(Requires Calculus)For the Case of the Multiple Regression Problem with Two

question 30

Essay

(Requires Calculus)For the case of the multiple regression problem with two explanatory
variables, show that minimizing the sum of squared residuals results in three conditions: $$\sum _ { i = 1 } ^ { n } \widehat { u _ { i } } = 0 ; \sum _ { i = 1 } ^ { n } \widehat { u _ { i } } X _ { 1 i } = 0 ; \sum _ { i = 1 } ^ { n } \widehat { u _ { i } } X _ { 2 i } = 0$$

---

Definitions:

Nuclear Families

A family unit consisting of two parents and their children (biological or adopted) living together in one household.

Allocaregiving

The provision of care and nurturing to offspring by individuals other than the biological parents, often seen in social species.

Supplemental Caregiving

Additional care provided to a child by someone other than the primary caregiver, often to support the family or developmental needs.

Nuclear Families

A family unit consisting of two parents and their children living together as a single household, considered a traditional family structure.