Consider the Following Multiple Regression Models (A)to (D)below $\widehat { \operatorname { Earn } _ { i } } = \widehat { \beta _ { 0 } } + \widehat { \beta } _ { 1 }$

question 47

Short Answer

Consider the following multiple regression models (a)to (d)below.DFemme = 1 if the individual is a female, and is zero otherwise; DMale is a binary variable which takes on
The value one if the individual is male, and is zero otherwise; DMarried is a binary
Variable which is unity for married individuals and is zero otherwise, and DSingle is (1-
DMarried).Regressing weekly earnings (Earn)on a set of explanatory variables, you will
Experience perfect multicollinearity in the following cases unless: a. $\widehat { \operatorname { Earn } _ { i } } = \widehat { \beta _ { 0 } } + \widehat { \beta } _ { 1 }$ DFemme $+ \widehat { \beta _ { 2 } }$ Dmale $+ \widehat { \beta _ { 3 } } X _ { 3 i }$ .
b. $\widehat { \text { Earn } _ { i } } = \widehat { \beta } _ { 0 } + \widehat { \beta } _ { 1 }$ DMarried $+ \widehat { \beta } _ { 2 }$ DSingle $+ \widehat { \beta } _ { 3 } X _ { 3 i }$ .
c. $\widehat { \operatorname { Earn } _ { i } } = \widehat { \beta _ { 0 } } + \widehat { \beta } _ { 1 }$ DFemme $+ \widehat { \beta } _ { 3 } X _ { 3 i }$ .

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Definitions:

Longitudinal Design

A research design that involves repeated observations of the same variables over short or long periods of time.

Cohort Design

A study design where a specific group of people (the cohort) is followed over time to observe outcomes within the group.

Nature Versus Nurture

A debate regarding the relative importance of an individual's innate qualities (nature) versus personal experiences (nurture) in determining or causing differences in physical and behavioral traits.

Genetic Makeup

The complete set of genes or genetic material present in a cell or organism, influencing its characteristics and traits.