Conditional Expectation of Response Variable given Predictor Variable in Statistical Modeling. Suppose we are given a set of data points (X_i, Y_i), i=1,2,...,n, where X_i is the predictor variable, and Y_i is the response variable.

Tessa Peters

Tessa Peters

Answered question

2022-10-31

Conditional Expectation of Response Variable given Predictor Variable in Statistical Modeling
Suppose we are given a set of data points ( X i , Y i ) , i = 1 , 2 , . . . , n, where X i is the predictor variable, and Y i is the response variable.
- In the context of statistical modelling, we are interested in expressing Y as
Y i = s ( X i ) + ϵ i
- This implies the assumption
E ( Y i | X i = x i ) = s ( X i )

Answer & Explanation

cdtortosadn

cdtortosadn

Beginner2022-11-01Added 19 answers

Step 1
E [ ϵ i | X i ] = 0
Step 2
is a common assumption in regression. ϵ is refers to the noise.
E ( Y i | X i = x i ) = E [ s ( X i ) + ϵ i | X i = x i ] = E [ s ( X i ) | X i = x i ] + E [ ϵ i | X i = x i ] = E [ s ( x i ) | X i = x i ] + 0 = s ( x i )

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