a constant variance (homoscedasticity), and if they exhibit any noticeable patterns (checking for linearity and normality).