A researcher is interested in the impact of joining a weight loss program in the past 12 months on the individuals weight loss. The analysis was restricted to people aged 16 and older who answered yes...

please answer all parts:

Extracted text: A researcher is interested in the impact of joining a weight loss program in the past 12 months on the individuals weight loss. The analysis was restricted to people aged 16 and older who answered yes to the question "During the past 12 months, have you tried to lose weight?" About 5% of the sample had joined a weight loss program in the past year. (i) Why do we restrict our analysis to those who answered yes to this question? (ii) Below is a subset of some of the other variables included in the survey. Questions were asked about actions taken in the past 12 months. Which ones do you believe should be included as covariates? Provide a justification for your choice. • Age BMI Gender Height Average minutes of exercise per week. Whether they tried to eat less calories. Whether they tried to eat less fat. Whether they tried to eat less carbs. (iii)The researcher has decided to use Propensity Score Analysis. What would be the appropriate estimator for this analysis: Average Treatment Effect (ATE), Average Treatment Effect on the Treated (ATT) or Average Treatment Effect on the Untreated (ATU)? Provide a justification for your choice.