Simple and Multiple Regression
Regression analysis is a popular statistical technique used in several fields including finance. It is a method that employs a set of statistical processes to determine the relationship between a dependent variable and one or more independent variables. Simple linear regression is a statistical tool used to quantify the relationship between a single independent variable and one dependent variable. On the other hand, multiple regression can be seen as an extension of simple linear regression. It is usually used when the researcher wants to estimate the value of one variable (dependent) based on the values of two or more variables (independent).
Auxiliary analyses are performed when a researcher wants to make estimates on incomplete data. Auxiliary variables are never part of the main analysis. They are usually associated with the probability of "missingness" in a variable. Also, they can be related to the incomplete variable itself. Including auxiliary variables in missing data analyses allows you to take into account the reason why data might miss at a random situation and also more information about the incomplete values.
Panel data is also sometimes referred to as longitudinal data. This type of data provides observations about different cross-sections at different times. Panel data series can be made up of the name of countries, firms, individuals, demographic groups, etc. The observations from panel data are usually collected chronologically and at a regular frequency, just like time-series data. Cross-sectional data can be seen as a special case of panel data in one dimension.
Time series can be defined as a sequence of numerical data points that are listed successively. This type of analysis is used in statistics to make a forecast for the future. In business, time series forecasting can be used to see how an economic variable, asset, or security changes over time. To understand time series, you must be well-versed in concepts such as exponential smoothing, differencing, stationarity, dependence, and specification.
Nonparametric statistics is used to make statistical inferences without any consideration of the underlying distribution. It perfectly fits a normal distribution without assumptions. Since nonparametric statistics heavily relies on rankings instead of numbers, its approach is usually ordinal. Nonparametric statistical methods can be of two types. One makes statistical inference without any regard for the underlying distribution. The other strives to discover the unknown underlying distribution of data that is being observed.
Statistical inference is the process of performing analysis on a result and drawing conclusions from a data subject. It can also be referred to as inferential statistics. It involves making critical decisions about the parameters of a population, based on random sampling. Statistical inference is applied in hypothesis testing and confidence intervals to estimate uncertainty or sample to sample variation. Types of statistical inference include multivariate regression, T-test, Bi-variate regression, Pearson Correlation, Chi-square statistics, etc.
Statistical Quality Control
Statistical quality control is the process of using statistical techniques to monitor and maintain the quality of products and services. One of the techniques used in statistical quality control is the acceptance of sampling. This method is often used when it is imperative to decide on accepting or rejecting a group of parts based on the quality found in a sample. Another technique known as statistical process control determines whether we should continue with the process or adjust it to achieve the desired quality. Statistical process control uses control charts (graphical displays).
Theory of Sampling
A sampling system estimates the specific properties of a population being studied. You can only know how good a sampling system is if the estimates obtained are accurate and precise. However, a good sampling system may occasionally give estimates that are far from the true value just like a poor system may. It is for this reason that a sampling system is usually judged by the distribution frequency of the many estimates obtained from repeated sampling. With this method, an excellent sampling system provides a frequency distribution with the least variance. The mean estimate is also the same as the true value.