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 the number of days on stay-at-home orders based on the order date, respondents' state of residence, and survey completion date to create the variable of a 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).

a.What is the research question (state it as a question) and who might care about the answer?

b.Write out the empirical model in an equation format based on the information provided above.

c.What do you hypothesize is the relationship between the outcome, phq4, and the main predictor of interest, sah_days, and why?

d.You find the correlation coefficient is 0.061.Interpret the relationship based on the correlation coefficient

Table 1 provides summary statistics of the variables and Table 2 is the regression output.

e.How well does your model fit the data (be clear about what information provided you could be used to assess this and your interpretation of the information)?

f.Interpret the coefficient estimate on sah_days and conduct a hypothesis test.

g.Interpret the coefficient estimates on the following variables and conduct hypothesis tests: gender, pcovid

h.Was a causal relationship identified (i.e. is the coefficient estimate on the main predictor variable biased)?Why or why not?

Table 1. Summary of variables Variable | Obs Mean Std. Dev. Min Max phg4 6,366 2.133993 2. 805748 12 sah days 6, 354 40.1728 13. 24659 67 coll 6, 403 . 1703889 . 3760034 1 gender 6, 403 . 4162112 . 4929679 pcovid 6,370 23. 89433 21 . 53016 100 pdie 6,365 20.39574 25. 07158 100 Table 2. Ordinary Least Squares Estimation Results phq4 | Coef. Std. Err. t Polt| [95% Conf. Interval] sah days . 0096943 . 0025499 3. 80 0.000 . 0046957 . 0146929 age -. 0360763 . 0022189 -16.26 D. 000 -. 0404261 -. 0317266 coll -. 0666597 . 0903337 -0.74 0 . 461 -. 2437445 . 1104252 gender - . 635857 . 0688721 -9.23 0.000 -. 7708697 -. 5008444 pcovid . 0119738 . 0017445 6.86 0.000 . 008554 0153936 pdie . 0140246 . 0015344 9.14 0.000 0110167 . 0170325 cons 3. 277173 . 1674557 19.57 0.000 2.948903 3. 605443 N=6, 324 R-squared=0. 0936 Adjusted R-squared=0. 0927 F Test (6, 6317) Prob > F (0. 0000)