Statistical Inference and Regression - Essay Example

Those who impress statistics tend to improve on the quality of data, the experimental designs, as well as survey sampling. They also give tools for forecasting, as well as prediction using statistical models. On the overall, statistics is quite applicable in many academic fields and it cuts across, the natural science, the social sciences, businesses and government. Statistical methods are used in summarizing and describing of collected data. Descriptive statistics is particularly useful in research work especially when communicating the experimental results.

Patterns in data can be modeled in such a way that it accounts for the uncertainty or randomness in the observation, which are then used in drawing of conclusion about the given population under study (Bethea, & Boullion, 2005). This is what is called the inferential statistics. Inferences are extremely crucial elements as far as scientific advancements are concerned. It helps in providing a means through which conclusions are drawn for the data that are subject to random variations. The application of both descriptive statistics and inferential statistics comprise applied statistics.

The theoretic statistics are concerned with the logical arguments that underlie justification of certain approaches to statistical inference. Mathematical statistics involves the manipulation of the probability distribution that is necessary for deriving outcomes that are closely related to methods of estimation and the inferences (Bethea, & Boullion, 2005). Probability cuts across various fields and encompasses many definitions. This paper discusses statistical inferences and cuts across other areas of statistics including regression, linear regression, nonlinear regression, least-squires method, and the maximum likelihood method.

Statistical Inference The term statistical inference as used in statistics is taken to mean the process of drawing or making conclusions from data that are subject to random variations. The example of statistical inference is the sampling variation or the observational errors (Bethea, & Boullion, 2005). More often than not, the terms inferential statistics, statistical inference and statistical induction are used in describing systems of procedures that may be used in drawing of concussions’ from data sets that arise from systems that are affected by random variations including random experimentation and observational errors.

The initial requirements of the system of processes for the inference and the induction are that the system produces reasonable answers whenever applied to defined situations. It should also be general enough so that it can be applied in all situations. Maximum likelihood method. Estimation problems involve estimating the value of the one or many population parameters from any random samples of the population (Bethea, & Boullion, 2005). Point and interval estimation are the two categories of estimation.

Interval estimation is used in determining the probability of the outcome that occurs in any given limits while point estimation takes Fisher’s estimation. The term likelihood is also, one key concept used in statistical inference, and it is always calculated for any fixed sample while providing information about the relative probability of any sample data that is as a function of the distribution parameters. The likelihood function is used to measure how likely a given data sample is as the function of