Linear Regression

Regression Lines - In Layman's Terms

To understand linear regression, it's necessary to understand the use of regression lines. A regression line is used in statistical analysis to define the difference between two variables. You can clearly imagine a regression line being used in engineering estimation of varying points. In the case of regression lines, one variable will be independent and the other dependent.

Mechanical designers often plot these on a grid where the dependent variable will be drawn according to the equation where Y is the dependent and X the independent variable. This is the purpose upon which the drawing is based. Engineers may use the standard linear regression equation to arrive at the correct configurations.

For example, certain lines on a plotted grid may represent a steel beam that must be attached to a load bearing beam. The load bearing beam represents an independent variable. The attached beam is wholly dependent on the load bearing beam for support. From this configuration, it's then possible to determine the weight load the finished structure will bear. The line of regression in this example is the location of the load bearing beam.

Linear Regression

Using the same example of steel beams, imagine that the mechanical designers are required to provide proof that the relationship between the attached beam and load bearing beam can bear a specific weight load of one thousand tons on a daily basis. The design plot would need to also include this aspect by inserting averages of tonnage most likely to be borne by the structure.

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Linear Regression in Statistics

In statistical engineering, linear regression expresses the major factors in the data used. As an example, air pressure through industrial ducts are dependent on the power of the air source, usually a fan or blower. It may also depend on the rate of the air velocity and whether it is induced or drafted through the duct system. A statistical engineer is charged with the duty of using the independent fan or blower to calculate the force of the air pressure in pounds per square inch of duct. This is accomplished through the use of linear regression on an expressed equation drawn onto a grid. This is often referred to as linear system analysis. In this example, a model is created by linear mapping between system inputs and system outputs. A system is set or an arrangement of instrumentation or other devices fully related or connected form a unit as a whole.

Linear Regression and Its Uses

The factors of greatest influence on an economy are spending, tax levels, interest rates and the overall monetary policies. Gross national product, unemployment rate, rate of inflation and consumer price index are economic outputs to arrive at the main dynamic. Statistically when data is collected on all of these factors, the end result is the condition of the economy. Linear regression is most often used by those involved in various polls and census bureaus that estimate the variables in a country's population.