The government's regression analysis
The government employed the linear regression approach to determine the link between the two variables. GDP1115, the GDP from 2011 to 2015, is the dependent variable, whereas trademarks TM9195 is the independent variable. This strategy necessitates the development of a hypothesis stating that the movement of the variable GDP1115 is dependent on TM9195. The government's primary results from this investigation are that a 1% rise in the average number of trademark applications between 1991 and 1995 resulted in a 0.304% increase in a country's Average Gross Domestic Product between 2011 and 2015. 12.683 is the constant number, with a standard error of 2.682. The model assumes that there is no autocorrelation of residuals of the dependent and independent variable. The variance of the residuals is assumed to be equal, that is, there is homoscedasticity of the GDP1115 and TM9195 residuals.
Possible improvements for the regression analysis
This regression analysis conducted by the government can be improved through a number of ways to get reliable results. One way is through including other variables that were involved in the interaction of GDP and trademarks into the model. In this case, the GDP level between 1991 and 1995 is one of the determinants of the GDP level from 2011 to 2015. Therefore, it should be included in the model for a more accurate analysis. This will increase the level of R squared. In addition, considering the significance of the variables involved is also very crucial. The focus of the model should be on proving whether the established hypothesis is right or not.
Regression results and conclusion
In my analysis, I regressed the 2011 to 2015 GDP against 1991 to 1995 GDP and trademarks of 1991 to 1995. The results indicate that the 2011 to 2015 GDP was indeed influenced by the trademarks as realized by government. However, in this case, the coefficient is lower at 0.040957 meaning that a 1% increase in trademarks led to a 0.040957% increase in the per-capita GDP of a country. This positive relationship is proves the null hypothesis right.
Introduction of a new variable and its impact
Introducing the GDP from 1991 to 1995 as a new variable in the regression leads to a higher level of R-squared at 0.836377. This means that 83.64% of the changes in the GDP by 2015 are explained by the changes in the variables in the model, that is trademarks and the previous GDP during the years those trademarks were issued. When adjusted for degrees of freedom, R-squared reaches 83.06%. The new variable which has been introduced in the model is significant at all levels of confidence intervals.
Limits of the analysis approach
The analysis approach I used also had a number of limitations. First, the available data was limited and thus not enough to do a comprehensive test to determine the relationship between the two variables that are mainly focused on. Due to this lack of sufficient data, some of the variables became insignificant despite proving that the government hypothesis was right. Another limitation is that we are only considering linear relationships between variables and ignore the possibility nonlinear relationships which are also very highly likely to exist but we lack the information in this case. Sometimes the causal and effect relationships are curved. Further, outliers in the data have a big impact on the results as they were not omitted. Furthermore, this approach only looks at the mean of the dependent variable and therefore does not give a complete description of the existing relationships among variables.
