# PUB 550 Discuss three strengths of the linear regression?

## PUB 550 Discuss three strengths of the linear regression?

PUB 550 Discuss three strengths of the linear regression?

A straightforward procedure, linear regression may be used to provide results that are adequate. In addition, compared to other complicated methods, these models may be trained quickly and effectively even on systems with less CPU capability. Comparing linear regression to some of the other machine learning techniques, linear regression has a significantly lower temporal complexity.

Linear regression’s mathematical formulae are also quite simple to comprehend and interpret. As a result, linear regression is simple to learn. Performance on datasets with linear separability. Finding the nature of the relationship between variables is frequently done using linear regression, which almost perfectly fits linearly separable datasets.

A peer-review that uses this method was (Improving the Prediction of Total Surgical Procedure Time Using Linear Regression Modeling). By utilizing linear regression models based on estimated surgeon-controlled time (eSCT) and additional TPT-relevant factors, they try to increase the accuracy of TPT forecasts. One challenge that they had interpreting was due to the vast number of categories, it was impossible to attribute the type of anesthetic utilized or the type of operation that was done.

### Reference:

Improving the Prediction of Total Surgical Procedure Time Using Linear Regression Modeling. (2017). Sec. Intensive Care Medicine and Anesthesiology.

Retrieved from:

Regression analysis is an important statistical method for the analysis of medical data. It enables the identification and characterization of relationships among multiple factors. It also enables the identification of prognostically relevant risk factors and the calculation of risk scores for individual prognostication.

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Linear regression is used to study the linear relationship between a dependent variable Y (blood pressure) and one or more independent variable X (age, weight, sex). The dependent variable Y must be continuous, while the independent variables may be either continuous (age), binary (sex), or categorical (social status).

A peer-reviewed article that used linear regression was a study conducted by a company called Deutsches Ärzteblatt International called Linear Regression Analysis which was part of a 14-series evaluation of Scientific Publications.

Some of the results of the study showed a brief introduction of the uni- and multivariable regression models, illustrative examples are given to explain what the important considerations are before a regression analysis is performed, and how the results should be interpreted. The reader should then be able to judge whether the method has been used correctly and interpret the results appropriately.

The conclusion showed that the performance and interpretation of linear regression analysis are subject to a variety of pitfalls.

### Reference

Schneider A, Hommel G, Blettner M. Linear regression analysis: part 14 of a series on evaluation of scientific publications. Dtsch Arztebl Int. 2010 Nov;107(44):776-82. doi: 10.3238/arztebl.2010.0776. Epub 2010 Nov 5. PMID: 21116397; PMCID: PMC2992018.

According to Schneider (2010) the purpose of regression analysis is an important statistical method for the analysis of medical data. It enables the identification and characterization of relationships among multiple factors. It also enables the identification of prognostically relevant risk factors and the calculation of risk scores for individual prognostication.

As Identified by Schneider (2010) Performing a linear regression makes sense only if the relationship is linear. Other methods must be used to study nonlinear relationships. The variable transformations and other, more complex techniques that can be used for this purpose.

According to GeeksforGeeks (2020) Linear Regression is susceptible to over-fitting but it can be avoided using some dimensionality reduction techniques, regularization techniques and cross validation. Linear regression also looks at a relationship between the mean of the dependent variables and the independent variables.

We can also summarize that linear regression is a great tool for data in a variable, however we can also attest that it is oversimplifies real world problems by assuming a linear relationship among variables.

### References

GeeksforGeeks. (2020). ML-Advantages and Disadvantages of Linear Regression. https://www.geeksforgeeks.org/ml-advantages-and-disadvantage-of-linear-regression

Schneider, A., Hommel, G., & Blettner, M. (2010). Linear regression analysis: part 14 of a series on evaluation of scientific publications.

The strengths of Linear regression are the fact that implementation is simple, On linearly separable datasets, the performance is excellent, and the regularization can help to reduce over fitting. For example, you may measure how much you eat and how much you weigh using regression analysis. The Linear regression’s disadvantages are that the under fitting is a problem for you, excessive sensitivity to outliers, and the data is assumed to be independent in linear regression.

