Social Research Glossary A B   Citation reference: Harvey, L., 2012-19, Social Research Glossary, Quality Research International, http://www.qualityresearchinternational.com/socialresearch/ This is a dynamic glossary and the author would welcome any e-mail suggestions for additions or amendments. Page updated 8 June, 2019 , © Lee Harvey 2012–2019. A fast-paced novel of conjecture and surprises

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Linearity

core definition

Linearity describes the relationship between two (or more) variables when they tend to change at the same rate.

explanatory context

Diagrammatically, a graph of one variable against another will show that the points tend to fall in straight line.

A linear model is a type of theory in which one variable (the dependent variable) is postulated to be related to one or more other variables (the independent variables) in a simple direct proportion—a straight line relationship.

When the empirically derived variables are plotted against each other on a graph they may approximate a linear relationship and the regression line of best fit is the line fitted to the data points as closely as possible. This is usually a straight line fitted according to the least squares criterion. The line of best fit, then, relates the dependent variable to the independent variable(s) in the linear model. The relationship expressed in this line is used to derive values of the dependent variable corresponding to known values of the independent variable(s).

analytical review

Kleitman (undated) explained the mathematical formulation:

A linear function, we have seen is a function whose graph lies on a straight line, and which can be described by giving its slope and its y intercept.

There is a special kind of linear function, which has a wonderful and important property that is often useful. These are linear functions whose y intercepts are 0 (for example functions like 3x or 5x). This means their graphs pass right through the origin, (the point with coordinates (0, 0)). Such functions are called homogeneous linear functions. They have the property that their values at any combination of two arguments is the same combination of their values at those arguments.

associated issues

related areas

Researching the Real World Section 8

Sources

Kleitman, undated, "3.3 Linearity" available at http://www-math.mit.edu/~djk/calculus_beginners/chapter03/section03.html, accessed 25 January 2013, still available 9 June 2019. A NOVEL