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Linear regression, known for its common use in statistics, is a model showing the relationship between predictor (dependent) variable and response (independent) variable. Simple linear regression is the most basic for linear regression, quantifying the relationship between predictor and response variables. When dealing with such relationships, analysts often use correlation and causation interchangeably, but they do not have a similar meaning. Causation is the influence by which one variable generates the change in the second variable, whereas correlation refers to a mutual relationship or connection between two or more variables. One can tell the existence of correlation between variable using a correlation coefficient which take values, ranging between -1 and 1. The strength of the correlation increases as the correlation coefficient moves towards away from zero (Rohrer, 2018). Workplace examples can be used in affirming the difference between causation and correlation, besides demonstrating linear regression.
An example of linear regression is witnessed in health sector. Medical researchers apply linear regression to understand the connection between blood pressure of patients and drug dosage. Explicitly, medical researchers may administer various drug dosages to patients, while simultaneously observing reactions in their blood pressure (BP). As a result, medical researchers might proceed to fitting a simple linear regression model using BP as a response variable and drug dosage as a predictor variable. Sheppard et al. (2021) explained how blood pressure can be controlled by administering various dosages of antihypertensive drug. A simple linear regression model extracted from such relationship is expressed in equation (1).
&&&&&&&&&&&. (Equation 1)Conclusively, from equation (1), the coefficient
represent blood pressure without a drug dosage. Above all, the coefficient
is the focus, representing the average shift in BP with a one unit increase in drug dosage. Ideally,
is the correlation coefficient between BP and drug dosage. It can take values between -1 and 1, notwithstanding it can also be zero. A negative
would mean that a surge in drug dosage is linked to a decrease in BP. When
is zero, then the rise in drug dosage is associated with no shift in BP. Furthermore, a positive
means that an upsurge in drug dosage associates with increase in BP. The example demonstrated in equation 1 expresses correlation, but not causation since many other influential factors (e.g., exercise) are kept constant.References
Rohrer, J. M. (2018). Thinking clearly about correlations and causation: Graphical causal models for observational data. Advances in Methods and Practices in Psychological Science, 1(1), 27-42.
Sheppard, J. P., Lown, M., Burt, J., Ford, G. A., Hobbs, F. R., Little, P., Mant, J., Payne, R. A., McManus R. J. & Optimise Investigators. (2021). Blood pressure changes following antihypertensive medication reduction, by drug class and dose chosen for withdrawal: exploratory analysis of data from the optimise trial. Frontiers in pharmacology, 12, 619088.
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