## Warning

It seems to me, as a consequence of patients (about 500 at the date this is published) being displaced to hospitals in other départements than the origin, that the number of beds is artificially decreasing in places (in the “Est région” mainly) and artificially increasing in others (e.g. Loire ?).

What is the utility of publishing area (department) statistics, if they do not reflect the cases originated in the area ?

## Comments

Both population and density of population are significant factors in explaining the COVID-29 outbreak in France. With an adjusted R squared of 79.5%, the regression is close to reach the norm of 85% (see also F and T statistics)

The slopes of the least squares adjusted lines continue rising, especially concerning population density. The concentration in population is the main influence behind the expected increases. The coefficient has risen, sofar, to 0,11. This represents the incremental increase in hospitals bed requirements, when population density increases by 1%. In other words, for every 10% increase in population density, there is a need of 1 additional hospitalisation bed resulting from COVID19 infection. E.g. with a density of 20860, the needs for Paris are of some additional 2000 beds, as of April 3rd .

This is an analysis based on public data, and subject to revisions or errors including the processing.

**Data sources:** Géodes – données en Santé Publique, INSEE.

## Analysis

Multiple Regression – COVID19 in hospitals 200403

Dependent variable: COVID19 in hospitals 200403

Independent variables:

Density

Population

. Standard T

Parameter Estimate Error Statistic P-Value

CONSTANT -51.2041 34.057 -1.50348 0.1359

Density 0.111556 0.00947515 11.7735 0.0000

Population 0.000394141 0.0000447703 8.80362 0.0000

Analysis of Variance

Source Sum of Squares Df Mean Square F-Ratio P-Value

Model 1.58856E7 2 7.94278E6 196.00 0.0000

Residual 3.97145E6 98 40525.0

Total (Corr.) 1.9857E7 100

R-squared = 79.9998 percent

R-squared (adjusted for d.f.) = 79.5916 percent

Standard Error of Est. = 201.308

Mean absolute error = 131.79

Durbin-Watson statistic = 1.38195 (P=0.0008)

Lag 1 residual autocorrelation = 0.305956

The StatAdvisor

The output shows the results of fitting a multiple linear regression model to describe the relationship between COVID19 in hospitals 200403 and 2 independent variables. The equation of the fitted model is

COVID19 in hospitals 200403 = -51.2041 + 0.111556*Density + 0.000394141*Population

Since the P-value in the ANOVA table is less than 0.05, there is a statistically significant relationship between the variables at the 95.0% confidence level.

The R-Squared statistic indicates that the model as fitted explains 79.9998% of the variability in COVID19 in hospitals 200403. The adjusted R-squared statistic, which is more suitable for comparing models with different numbers of independent variables, is 79.5916%. The standard error of the estimate shows the standard deviation of the residuals to be 201.308. This value can be used to construct prediction limits for new observations by selecting the Reports option from the text menu. The mean absolute error (MAE) of 131.79 is the average value of the residuals. The Durbin-Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P-value is less than 0.05, there is an indication of possible serial correlation at the 95.0% confidence level. Plot the residuals versus row order to see if there is any pattern that can be seen.

In determining whether the model can be simplified, notice that the highest P-value on the independent variables is 0.0000, belonging to Population. Since the P-value is less than 0.05, that term is statistically significant at the 95.0% confidence level. Consequently, you probably don’t want to remove any variables from the model.