$1.$ Computer Exercise C$5$

For this exercise, you will be using a variation of RDCHEM, which contains cross$-$sectional data on firm sales, profit margins, and research and development $($R&D$)$ spending in the chemical industry.

The following section gives detailed information about the variables within the data set:

Variable Descriptions

rdrd$=$ R&D spending, in millions of US dollars;salessales$=$ firm sales, in millions of US dollars;profitsprofits$=$ profits, in millions of US dollars;rdintensrdintens$=$ rdrd$$as percent of salessales;profmargprofmarg$=$ profitsprofits$$as percent of salessales;salessqsalessq$=$ sales$2$sales$2$;lsaleslsales$=$ log$($sales$)$logsales;lrdlrd$=$ log$($rd$)$logrd$.$

Open any of the following data files to reference the data from RDCHEM$\_4.$ Use the chosen data file to answer each of the following questions.

$$

Open R File

$$

Open Excel File

$$

Open Stata File

Note: Due to the limitations of Excel, use another software package to complete this problem.

Use the data to examine further the effects of outliers on OLS and least absolute deviations $($LAD$)$ estimates. The model is: rdintens$=$$0+$$1$sales$+$$2$sales$2+$$3$profmarg$+$urdintens$=$$0+$$1$sales$+$$2$sales$2+$$3$profmarg$+$u$,$ where you should first change salessales$$to be in billions of dollars to make the estimates easier to interpret.

$($i$)$

Estimate: rdintens$=$$0+$$1$sales$+$$2$sales$2+$$3$profmarg$+$urdintens$=$$0+$$1$sales$+$$2$sales$2+$$3$profmarg$+$u$,$ by OLS, both with and without the firm having annual sales of almost $$40$ billion.

The estimated equation using all companies in the data set is: rdintens$$rdintens$^=+$salessales$+$sales$2$sales$2+$profmargprofmarg$.$

The estimated equation without the company having annual sales of almost $$40$ billion is: rdintens$$rdintens$^=+$salessales$+$sales$2$sales$2+$profmargprofmarg$.$

True or False: Based on the OLS regression results, the largest firm does not influence the coefficient estimates.

True

False

$($ii$)$

Estimate: rdintens$=$$0+$$1$sales$+$$2$sales$2+$$3$profmarg$+$urdintens$=$$0+$$1$sales$+$$2$sales$2+$$3$profmarg$+$u$,$ by LAD, both with and without the firm having annual sales of almost $$40$ billion.

The estimated equation using all companies in the data set is: rdintens$$rdintens$^=+$salessales$+$sales$2$sales$2+$profmargprofmarg$.$

The estimated equation without the company having annual sales of almost $$40$ billion is: rdintens$$rdintens$^=+$salessales$+$sales$2$sales$2+$profmargprofmarg$.$

True or False: Based on the LAD regression results, the largest firm does not influence the coefficient estimates.

True

False

$($iii$)$

Based on your findings in parts $($i$)$ and $($ii$),$ which estimation method is more resilient to outliers?

OLS

LAD

From the results it is unclear which method is more resilient to outliers.