Question

. A study was conducted to assess the relationships among autism (the response), sex, age, and exposure to mercury. The output relating autism (group01) to sex is below. The response is coded as 1 for autism and 0 for no autism. Gender is coded as 1 for male and 0 for female 137 0.82 0.3641 0.0045 Logistic regression Number of obs LR chi2 (1) Prob > chi2 Pseudo R2 Log likelihood91.871301 Coef. Std. Err. [95% Conf. Interval] group01 I 4618185076022 con -9.05e-16 -471404.5 0.91 0.363 -0.00 1.000 -.533064 -.9239359 1.4567 9239359 sex Calculate and interpret the odds ratio relating sex to autism. a. b. Calculate and interpret the 95% confidence interval for the odds ratio you calculated n part a A new model was run relating autism to sex and blood levels of mercury. Based on the output, would you include both predictors in your final model. Explain. c. 137 5.50 0.0640 0.0298 Logistic regression Number of obs LR chi2(2) Prob > chi2 Pseudo R2 Log likeliho d =-89.534661 group01 I Coef. Std. Err [958 Conf. Interval] 1.22 0.222 2.00 0.046 -1.13 0.257 5300449 bloodmercurynmoll .0290419 0145507 cons -.6500833 5731724 -.3914399 .0005231 -1.77348 .647429 1.686298 .0575608 8ex 348 473314

Answer 1

1. The logistic regression equation is:

Logit(autism) = 0.451818 (sex) – 9.05e-16

Odds Ratio = e^(0.451818) = 1.57

The odds ratio means that being a male puts you at 1.57 times greater odds of having autism than females.

2. The 95% confidence interval for odds ratio is:

Lower bound: e^ (-0.533064) = 0.587

Upper bound: e^ (1.4567) = 4.29

The interpretation of the confidence interval is we are 95% confident that the true odds ratio would be likely to lie in the range of 0.587 – 4.29

3. We can see that in the second regression model, the new variable came out to be significant in predicting the response variable (autism) and the ‘sex’ variable had a less p-value than the 1^st model. Also, pseudo R-square value is more in the second model. Hence, we will include both predictors in our final model.