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Econometrix

Test for Significance of Coefficient In order to test the significance of the coefficient, the following hypotheses have been drawn. Ho: The coefficient is equal to zero H1: The coefficient is greater than zero Test Statistics In order to test the significance of the coefficient of Age, t statistic is needed to be calculated. Formula In the given case, the estimated coefficient may be referred as ?Age = 0.043 while the Standard error for ?Age = 0.003. Therefore, Now for the given data set the t tabulated value had been found using the degree of freedom in the given case is 21600 – 3= 21597. The significance level for the test is 1%. The t critical value for the given data is found to be 2.326 (Allison, 1991). Decision Rule The Null hypothesis is rejected if t calculated is greater than t tabulated. Conclusion Since the t calculated value is greater than the t tabulated value i.e. 14.3333>2.326, hence the criteria suggests rejecting the null hypothesis. So it can be concluded that the coefficient value is not equal to zero. 1b. The equation required for the desired calculation is In the given case, Age= 30 years Size= 100 employees Therefore, the earnings calculated for the given age and size is equal to 7.337 pounds (Belsley, Kuh & Welsch, 2005). 1c) It depends as it sounds logical that a person with higher education would be earning greater than the one who has less education. Therefore, assuming that bigger organizations hire more educated people, it may be assumed that on average there is less probability that an organization employees older people. Omitting education in case if it is related to age was necessary to rule out the chances of error caused due to the correlation existing between age and education as an increase in age is termed to be negatively associated with education. Thus the model would have implied the issue of multicollinearity. When variables are extremely correlated, the variability explained exclusively by the single variables can be minor despite the fact that the variation explicated by the variables brought together is great. (Wooldridge, 2012). d. Model 2 (2.430) (0.053) (0.285) The sample size is 83, while R2 is 0.036 1d) By and large, with an increase in sample size, the estimated values tend to be better predictor of the population parameters. Therefore, with each additional observation that is admitted in the sample, the amount of information increases and that additional information usually aids in providing better statistics. Thus if the model provides a better estimating results, the standard errors will be reduced. The model 1 has been framed using an extensively large size of sample while model 2 has eliminated the general public and has enlisted only a specified fragment of the whole population resulting in a decreased size of sample. This ultimately targets the standard errors as they are increased due to the declined size of the sample. This contemplates the information that larger samples will bring forth more accurate estimates of the coefficients’ in a regression analysis (Aiken & West, 1991). e) Hypothesis testing for model 1 Where k=3, N= 21600 while R2=0.025 (Aiken & West, 1991) Calculating the F statistic Let the level of significance be 0.05, the F critical value in that case will be 2.6. Since the F calculated value is less than the F critical, hence,
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