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**SOME IMPORTANT STATISTICS HOMEWORK TOPICS:**

**Matlab** is the abbreviation for Matrix Laboratory, is a proprietary programming language and multiparadigm numerical computing environment that was designed primarily to be used by engineers and scientists. The feature that distinguishes Matlab is its language since it is a matrix-based language through which computational mathematics can be conveniently expressed. Matlab is used in academia for research purposes, and it is also used in various industries. It can be useful in organizing, sorting, and analysing complex sets of data from fields as diverse as finance or climatology. Using Matlab, one can analyse data, develop algorithms, create models and applications.

**Matlab features include:**

1. Thousands of in-built functions for statistical analysis, signal processing, and machine learning.

2. Processing abilities which particularly apply to scientific or engineering data.

3. Scope for data visualization which is customizable and considerably interactive.

4. Scope for analysing Big Data without having to make great changes in the codes.

5. Automatic generation of reports after analysis which can be easily shared.

6. Simple codes and added hardware can improve performance.

7. There is scope for extensive professional documentation.

The statistical analysis feature makes Matlab an important programming language and computing environment. It includes various statistical analysis methods, as below:

- Analysis of variance
- Reducing data sets
- Fitting distributions
- Fitting regression models
- Performing simulation of randomly generated numbers
- Managing data
- Visualizing data
- Calculation of summary statistics
- Tests of significance
- Data filtering
- Descriptive statistics
- Hypothesis testing and ANOVA, and so on.

Matlab’s spatial statistics toolbox is well suited for estimating large-scale lattice models. The toolbox consists of prebuilt codes for conditional spatial autoregressions (CAR), simultaneous spatial autoregression (SAR), mixed regressive spatially autoregressive (MRSA) models, and so on. Such in-built codes can also be used for finding log-determinants and for creating sparse spatial weight matrices. All common estimators which are used in econometrics are therefore included in the Matlab spatial statistics toolbox, making it ideal for this field of study. These estimators can also enhance computation speed so as to expand the size of the data set analysed. Different versions of the toolbox have their unique features to offer, for instance, Spatial Statistics Toolbox 1.1 include 506 observation spatial data set about pollution, 3107 observation spatial dataset about US presidential election turnout, 20640 observational spatial data set about California house valuations, and so on. Likewise, Spatial Statistics Toolbox 2.0 contains spatiotemporal data from Baton Rouge.

While Excel is popularly used for basic data analysis applications, most industries and academicians do not have faith in excel for the elaborate analysis they are required to perform, and MATLAB can supplement the limitations of excel in this regard. MATLAB has thousands of in-built mathematical and advanced analysis features which can help to automate the analysis, and support representation of analysed data/ reports with visualization tools. Data science is made easy by MATLAB since it performs the following tasks:

- ➤It helps users to access data that are stored in data files, cloud storage, flat files, or data historians. Users can also connect to live sources like financial data feeds and data acquisition hardware.
- ➤It can document data analysis with Live Editor notebook environment and MATLAB graphics.
- ➤Its data types and pre-processing capabilities for interactive and programmatic data preparation can be used to organize and sort data; this can include the use of apps for ground truth labelling.
- ➤Machine learning models can be automatically converted to C/C++ codes.
- ➤Machine learning and deep learning apps help to explore diverse approaches.
- ➤Deep learning and machine learning tools can be fine-tuned using hyperparameter tuning, automated feature selection, and model selection algorithms.

In exploratory data analysis, the interactive features of Matlab can be used derive subsets of data and to statistically analyse numerous groups of related data. Matlab can automatically generate codes for performing the tasks, and users have access to interactive documents called to live scripts to record the steps of their analysis, to communicate the results, and they can also use these documents to share interactive controls with other users who can in turn conduct their own experiments by selecting from the said group of data. While using exploratory data analysis requires pre-existing knowledge of statistics, it does not require an existing knowledge of programming, thereby making it possible for people from different backgrounds and industries to make the most of Matlab

This particular toolbox includes apps and functions that allow the users to describe, analyse, or model data as per their requirements. With this toolkit, one can perform hypothesis tests, fit probability distributions to given data sets, employ descriptive statistics and plots for exploratory data analysis, extract random numbers for simulations, deduce inferences from data using regression and classification algorithm, and build predictive models. In order to accommodate multidimensional data analysis, this toolbox include stepwise regression, feature selection, regularization, principle components analysis (PCA), and similar models which enable the users to figure out which feature or variables potentially affect their models. Apart from statistical tools, there are several machine learning tools such as hierarchical clustering, hidden Markov models, support vector machines (SVM), Gaussian mixture models, boosted and bagged decision trees, k-medoids, k-means, k-nearest neighbour, and so on. The toolkit can be used for computation of data sets which are otherwise too big to be stored in memory.

MATLAB Financial Toolbox includes functions that enable mathematical modelling and statistical analysis of financial data. There are several goals which can be achieved simultaneously, such as, one can perform time series analysis including regression or transformation with missing data, conversion between trading calendars, day count conventions, and so on. The financial toolbox can be used to gauge risk, estimate investment performance, model credit scorecards, analyse yield curves, and so on. Portfolios of individuals or organizations can be optimized by considering such factors as the number of assets, transaction costs, turnover and semi-continuous constraints.

Apart from this, MATLAB codes can be used to promptly prototype and enhance financial models for management of risk and quantitative finance. Leading financial organizations across the globe depend on MATLAB for performing stress tests, determining interest rates, trading complex instruments in microseconds, managing billion dollars portfolios, and so on. Following MATLAB features make it ideal for statistical analysis in finance:

- Matlab operates with great speed and is capable of running portfolio risk analysis 64 times faster the Python, 100 times faster than Excel or BVA, and 120 times faster than R.
- Matlab’s inbuilt apps and tools can be used to visualize results along the course of analysis, and this allows users to debug if and when necessary.
- Documentation is generated automatically to allow for regulatory approval and model reviewing.
- Big and streaming data from traditional as well as alternative sources can be utilized by Matlab.

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