Both population and density of population are significant factors in explaining the COVID-29 outbreak in France. With an adjusted R squared of 74.4%, the regression continues to gain in signification (see also F and T statistics)
The slopes of the least squares adjusted lines continue rising, especially concerning popularion density. In other words the concentration of population is the main influence behind the expected increases. A decline will signal that the peak in the pandemic has been passed.
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.
Multiple Regression – COVID19 in hospitals 200329
Dependent variable: COVID19 in hospitals 200329
Inhabitants per km²
. Standard T
Parameter Estimate Error Statistic P-Value
CONSTANT -26.9713 26.9506 -1.00077 0.3194
Inhabitants per km² 0.0768737 0.00749688 10.2541 0.0000
Population 0.000266677 0.000035429 7.52708 0.0000
Analysis of Variance
Source Sum of Squares Df Mean Square F-Ratio P-Value
Model 7.43789E6 2 3.71894E6 146.61 0.0000
Residual 2.48582E6 98 25365.5
Total (Corr.) 9.92371E6 100
R-squared = 74.9507 percent
R-squared (adjusted for d.f.) = 74.4395 percent
Standard Error of Est. = 159.266
Mean absolute error = 97.8685
Durbin-Watson statistic = 1.31442 (P=0.0002)
Lag 1 residual autocorrelation = 0.33913
The output shows the results of fitting a multiple linear regression model to describe the relationship between COVID19 in hospitals 200329 and 2 independent variables. The equation of the fitted model is
COVID19 in hospitals 200329 = -26.9713 + 0.0768737*Inhabitants per km² + 0.000266677*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 74.9507% of the variability in COVID19 in hospitals 200329. The adjusted R-squared statistic, which is more suitable for comparing models with different numbers of independent variables, is 74.4395%. The standard error of the estimate shows the standard deviation of the residuals to be 159.266. 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 97.8685 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.