By April 2020, 44 states had instituted stay-at-home (SAH) orders to slow the spread of coronavirus disease 2019 (COVID-19). The duration of stay-at-home days varied across states, lasting from 3.5 weeks to over 2 months. The strategy reduced the spread of illness, but had social and economic costs.While higher levels of psychological stress have been documented, we want to know how much stay-at-home orders contributed to psychological stress.We have data collected every two weeks between March 10 and May 24, 2020, from the Understanding America Study (UAS) COVID-19 survey, a probability-based internet panel of about 9,000 US adults ages 18 and older.The UAS COVID-19 survey included the Patient Health Questionnaire for Depression and Anxiety (PHQ-4), which asks about feelings related to depression and anxiety and results in a score from 1 (no depression/anxiety) to 12 (highest level of depression/anxiety). We measured number of days on stay-at-home orders based on order date, respondents' state of residence, and survey completion date to create the variable of number of stay at home days for each person (say_days). We used ordinary least squares to estimate the relationship between PHQ-4 score and accumulated stay-at-home days, and included in our model other potential confounders (variable name in output tables is in parenthesis): age (age), college educated (coll), male gender (gender), probability of contracting COVID (pcovid), probability of dying from COVID (pdie).

1. What is the research question (state it as a question) and who might care about the answer?
2. Write out the empirical model in an equation format based on the information provided above.
3. What do you hypothesize is the relationship between the outcome, phq4 and main predictor of interest, sah_days, and why?
4. You find the correlation coefficient is 0.061.Interpret the relationship based on the correlation coefficient