The Following Interactions Between Binary and Continuous Variables Are Possible $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } D _ { i } + \beta _ { 3 } \left( X _ { i } \times D _ { i } \right) + u _ { i }$

question 52

Short Answer

The following interactions between binary and continuous variables are possible, with the exception of a. $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } D _ { i } + \beta _ { 3 } \left( X _ { i } \times D _ { i } \right) + u _ { i }$ .
b. $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } \left( X _ { i } \times D _ { i } \right) + u _ { i }$ .
c. $Y _ { i } = \left( \beta _ { 0 } + D _ { i } \right) + \beta _ { 1 } X _ { i } + u _ { i }$ .
d. $Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + \beta _ { 2 } D _ { i } + u _ { i }$ .

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Definitions:

Introverted Loners

Individuals who prefer solitary activities and enjoy spending time alone, often feeling drained by social interactions.

Future Achievements

Goals or accomplishments an individual aims to realize in the future, often motivating present actions and planning.

Performance Attainment

The achievement of performance goals or targets, typically within a specified time frame or under certain conditions.

Vicarious Experiences

Learning or emotional experiences gained by watching, reading about, or hearing about the actions of others rather than through direct personal experience.