This is a hypothetical, no other data is given or missing:

Regressions

In a study of concentration of fine particles in the air and COVID mortalityin the US, the authors find that a 1 unit increase in fine particles significantly (at 95 percent level) increases COVID mortality by more than 1%.

1. If you constructed a 95 confidence interval for the coefficient on concentration of fine particles in air, would it: (a) include 1; (b) include 0; (c) include 2? Please provide reasoning for why it has to include or not a specific value - and state if we do not have enough information to reach a conclusion. Answer: Not enough information is given to reach a conclusion because the range of a SE is needed.
2. The authors include 17 control variables in their study. In general, when we decide whether a variable *must* be controlled for, what do we need to know about the relationship between the variable we are thinking of including, the outcome variable, and the main causal variable of interest?
3. If you want to control for more variables, is it generally important that you have more observations - why or why not?
4. The authors show that omitting the control for hospital beds pushes the coefficient of COVID mortality down - what can you say about the likely relationship between hospital beds and fine-particle concentration? Assume that more hospital beds generally mean that mortality is lower.
5. In observational studies, can we ever hope that we have included all relevant controls? Discuss the importance of measuring relevant observed and unobserved variables. Answer: No, because there could be a number of confounders not covered within the study. A theory can only cover so much which leads to omitted variable bias.