a. The odds for having back problems for both females and males is 0.78 and 0.22 respectively
b. The odds ratio for having back problems for females versus males is 3.55
c. The difference can be due to the effect of adjusting for backpack weight and body weight in the multiple logistic regression model.
How to compute the odds for having back problems
a. To compute the odds for having back problems for both females and males, use the given percentages.
For females: back problem odds = 44% / (100% - 44%) = 44% / 56% ≈ 0.78
For males: back problem odds = 18% / (100% - 18%) = 18% / 82% ≈ 0.22
b. The odds ratio for having back problems for females versus males can be computed by taking the ratio of the odds for females to the odds for males.
Odds ratio = (back problem odds for females) / (back problem odds for males) ≈ 0.78 / 0.22 ≈ 3.55
c. The odds ratio calculated in part (b) (approximately 3.55) differs from the given odds ratio of 4.24. This difference can be due to the effect of adjusting for backpack weight and body weight in the multiple logistic regression model.
The odds ratio provided in the logistic regression model is adjusted for these factors, meaning that it takes into account the influence of backpack weight and body weight on the likelihood of back problems. The odds ratio of 4.24 reflects the association between female gender and back problems after accounting for these variables.
In contrast, the odds ratio calculated based on the percentages (approximately 3.59) does not consider the effect of backpack weight and body weight. It represents the crude association between female gender and back problems without accounting for other factors.
Therefore, the difference between the given odds ratio and the calculated odds ratio is likely due to the effect of the additional variables included in the logistic regression model, which can influence the relationship between gender and back problems.