Suppose you estimate the sample multiple linear regression function $\hat { y } _ { i } = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } x _ { 1 i } + \hat { \beta } _ { 2 } x _ { 2 i }$
where x_2i is a binary dummy variable equal to 1 if the individual possess a given characteristic and 0 if he or she does not.Demonstrate and explain how to interpret $\hat { \beta } _ { 2 }$
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Question

Suppose you estimate the sample multiple linear regression function

\hat { y } _ { i } = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } x _ { 1 i } + \hat { \beta } _ { 2 } x _ { 2 i }

where x_2i is a binary dummy variable equal to 1 if the individual possess a given characteristic and 0 if he or she does not.Demonstrate and explain how to interpret

\hat { \beta } _ { 2 }

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Quizplus · Accepted Answer

The Answer of Suppose you estimate the sample multiple linear regression function $$\hat { y } _ { i } = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } x _ { 1 i } + \hat { \beta } _ { 2 } x _ { 2 i }$$ where x_2i is a binary dummy variable equal to 1 if the individual possess a given characteristic and 0 if he or she does not.Demonstrate and explain how to interpret $\hat { \beta } _ { 2 }$ .

Suppose You Estimate the Sample Multiple Linear Regression Function y^i=β^0+β^1x1i+β^2x2i\hat { y } _ { i } = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } x _ { 1 i } + \hat { \beta } _ { 2 } x _ { 2 i }y^​i​=β^​0​+β^​1​x1i​+β^​2​x2i​

Suppose You Estimate the Sample Multiple Linear Regression Function $\hat { y } _ { i } = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } x _ { 1 i } + \hat { \beta } _ { 2 } x _ { 2 i }$