Regression Analysis - Speech or Presentation Example

In essence, it allows for evaluation of the fixed and random effects models in non-linear modeling frameworks and simply assumes parameter and variable non-linearity. Assumption 2: Expected value of error is zero This assumption presumes that the error component will return a zero mean meaning that the observed mean will not be systematically distorted away from the true value by the error (and this contrasts with a systematic bias effect which would distort the observed mean away from its true value) (Good & Hardin, 2009).

Assumption 3: Autocorrelation Amongst the assumptions often made in regression analysis is that error terms not dependent on each other or rather non-correlated. This is however not always the case. When this assumption is violated, despite the fact that the regression model is still usable, in prediction value, its usefulness is largely diminished. This study considering the relationship between the variables seeks to assume its presence and hence proof that the model’s usability is largely diminished.

The estimated regression parameters, a, b1, b2, . . . ,bk, are left as unbiased estimators of the respective real values, A, B1, B2, . . ,Bk, and hence the model remains appropriate for establishment of point estimates of A, B, and others., and it can be used in prediction of values of Y for X value sets (Good & Hardin, 2009) (Good & Hardin, 2009). Autocorrelation is often a product of errors correlation. It broadens the scope of thinking to look at different observations which result from varying distributions which are non-explanatory.

Assumption 4: Heteroskadascity Sphericality assumption often implies that there exists homoskedasticity of errors, and that variance is constant across cases. Violation of this offers heteroskedasticity whereby the predictive model does particularly poor in some set of circumstances. Take for instance in this case where there is a possibility that unemployment or gas prices across countries may be reliable but there is lesser proof to believe in the data relating to the same obtained from other countries.

Such a case would give rise to increased random variation, and hence huge mean error variances, in the respective countries. In general, Heteroskedasticity occurs in instances where the homoskedasticity assumption is violated, giving rise to Assumption 5: Multi-collinearity assumption Whenever there exists moderate to high intercorrelation amongst predictor variables, multi-collinearity is believed to arise. Typically, multi-collinearity presents a real research problem when multiple regressions are used.

These include its severe limiting of R’s size given that predictors follow a variance as much the same as that of y, creating a difficulty in determination of the worth of a predictor due confounding of the effects as a result of correlation between them, and an increment in regression coefficient variants (Good & Hardin, 2009). In this case’s, a number of variables are considered in the model including gas price, excluding food prices, unemployment, and personal expenditure which was removed due to its high correlation to the other variables.

However, even with the inclusion of the other variables, it is still believed that the other variables have some slight correlation to each other. For instance, food services are likely to be impacted on by gas prices and the same is true for unemployment rates. Conclusion Understanding relationship