Linear regression is useful in weather prediction but not with full accuracy. The temperature represents the dependent variable. I say the issue is that there are soil, atmospheric pressure, humidity, and winds that play a role in environmental weather and represents the independent variable. This shows how two variables have a linear connection. The independent variable such as the humidity affects the temperature of the environment therefore its dependent on it. Sharapov (2022) states that linear regression does well with weather forecasting and does better with less independent variables. The linear regression is used in this way to determine the connection between two variables. In addition, it aids in the prediction of the dependent variable.

### References:

Sharapov, R. V. (2022). Using Linear Regression for Weather Prediction. *2022 Wave Electronics and Its Application in Information and Telecommunication Systems (WECONF), Wave Electronics and Its Application in Information and Telecommunication Systems (WECONF), 2022*, 1–4. https://doi-org.lopes.idm.oclc.org/10.1109/WECONF55058.2022.9803493

The mathematical technique used in linear-regression models is straightforward and may be used to make predictions. Numerous corporate and academic disciplines can benefit from the use of linear regression. From the biological, behavioral, environmental, and social sciences to business, linear regression is employed widely. Future predictions may now be made scientifically and with high reliability using linear-regression models. The features of linear-regression models are well understood and can be trained extremely rapidly since linear regression is a statistical technique that has been around for a very long time.

The use of linear regression techniques can help business and organizational leaders make better decisions. Organizations gather vast amounts of data, and linear regression enables them to use that data, rather than depending on experience and intuition, to better manage reality. It is possible to turn enormous volumes of raw data into useful knowledge. By revealing patterns and links that your business colleagues may have previously observed and assumed they already understood, you can also utilize linear regression to deliver greater insights. For instance, analyzing sales and purchase data might reveal specific buying trends on certain days or at particular times. Regression analysis insights may be used by business executives to forecast periods of increased demand for their products.

### Reference:

Improving the Prediction of Total Surgical Procedure Time Using Linear Regression Modeling. (2017). Sec. Intensive Care Medicine and Anesthesiology.

Linear Regression is known used as type of predictive analysis. The main objective of regression is to examine two things which are as follows: to check if a set of predictor variables do a good job in predicting an outcome (dependent) variable, and which variable are important predictors of the outcome variable (Statistics Solutions, n.d.). These regressions are utilized to explain the relationship between one dependent variable and one or more independent variables.

There are three major functions of linear regression. The first function is determining the strength of predictors (Statistics Solution, n.d.). It identifies the strength of the effect that the independent variable(s) have on a dependent variable. The second function is forecasting an effect (Statistics Solutions, n.d.). This regression analysis can forecast the impact of change that helps us to understand how much the dependent variable changes with a change in one or more independent variables. The third and last function is trend forecasting (Statistics Solutions, n.d.). It predicts trends and future values that can be used to get point estimates.

One example of peer-reviewed study that used linear regression is a study to identify general factors for quantitative predictions of implant stability quotient values using Multivariate linear regression. Multivariate linear regression is a technique used to determine the estimates a single regression model with more than one outcome variable (University of California Los Angeles Advanced Research Computing, n.d.). The study used multivariate linear regression to determine the possible influencing factors for a mathematical prediction of implant stability quotient (ISQ) values in clinical practice (Huang et al., 2017). It was utilized to analyze the influence of the following 11 candidate factors for stability prediction: sex, age, maxillary/mandibular location, bone type, immediate/delayed implantation, bone grafting, insertion torque, I-stage or II-stage healing pattern, implant diameter, implant length and T1-T2 time interval.

### Reference

Huang, H., Xu, Z., Shao, X., Wismeijer, D., Sun, P., Wang, J., & Wu, G. (2017). Multivariate linear regression analysis to identify general factors for quantitative predictions of implant stability quotient values. DOI: https://doi.org/10.1371/journal.pone.0187010

Statistic Solutions. (n.d.). What is linear regression? Retrieved from https://www.statisticssolutions.com/free-resources/directory-of-statistical-analyses/what-is-linear-regression/9

University of California Los Angeles Advanced Research Computing. (n.d.). Multivariate regression analysis, stata data analysis. Retrieved from https://stats.oarc.ucla.edu/stata/dae/multivariate-regressionanalysis/#:~:text=As%20the%20name%20implies%2C%20multivariate,is%20a%20multivariate%20multiple%20regression.