(Requires Some Calculus)Consider the Sample Regression Function $Y _ { i } = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } X _ { 1 i } + \hat { \beta } _ { 2 } X _ { 2 i }$

question 9

Essay

(Requires some Calculus)Consider the sample regression function . $Y _ { i } = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } X _ { 1 i } + \hat { \beta } _ { 2 } X _ { 2 i }$ Take the total derivative. Next show that the partial derivative $\frac { \Delta Y _ { i } } { \Delta X _ { 1 i } }$ is obtained by holding $X _ { 2 i }$ constant, or controlling for $X _ { 2 i }$

---

Definitions:

Shares Outstanding

The total number of shares of a corporation's stock that are owned by shareholders, including restrictions shares and those held by the public.

Synergy Value

The additional value created by combining two companies, expected to be greater than the sum of their parts.

Equity-Financed

Funding company operations, projects, or purchases through the issuance of stock, thereby raising capital without incurring debt.

NPV

Net Present Value (NPV) is a financial metric used to evaluate the profitability of an investment or project, by calculating the difference between the present value of cash inflows and outflows over a period.