You were asked to help with an analysis of birth weights (BW) of 10,000 infants born in NYC during a certain period of time.   The aim of the analysis is to see whether the birth weights of the infants are associated with mothers’ AGE at birth (continuous variable in years), mothers’ current HOUSING status (“own” and “not-own”; “own” is the reference group),  and NYC boroughs (the BOROUGH variable contains 5 categories “Manhattan”, “Bronx”, “Brooklyn”, “Queens” and “Staten Island”; “Manhattan” is the reference group). Write down the population model that estimates the effect of mother’s AGE on BW differently for each level of current HOUSING status. If you use dummy or binary variables, specify what they mean. Write down the population model that estimates the effect of mother’s AGE on BW differently for each level of current HOUSING status while adjusting

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You were asked to help with an analysis of birth weights (BW) of 10,000 infants born in NYC during a certain period of time.

 

The aim of the analysis is to see whether the birth weights of the infants are associated with mothers’ AGE at birth (continuous variable in years), mothers’ current HOUSING status (“own” and “not-own”; “own” is the reference group),  and NYC boroughs (the BOROUGH variable contains 5 categories “Manhattan”, “Bronx”, “Brooklyn”, “Queens” and “Staten Island”; “Manhattan” is the reference group).

  1. Write down the population model that estimates the effect of mother’s AGE on BW differently for each level of current HOUSING status. If you use dummy or binary variables, specify what they mean.
  2. Write down the population model that estimates the effect of mother’s AGE on BW differently for each level of current HOUSING status while adjusting for BOROUGH. If you use dummy or binary variables, specify what they mean.
  3. How many degrees of freedom will be in the numerator and denominator of the Partial F-test that tests the association between the predictor BOROUGH and outcome BW while adjusting for the interaction between AGE and HOUSING ? How many parallel lines will there be?
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