Case study: linear regression analysis of COVID data

Case study: linear regression analysis of COVID data from Carnegie Mellon's COVIDcast project

Overview of the data and the code

Carnegie Mellon’s COVIDcast is an academic project that tracks real-time coronavirus statistics. The team uses various data collection methods and exposes data for download in various formats. This case study uses data that were collected using daily Facebook surveys with the aim of examining the possible correlation between wearing a face-mask and showing symptoms like those of SARS-CoV-2—hereinafter COVID. Specifically, three so-called signals are recorded.

  • Does the respondent wear a face mask?

  • Does the respondent have COVID-like symptoms?

  • Does the respondent know someone in their community who has COVID-like symptoms?

Each signal is expressed as a percentage relative to the number of people who answered the particular question.

The download format, for each signal, is a comma-separated values file—hereinafter .csv file. The download page says this:

We are happy for you to use this [sic] data in products and publications. Please acknowledge us as a source: Data from Delphi COVIDcast, covidcast.cmu.edu.

This case study shows you how to use the ysqlsh \COPY metacommand to load each downloaded file into its own table, how to check that the values conform to rules that the COVIDcast team has documented, and how to join the rows in these staging tables into a single table with this format:

survey_date                 date     not null } primary
state                       text     not null }   key
mask_wearing_pct            numeric  not null
mask_wearing_stderr         numeric  not null
mask_wearing_sample_size    integer  not null
symptoms_pct                numeric  not null
symptoms_stderr             numeric  not null
symptoms_sample_size        integer  not null
cmnty_symptoms_pct          numeric  not null
cmnty_symptoms_stderr       numeric  not null
cmnty_symptoms_sample_size  integer  not null

It then shows you how to use the linear-regression functions regr_r2(), regr_slope(), and regr_intercept() to examine the correlation between mask-wearing and COVID-like symptoms. The section Functions for linear regression analysis explains the general background for these functions.

The remaining account of this case-study is divided into three parts:

Download a zip of all the files that this case study uses

All of the .sql scripts that this case-study presents for copy-and-paste at the ysqlsh prompt are included for download in a zip-file. The zip also includes the three csv files that you will download from the Carnegie Mellon COVIDcast site. This will allow you, after you've studied the account of the case study and run the files one by one, then to run everything by starting a single master script that will ingest the data and spool the reports the this study explains to files. It will allow you easily to re-run the analysis on newer data as these become available.

It is expected that the raw data will be available from the COVIDcast site into the indefinite future. But the downloadable self-contained zip-fie of the complete case study assures readers of the longevity of this study's pedagogy.

Download covid-data-case-study.zip.

After unzipping it on a convenient new directory, you'll see a README.txt. It tells you to run 0.sql. You'll see this in the top directory. It looks like this:

\i ingest-the-data.sql
\i analysis-queries.sql
\i synthetic-data.sql

Simply start it in ysqlsh. You can run it time and again. It always finishes silently. You can see the reports that it produces on the "analysis-results" directory and confirm that the files that are spooled are identical to the corresponding reference copies that are delivered in the zip-file.

Conclusion

The function regr_r2() implements a measure that the literature refers to as "R-squared". When the "R-squared" value is 0.6, it means that 60% of the relationship of the putative dependent variable (incidence of COVID-like symptoms) to the putative independent variable (mask-wearing) is explained by a simple "y = m*x + c" linear dependence—and that the remaining 40% is unexplained. A value greater than about 60% is generally taken to indicate that the putative dependent variable really does depend upon the putative independent variable.

The downloaded COVIDcast data spanned a fifty day period (from 13-Sep-2020 through 1-Nov-2020). The value of "R-squared" was computed, in turn, for each of these days. It was greater than or equal to 60% on about 80% of these days.

This outcome means that empirical evidence supports the claim that wearing a mask does indeed inhibit the spread of COVID.