Statistical Modeling and Regression

Regression analysis is a set of statistical processes used in statistical modelling to estimate the relationships between a dependent variable (often referred to as the ‘outcome’ or ‘response’ variable, or a ‘label’ in machine learning parlance) and one or more independent variables (often referred to as ‘predictors,’ ‘covariates,’ ‘explanatory variables,’ or ‘features’). Linear regression is the most common type of regression analysis, in which the line (or a more complex linear combination) that best fits the data according to a specific mathematical criterion is found. The ordinary least squares method, for example, computes the unique line (or hyperplane) that minimises the sum of squared differences between the true data and that line (or hyperplane). This allows the researcher to estimate the conditional expectation (or population average value) of the dependent variable when the independent variables take on a given set of values for specific mathematical reasons (see linear regression). Less common types of regression employ slightly different procedures to estimate alternative location parameters (e.g., quantile regression or Necessary Condition Analysis[1]) or the conditional expectation across a broader range of non-linear models (e.g., nonparametric regression).

KEY FEATURE

Statistical modelling is a complex method of generating sample data and making real-world predictions that employs a plethora of statistical models and explicit assumptions.

A mathematical link exists between random and non-random variables. It allows data scientists to see correlations between random variables and strategically analyse information.

It can generate comprehensible visualisations by applying statistical models to raw data, allowing data scientists to discover correlations between variables and generate predictions.

Common data sets for statistical analysis include census data, public health data, and social media data.

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Key Topics

    What Exactly Is Statistical Modeling?

    Statistical modelling is the process of applying statistical analysis to datasets in data science. A statistical model is a mathematical model that describes the relationship between one or more random variables and other non-random variables. The application of statistical modelling to raw data assists data scientists in approaching data analysis strategically by providing intuitive visualisations that aid in identifying relationships between variables and making predictions.
    Internet of Things (IoT) sensors, census data, public health data, social media data, imagery data, and other public sector data that benefit from real-world predictions are common data sets for statistical analysis.

    Techniques for Statistical Modeling

    Gathering data from spreadsheets, databases, data lakes, or the cloud is the first step in developing a statistical model. The two most common statistical modelling methods for analysing this data are supervised learning and unsupervised learning. Examples of popular statistical models include logistic regression, time series analysis, clustering, and decision trees.

    Supervised learning techniques include regression models and classification models:

    a) Regression Models: A regression model is a type of statistical model that examines the relationship between a dependent and an independent variable. Regression models that are commonly used include logistic, polynomial, and linear regression models.
    b) Classification Models: A type of machine learning in which an algorithm analyses an existing, large and complex set of known data points in order to understand and then appropriately classify the data; common models include decision trees, Naive Bayes, nearest neighbour, random forests, and neural networking models, all of which are commonly used in Artificial Intelligence.

    Clustering algorithms and association rules are examples of unsupervised learning techniques:

    a) K-means clustering: divides a set number of data points into a set number of groups based on similarities.
    b) Reinforcement learning: It is a branch of deep learning that involves models iterating over many attempts, rewarding moves that result in desirable outcomes and penalising steps that result in undesirable outcomes, thereby training the algorithm to learn the optimal process.

    Statistical models are classified into three types: parametric, nonparametric, and semiparametric:

    1. Parametric: A family of probability distributions with a finite number of parameters is referred to as a metric.
    2. Nonparametric models: are those in which the number and nature of the parameters are not fixed in advance.
    3. Semiparametric: the parameter has a finite-dimensional (parametric) component as well as an infinite-dimensional component (nonparametric).
    The most common statistical modelling approach used in data analysis is regression analysis, which serves as the foundation for more advanced statistical and machine learning modelling. This course will provide you with a solid foundation in the use of commonly used regression analysis tools. The fundamentals of regression analysis will be covered, including linear regression, logistic regression, Poisson regression, generalised linear regression, and model selection.
    You will be exposed to not only fundamental concepts of regression analysis but also numerous data examples using the R statistical software throughout this course. As a result, by the end of this course, you will be familiar with the implementation of regression models using the R statistical software, as well as the interpretation of the results obtained from such implementations. This course is about the opportunity for personal discovery rather than mastering a set of techniques.

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    There Are The Following Statistical Modelling Nodes Available

    • A continuous target is predicted by linear regression models based on linear relationships between the target and one or more predictors.
    • Logistic regression is a statistical technique for categorising records based on input field values. It is similar to linear regression, but it uses a categorical target field rather than a numeric range.
    • To reduce the complexity of your data, the PCA/Factor node offers powerful data-reduction techniques. Principal component analysis (PCA) identifies linear combinations of input fields that capture the most variance across the entire set of fields, where the components are orthogonal (perpendicular) to each other.
    • Factor analysis seeks to identify underlying factors that explain the pattern of correlations observed in a set of fields. The goal of both approaches is to identify a small number of derived fields that effectively summarise the information in the original set of fields.
    • Discriminant analysis makes more stringent assumptions than logistic regression, but when those assumptions are met, it can be a valuable alternative or supplement to logistic regression analysis.
    • The Generalized Linear model extends the general linear model by defining a link function that connects the dependent variable to the factors and covariates. Furthermore, the model allows for a non-normal distribution of the dependent variable. It covers the functionality of a wide range of statistical models, including linear regression, logistic regression, count data loglinear models, and interval-censored survival models.
    • A generalised linear mixed model (GLMM) extends the linear model by allowing the target to have a non-normal distribution, to be linearly related to the factors and covariates through a specified link function, and to be correlated. From simple linear regression to complex multilevel models for non-normal longitudinal data, generalised linear mixed models cover a wide range of models.
    • The Cox regression node allows you to create a survival model for time-to-event data that includes censored records. For given values of the input variables, the model generates a survival function that predicts the likelihood that the event of interest occurred at a given time (t).

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