Multicollinearity and the \"Variance Inflation Factor.\" The \"variance inflation factor\" can be used to consider the presence of multicollinearity within a multiple regression model. You are given the data set: business.dta which comes from the \"World Bank Doing Business\" project. (http://www.doingbusiness.org/) Note that the data you will be using is from 2009 and the variables are defined: (a) Estimate the following model and write out your estimated model: cost= 0 + 1 documents+ 2 days+ 3 hiring+ 4 firing+u c^ ost=626.516736.95686 documents+ 38.13033 days+1.719388 hiring.4138276 firing (b) What is the value for VIF that the textbook suggests is often used to suggest whether multicollinearity is a problem in the regression? Interpret what this high value for the VIF means. The textbook suggests a value of 10 is often used to suggest whether multicollarity is a problem in the regression. (c) For each of the X-regressors in the model please fill in the following table. You can use the STATA menus/command. Variable documents days hiring firing VIF 1.48 1.49 1.17 1.19 (d) Verify the VIF for \"documents\" by running the required regression to compute this on your own. Write out the estimated model after you have run the regression: ^ documents=4.927149+.0715698 days +.0034158 hiring.000825 firing Report the important value from the output and show/verify the computation of the VIF. R2 = 0.3228 VIFdocuments = 1/(1 - R2documents ) = 1/(1-0.3228) = 1.47666863556 = 1.48 (e) Note that another way to consider multicollinearity as a problem would be to consider the correlation among the X-regressions themselves. In Stata, create a correlation matrix of the X variables. (You can find the command through the Statistics -> Summaries ... -> Summary or the command correlate documents days hiring firing ) documents days hiring firing docume~s days hiring firing 1.0000 0.5668 0.0718 0.0853 1.0000 0.0574 0.1379 1.0000 0.3789 1.0000 Are these results what you would expect based on the VIFs? Explain, please use specific correlations and VIFs in your explanation where possible. Which of these, VIFs or correlations, would you consider more useful in \"diagnosing\" multicollinearity? Explain. (Hint: consider the important idea that correlation, by definition, captures a bivariate relationship in your answer.)