It Is Not Hard,but Tedious,to Derive the OLS Formulae for the Slope

question 60

Essay

It is not hard,but tedious,to derive the OLS formulae for the slope coefficient in the multiple regression case with two explanatory variables.The formula for the first regression slope is (small letters refer to deviations from means as in ).
Show that this formula reduces to the slope coefficient for the linear regression model with one regressor if the sample correlation between the two explanatory variables is zero.Given this result,what can you say about the effect of omitting the second explanatory variable from the regression?

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Definitions:

Revenue Expenditures

Expenses incurred during the normal operation of a business that are expected to be consumed within the same accounting period.

Capital Expenditures

Funds used by a company to acquire or upgrade physical assets such as property, industrial buildings, or equipment.

Net Income

The total profit or loss of a company after all revenues, expenses, and taxes have been accounted for.

Owner's Equity

Owner's equity represents the owner's claim to the assets of a business, calculated as the business's total assets minus its total liabilities.