Present Linear Resgression Analysis

Auditing

To what degree does the level of citizen participation influence organizational accountability factors as perceived by the citizens?

Citizen participation is more of a determinant than anything else pertaining to the influential matter of perceived / perceptual organizational accountability factors. However, "evidence is inconclusive as to why some local governments include citizen participation in the budget process while others do not." In fact, "little generalizable empirical knowledge" exists or is readily available "about the use of participation in budgeting" (Zhang, Yang 2009). The distinction of dependent vs. independent, in every form of government, is easily misconstrued.

In the eye of a dictatorship or a monarchy, citizen participation, though to a much lesser degree than inside a democracy, is still more of a determinant than anything else, at least pertaining to the influential matter of perceived or perceptual organizational accountability factors; otherwise, subversiveness and disorder (revolt) occurs. Still, where does the divide between the two terms truly exist? And why can it easily become blurred? All organizational accountability factors must be exactly that, organizational; but also convergent, too.

In fact, it can be recognized, in the majority of elemental arenas, as the most important implement to be used within these disciplines. The statistical approach in representing the relationship between a scalar variable ("Y," dependent variable or regressand) and one or more variables denoted ("X," independent variable or regressor) constitutes the concept of Linear Regression (Tibshirani, 1996).

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 errors are normally distributed. This method has good statistical properties for a much broader class of distributions, except for efficiency, however, in spite of the fact of this assumption (Hayashi, Fumio (2000). Econometrics. Princeton University Press).

In view of this fact, dependent linear models of their unknown parameters are more susceptible than their non-linearly related counterparts. The resulting estimators, then, become more easily determinant due to these existent statistical properties. However, this leads to another complication; the response function then implies that the outcome is binary. Though possible to estimate the simple linear regression model, the independent variable y takes on the binary values of either 0 or 1 (Hayashi, Fumio (2000). Econometrics. Princeton University Press).

But are the problems? Why are there problems?

"Well, yes. Actually, there are three particular problems that arise with binary dependent variables in linear regression models. Each of these makes the use of linear regression inappropriate and signifies the need for an alternative approach. The discussion that follows emphasizes the central argument surrounding the use of logistic regression" (Yang, Miller, 2008).

The Handbook of Research Methods in Public. Administration next provides these three reasons:

The error terms cannot be distributed normally... [so] the assumption of normally distributed errors cannot be appropriate.

The error terms do not have equal variances when the response variable is an indicator variable taking on variables of 0 and 1. The happens because the variance of Y depends on the value of X; consequently, the error variances are different for different levels of X. As a result, ordinary least squares is no longer optimal.

Finally, the response function represents the set of probabilities when the outcome variable is equal to either 0 or 1. The mean responses from the response function thus are constrained within the limits of 0 and 1, because 0

Conclusion: Data analysis for relationship between citizen participation and governmental accountability

This essay concerns the aforementioned competing theoretical perspectives and, through the means of statistical analysis (hopefully) presented in Layman's terms, examines how the infiltration of citizen participation in the budget process is associated with city controllers' elemental profession, bureaucratic environment, along with the representative regard for all abiding citizens. On very much a scale of both Linear Regression and Ordinary Least Squares, community building and contractual arrangements amongst citizens cause that fitting circular endeavor needed to create the reason for the employment of these professionals. City organizers, city planners, all Urban design event organizers are as detrimental as the X-y balance of the citizenry and citizen involvement.