Linear Regression: Implementation and Statistical Analysis of Methods

This report provides an overview of linear regression, a fundamental concept in machine learning and statistics. It explains how linear regression models are used to analyze and predict the relationship between variables, distinguishing between dependent and independent variables. The report details the processes involved, including statistical methods for calculating coefficients and the use of techniques such as gradient descent for optimizing models. The report covers the application of linear regression, including the use of statistical tools, such as means, deviations, standard, covariance and correlations. The report further highlights the importance of understanding learning rates and the iterative process of minimizing squared errors. The report concludes with a discussion of the core concepts, along with relevant references to support the analysis.

Running head: LINER REGRESSION
LINER REGRESSION
Name of Student
Name of University
Author’s Note

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Liner regression
Linear regression is one of the algorithms that is popular as well as understood in the
field of machine learning. linear regression had been developed within the field of statistics
besides being studied in the form of a model for the purpose of gaining knowledge regarding
relation between input as well as output variable that are numeric in nature (Fox, 2015). This
had been further bowed by the field of machine learning. It can be described as statistical as
well as machine learning algorithm.
How it is used and how it works
The model of linear regression are utilized for the purpose of showing as well as
predicting the relation between two factors or variables. The fact which is usually used for
prediction is known as the dependent variable. The factor which is used for predicting the
value of dependent variable is known as independent variable (Austin & Steyerberg, 2015).
Regression analysis is used for the purpose of researching because it establishes the fact that
a particular correlation exists among numerous variables. A particular line within the linear
regression which fits numerous data points properly might not represent anything regarding
the cause as well as effect relationship. In a linear regression every observation has 2 values.
Initial value is for variable that is dependent in nature and anther is for independent one
(Chiarini & Brunetti, 2019). In case of simple liner regression when the user has one output,
the user could use statistics for estimating numerous coefficients. This needs the user to
calculate various statistical properties from data like means, deviations, standard, covariance
and correlations. The data should be available for traversing as well as calculating the
statistics.
In case of ordinary least squares, the user makes use of numerous processes that help
in reducing the overall sum of the squared residuals. In case of more than one inputs, the user

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would be allowed to use a certain process of optimization of values of numerous coefficients
with the help of minimizing the faults of model on the data obtained from training. This
particular operation is called Gradient Descent and hence it functions with the help of starting
with values for every efficient, these values are randomly selected. The sum of all the errors
after squaring them is calculated for every set of input as well as output (Faraway, 2016). A
particular learning rate is utilized in the form of a scale factor, besides these the coefficients
are supposed to be updated towards the direction of minimisation of errors. This particular
procedure is repeated again and again till the time when a minimum squared fault is obtained
or the user is unable to perform any further improvements (Austin & Steyerberg, 2015). At
the time of using these methods the user is supposed to select a certain parameter for learning
rate, this parameter would be helpful in determining the overall size of the step undertaken
for bringing about improvement in order to take on every iteration of the entire process.

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References
Austin, P. C., & Steyerberg, E. W. (2015). The number of subjects per variable required in
linear regression analyses. Journal of clinical epidemiology, 68(6), 627-636.
Chiarini, A., & Brunetti, F. (2019). What really matters for a successful implementation of
Lean production? A multiple linear regression model based on European
manufacturing companies. Production Planning & Control, 1-11.
Faraway, J. J. (2016). Extending the linear model with R: generalized linear, mixed effects
and nonparametric regression models. Chapman and Hall/CRC.
Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications.