Case $14$: Return on Capital for Four Different Sectors

The table that follows presents financial data of some companies drawn from four different industry sectors$.$ The data include return on capital, sales, operating margin, and debt$-$to$-$capital ratio all pertaining to the same latest $12$ months for which data were available for that company. The period may be different for different companies, but we shall ignore that fact.

Using suitable indicator variables to represent the sector of each company, regress the return on capital against all other variables, including the indicator variables.

The sectors are to be ranked in descending order of return on capital. Based on the regression results, what will that ranking be$?$

It is claimed that the sector that a company belongs to does not affect its return on capital. Conduct a partial $F$ test to see if all the indicator variables can be dropped from the regression model.

For each of the four sectors$,$ give a $95\%$ prediction interval for the expected return on capital for a company with the following annual data: sales of $$2$ billion, operating margin of $35\%,$ and a debt$-$tocapital ratio of $50\%.$