Use economic theory to form an hypothesis regarding the relationship between two variable found in the data set.
For Economics to have a testable hypothesis it requires an economic theory. Any theory mostly requires the use and application of mathematics to be valid. It has been proven that without theory and testable hypotheses it will be very hard to understand the economy. In this data set, the dependable variable is usual hours per week at main job and the independent variable is a usual hourly wages, employees only. The hypothesis that can be tested using these two variables, that is the independent and the dependent variable, is to check if there is an association between the two variables.
Hypothesis is:
H0: there is no association between the usual hours per week at the main job and the usual hourly wages, employees only
Ha: there is association between the usual hours per week at the main job and the usual hourly wages, employees only
Specify and estimate a regression that will allow you to test your hypothesis using the observations from the dataset. Explain your choice of dependent variables.
There are mainly two regression analyses that one can run when analyzing a data set. First is the multiple regression analysis; multiple regression analysis is mainly used when there are very many dependable variables or explanatory variables. It gives each of the contribution of each explanatory variable to the model and one can easily see which variable is important and which ones are not important. An important variable is one which when removed from the model it affect the R –squared and the validity of the whole model while those variables that are not important even when removed the model remains the same. The second main regression analysis which is also commonly used is the linear regression model. This model is mainly used when there is only one dependent variable and one independent variable. In this data set the most appropriate regression model to be used is the linear regression model. This is because there is only one independent variable and one dependent variable. The independent variable is the usual hourly wages, employees only and the dependent variable is the usual hours per week at main job. The main thing that the regression analysis is going to help in finding out is when there is association between the independent variable and the dependent variable.
Carry out appropriate diagnostic tests on your estimated equation based on the potential CLR violations.
There are different tests that can be carried out in this data set. The following are some of the assumptions which must be observed to make the hypothesis be tested to be valid. The errors should have a zero mean. The variance of the errors should be constant. The errors should be statistically independent of one another. There is no relationship between the error and the corresponding dependable variable. The errors are normally distributed.
Test your hypothesis
Hypothesis is:
H0: there is no association between the usual hours per week at the main job and the usual hourly wages, employees only
Ha: there is association between the usual hours per week at the main job and the usual hourly wages, employees only
Report results of the estimation and tests. Results should include estimated regression, any diagnostic tests, hypothesis tests and descriptive statistics of regression variables.
Regression Analysis
The regression analysis done in this data set is a linear regression analysis this is because there is only one independent variable and one dependent variable. The linear regression model sometimes is called the ordinary least squares. From the analysis one can form a linear equation. From the analysis the multiple R is 0.25 and the Multiple R Squared is 0.062. The multiple R shows the percentage of the independent variable that can be explained using the dependent variable. From the analysis it is shows that only six percent of the independent variable can be explained by the dependent variable. This clearly shows that there is no association between the usual hours per week at main job and the usual hourly wages, employees only. From the hypothesis we fail to reject the null hypothesis and conclude that there is no association between the usual hours per week at main job and the usual hourly wages, employees only. The value of the F is also extremely big showing that there is no association and that the independent variable and the dependable variables are significantly different.
Scatter plot analysis
The scatter plot shows the plot of usual hours per week at main job against the usual hourly wages, employees only. From the plot it is clear that there is very little association between the dependent variable and the independent variable. There is a concentration between early hours. The line of best fit has left most of the plots. The points in the scatter plot are every, they are not linear. This also clearly shows that there is no relationship between the independent and the dependent variable.
