(Requires Appendix Material) Your Textbook Shows That OLS Is a Linear

question 12

Essay

(Requires Appendix material) Your textbook shows that OLS is a linear estimator
$\hat { \beta } _ { 1 } = \sum _ { i = 1 } ^ { n } \hat { a } _ { i } Y _ { i } , \text { where } \hat { a } _ { i } = \frac { X _ { i } - \bar { X } } { \sum _ { i = 1 } ^ { n } \left( X _ { i } - \bar { X } \right) ^ { 2 } }$ .
For OLS to be conditionally unbiased, the following two conditions must hold:
$\sum _ { i = 1 } ^ { n } \hat { a } _ { i } = 0 \text { and } \sum _ { i = 1 } ^ { n } \hat { a } _ { i } X _ { i } = 1$
Show that this is the case.

---

Definitions:

Exchange Rate

The value of one country's currency in terms of another currency.

Import

The purchase of goods or services produced in a foreign country for use in the domestic market.

Raspberries

A small, red, edible fruit from the genus Rubus, known for its sweet taste and rich vitamin content, often used in desserts and jams.

Exchange Rate

The value of one currency expressed in terms of another currency.