# Suppose we have data from a health survey conducted in year2

Suppose we have data from a health survey conducted in year2010. Data were obtained from a random sample of 2342 persons.A dichotomous logistic regression analysis was conducted inthe following way:Dependent Variable (Y): Self-reported general health (1 ifnot healthy, 0 if healthy) Independent Variables: Gender (1 if female, 0 if male)Age (in years)Race/Ethnicity (binary variablesfor “Non-Hispanic Black” “Hispanic” and “Others”; the reference category is“Non-Hispanic White”)Form of the equation:  where p is the probability of beingself-reportedly unhealthy and Xj’s(j=1, 2, …, k) are independent variables. Age range of the sample: 25-84.  The log(p/(1-p))is also called log odds. (Note, thelogarithm we used in the class is natural log. If you use EXCEL, make sure touse the ln() function instead of the log() function).The computer output is given below. The column labeled“Beta” shows estimated regression coefficients, i.e., α and β’s in the aboveequation. (It can be interpreted that beta’s for the reference categories,“Male” and “Non-Hispanic White”, are fixed to be zero.)VariablesBetaP-valueExp(beta)intercept-3.184<0.0010.041Gender (Female)0.0500.5381.051Age0.026<0.0011.026Race/Ethnicity  Non-Hispanic Black0.806<0.0012.240  Hispanic1.314<0.0013.722  Others0.4230.0701.527N=2342.1-1. Suppose that the data set includes a 30-year oldHispanic man. What is his log odds of being self-reportedly unhealthy according to thisregression equation? 1-2. What are his odds of being self-reportedly unhealthy according to thisregression equation? 1-3. What is the probability for him to be self-reportedly unhealthy, according tothis regression equation? 1-4. The above table shows that exp(beta) for“Hispanic” is 3.722  ( = exp(1.314) ).What does this number mean? (Hint: Note that the reference category for Race/Ethnicityis “Non-Hispanic White”.)1-5. The above table shows that exp(beta) for “Age”is 1.026 ( = exp(0.026) ). What does this number mean? 1-6. Let us consider the odds (or log odds) of being self reportedly unhealthyfor Non-Hispanic White, adjusted for gender and age, and that for Non-HispanicBlack. Are they statistically significantly different at the 0.05 level by thetwo-sided test? Why or why not?