Linear Model Essay ⋆ Political Science Essay Examples ⋆ EssayEmpire

Due to their simplicity, linear models are easy to understand and interpret, which makes them the basis for most of the statistical analyses used in applied political science and social research. The simplest way to understand them is with a two-variable case. Suppose that Y is a response variable (or dependent variable) and x is an explanatory variable (or independent variable). A straight line relating Y to x has an equation of the form:

Y = a + b x + e

In this equation, b is the slope, the amount by which Y changes when x increases by one unit, while a is the intercept—the value of Y when x = 0.The value e is the error term; i.e. the expression that captures the difference between the data observed and the model that fits the data. Linear models can be used to understand the relationship between the two variables and to predict the response of Y for a specific value that the explanatory variable x might assume. A more complex linear model would assume multiple independent variables as predictors of the response variable. The linear model is the foundation for the t-test, analysis of variance (ANOVA), analysis of covariance (ANCOVA), regression analysis, and many of the multivariate methods including factor analysis, cluster analysis, time series, and others statistics that are constantly used in political science and other social sciences.

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