Linear regression is a type of statistical technique which is used to model the relationship between a dependent variable (Y) and one or more independent variables (X). Linear regression achieves this by determining the most appropriate linear equation that closely matches the data. The objective is to identify the line that provides the closest fit, minimizing the disparity between predicted and actual values.
Components of a Linear Regression
Essentially, there are two components of a linear regression, dependent and independent variables. These are terms used to describe the variables involved in the regression analysis.
Dependent Variable: This is also known as the response variable or output variable. It is the variable that is being predicted or interpreted by the independent variable(s). It is a value that depends on the independent variable(s). The dependent variable is expressed as “Y” in the context of linear regression.
Continuing with the previous example, the weight of a person would be the dependent variable. The goal of the study would be to determine how age, height, and exercise duration (independent variables) affect the person’s weight (dependent variable).
Independent Variable: This is also known as the predictor variable or input variable. It is assumed to have an influence or impact on the dependent variable. It is expressed as “X” in the context of linear regression. The independent variable is either manipulated by the analyst or researcher or, it naturally keeps occurring.
Example to Show Single Independent Variable:
If A wants to predict the test scores of B and his classmates (Y) based on the number of hours they studied (X). A will collect data from all B’s classmates and their corresponding test scores and hours studied. By performing linear regression, A can estimate the relationship between the hours studied and the test scores. The equation expressing this may look like this: Test Score = 3.5 * Hours Studied + 60. This equation depicts that for every additional hour studied, the test score is expected to increase by 3.5 points, with a baseline score of 60.
Example to Show Multiple Independent Variables:
If Amaka wants to predict the sale price (Y) for a bare land in Abuja based on its size in square feet (X1) and the number of appurtenances (X2). Amaka would gather data on various bare lands, including their sale prices, sizes, and existing appurtenances counts. By using multiple linear regression, Amaka can establish that a relationship between these variables exist. The equation may be expressed like this: Sale Price = 20,000 * Size + 500,000 * appurtenances + 1,000,000. This equation indicates that for every additional square foot, the sale price is expected to increase by N20,000, and for every additional appurtenance, the price is expected to increase by N500,000, with a baseline price of N1,000,000.
From the examples above, linear regression helps determine the relationship between the independent and dependent variables and provides a predictive model for future observations. It enables one make informed decisions, predict unknown values, and understand the impact of each independent variable on the dependent variable.
In conclusion, simple and multiple linear regression enable us to understand and quantify the relationship between independent and dependent variables and provides a predictive model for observing future trends. The independent variable(s) depicts the factors that are believed to impact or cause the changes in the dependent variable. On the other hand, the dependent variable express the outcome or response that is being predicted or expressed by the independent variable(s) in a linear regression analysis.
