Data Analysis Chapter on "Present Linear Regression Analysis"

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Rather than a sole focus on the joint probability distribution of y and X (the domain of multivariate analysis), however, Linear Regression becomes based around the conditional probability distribution of y given X (Tibshirani, 1996). Without it, any type of predictive forecast would be impossible. Pertaining to linear regression, unknown model parameters are estimated due to the data modeled through usage of linear functions, which are then regarded as linear models.

In order to detail so as to designate any and every possible relationship between variables, the concept of Linear Regression subsumes the broad nature of social, behavioral, and even the biological sciences. More than merely academically based; more than behaviorally, cognitively, or even subconsciously based; and greater than solely biologically based; Linear Regression is all encompassing, broadly-based so as to detract from being biased. Wordplay aside, Linear Regression was the first type of regression analysis, the return to a former or less developed state, to be analyzed as extensively. Moreover, Linear Regression maintains the aura of being the focal regressive method applied within these numerous practical applications.

So much terminology exists that seems to be easily interlinked if not displaced. Terms such as Linear Regression and Ordinary Linear Squares, which tie in with the misplacement between citizen participation and governmental accountability. Linear regression and the absolute deviations regression, alongside the Ordinary Linear Squares and their linkage with non-linear models are relative and closely linked, but they are nowhere near synonymous. They each maintain a distinct identity. As per citizen participation and governmental accountability, the divide between distinction of the terms is just as easily blurred.

Ordinary Least Squares

Ordinary Least Squares comprises the method for estimating the unknown parameters within a linear regression model. "Minimizing the sum of squared vertical distances between the observed responses in the data set, and the responses predicted by the linear approximation. The resulting estimator can be expressed by a simple formula, especially in the case of a single regressor on the right-hand side" (Lai, Robbins, Wei, 1978).

The Ordinary Least Squares estimator is consistent when the regressors are exogenous and there is no multicollinearity. Moreover, the Ordinary Least Squares estimator is optimal in the class of linear unbiased estimators. When the errors are homoscedastic and serially uncorrelated Ordinary Least Squares can be derived as a maximum likelihood estimator under the assumption that the… READ MORE