Ajay Ohri

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When presented with a set of data for any purpose, itâ€™s important to interpret it correctly, draw the right conclusions, and make accurate approximations based on the information at hand. Statistics offers an organized and mathematical approach to ensure this in the form of statistical models.

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An introduction to statistical modelling is pivotal for any data analyst to make sense of the data and make scientific predictions. In its essence, statistical modelling is a process using statistical models to analyze a set of data. Statistical models are mathematical representations of the observed data.

Statistical modelling methods are a powerful tool in understanding consolidated data and making generalized predictions using this data. A statistical model could be in the form of a mathematical equation or a visual representation of the information.

There are several statistical modeling techniques used during data exploration. Here are some of the common techniques:

Linear regression uses a linear equation to model the relationship between two variables, where one variable is dependent and the other is independent. If one independent variable is utilized to predict a dependent variable, it is called simple linear regression. If more than one independent variable is used to predict a dependent variable, itâ€™s called a multiple linear regression.

Classifications groups the data into different categories to allow for a more accurate prediction and analysis. This technique can enable effective analysis of very large data sets. There are two major techniques under classification:

**Logistic Regression**

When the dependent variable is binary, the logistic regression technique is used to model and predict the relationship between the binary variable and one or more independent variables.

**Discriminative Analysis**

Here, two or more groups are known as prior and new observations are grouped into known clusters based on the measured features. The distribution of the predictor variable X is modeled separately into each of the response classes, Bayesâ€™ theorem is then used to calculate the probability of each response class, based on the value of X.

In this technique, repeated samples are drawn from the original set of data, creating a unique sampling distribution based on actual data. It uses experimental methods as opposed to analytical methods to create a unique sampling distribution. Since the samples drawn are unbiased, the estimates obtained are also unbiased.

**Knowledge of two main concepts are essential to understand the concept of resampling in its entirety:**

**Bootstrapping**

This takes into account the data samples that werenâ€™t selected in the initial sample as a replacement. The process is repeated several times and the average score is calculated for the estimation of the model performance.

**Cross-Validation**

The training data is divided into k number of parts. Here, k â€“ 1 parts are considered training sets, and the one remaining set is used as the test set. This is repeated k number of times and the average of the k scores are calculated as the performance estimation.

Here the data under observation is modeled using a non-linear combination of model parameters and this is dependent on one or more independent variables. The data is then fitted using a method of successive approximations.

In a tree-based method, the predictor space is segmented into different simple regions. The set of splitting rules can be summarized in a tree, giving it the name decision-tree method. This can be used for both, regression and classification problems. Bagging, boosting, and random forest algorithm are some of the approaches used in this method.

Unsupervised learning relies on the algorithm to identify a pattern in the data. Here the categories of data are not known. For example, in clustering, closely related items are grouped, making it a method of unsupervised learning.

This forecasting model can be used to predict future values based on historical values. It is used to identify the phenomenon represented by the data and then integrated with other data to draw predictions for the future.

Modeled loosely on the human brain, these are algorithms designed to identify patterns in the data. Neural networks have non-linear elements that process information, called neurons. These are arranged in layers and normally executed in parallel. Neural networks are being increasingly used to make predictions and classifications as they have minimal demands on assumptions and model structure and can approximate a wide range of models.

The different types of statistical models are essentially the statistical methods used for computation. These are the mathematical equations and visual representations that make statistical modeling possible. Some of them are:

- Linear regression
- Logistic regression
- Cluster analysis
- Factor analysis
- Analysis of variation (ANOVA)
- Chi-squared test
- Correlation
- Decision trees
- Time series
- Experimental design
- Bayesian theory â€“ NaÃ¯ve Bayes classifier
- Pearsonâ€™s r
- Sampling
- Association rules
- Matrix operations
- K-nearest neighbor algorithm (k-NN)

Statistical modeling holds an important place in all types of data analysis, making it relevant to various fields of science and industry. This especially holds in the data analytics field, where analysts rely heavily on statistical methods and techniques to interpret and draw conclusions from any given dataset.

**Statistical modelling in pharmaceutical research and development**

Statistical models are being introduced into the pharmaceutical industry to determine the efficacy of drugs for particular individuals, ensuring that individuals are given the right drugs for optimal response. Statistical techniques are used to filter biomarkers from the data, using which models are developed to predict the groups in which the drugs are most effective.

**Statistical modelling in R**

Owing to the extensive usage of statistical modeling in data science, convenient tools embedded within the R programming language. R allows analysts to run various statistical models and is built specifically for statistical analysis and data mining. It can also enable the analyst to create software and applications that allow for reliable statistical analysis. Its graphical interface is also beneficial for data clustering, time-series, lineal modeling, etc.

**Statistical modelling in Excel**

Excel can be used conveniently for statistical analysis of basic data. It may not be ideal for huge sets of data, where R and Python work seamlessly. Microsoft Excel provides several add-in tools under the Data tab. Enabling the Data Analysis tool on Excel opens a wide range of convenient statistical analysis options, including descriptive analysis, ANOVA, moving average, regression, and sampling.

It is safe to say that statistical modeling is an essential part of data analysis and is used across industries. Statistical models and techniques can present large datasets as mathematical representations, enabling approximations and accurate predictions.

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