This document provides an overview of descriptive and inferential statistics, as well as regression analysis. Descriptive statistics summarize and describe data through measures like averages and proportions. Inferential statistics make predictions about larger populations based on samples and allow generalizing beyond the data. Regression analysis helps understand relationships between dependent and independent variables and can be used for prediction and exploring variable relationships. Common uses of these statistical techniques include medical research, demographics, forecasting, and exploring causal relationships.

1. A REVIEW OF STATISTICS Computational Linguistics Sergio Alba González

2. Descriptive Statistics It is used to say something about a set of information that has been collected only. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data. With descriptive statistics you are simply describing what is or what the data shows (what's going on in our data). Descriptive statistics help us to simply large amounts of data in a sensible way. Each descriptive statistic reduces lots of data into a simpler summary. So every time you try to describe a large set of observations with a single indicator you run the risk of distorting the original data or losing important details. Even given these limitations, descriptive statistics provide a powerful summary that may enable comparisons across people or other units.

3. Common uses : Some examples of the use of descriptive statistics occurs in medical research studies (e.g. for each treatment or exposure group), and demographic or clinical characteristics such as the average age, the proportion of subjects with each gender, etc.

4. Inferential Statistics It is used to make predictions or comparisons about a larger group (a population) using informaton gathered about a small part of that population. Unlike descriptive statistics, inferential statistics are often complex and may have several different interpretations. Though, inferential statistics involves generalizing beyong the data, something that descriptive statistics does not do. It is extremely important to understand how the sample being studied was drawn from the population. The sample should be as representative of the population as possible. There are several valid ways of creating a sample from a population, but inferential statistics works best when the sample is drawn at random from the population. Given a large enough sample, drawing at random ensures a fair and representative sample of a population.

5. Common uses : With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population might think, to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study and to make inferences from our data to more general conditions

6. Regression Regression analysis helps us understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables — that is, the average value of the dependent variable when the independent variables are held fixed. Less commonly, the focus is on a quantile , or other location parameter of the conditional distribution of the dependent variable given the independent variables.

7. Common uses : Regression analysis is widely used for prediction (including forecasting of time-series data). It is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables. The performance of regression analysis methods in practice depends on the form of the data-generating process. A large body of techniques for carrying out regression analysis has been developed:- L inear regression , - O rdinary least squares regression , - Nonparametric regression , etc.

8. Bibliography I took this information from: Class handbook (An Introduction to Statistics) by Keone Hon. Wikipedia, the free encyclopedia.