## 3 Methods  
### Data Screening  
Because monitoring records were gathered from different sources with different timestamps, it was decided to work with daily statistics. For outdoor environmental variables, daily means or daily totals were determined depending on the most common format found in climatological reports. For indoor air temperature, the mean was also the selected statistic; however, because CO\({}_{2}\) sensor readings higher than 2000 ppm were truncated, as suggested in [72], the median was used as a measure of central tendency for indoor CO\({}_{2}\) concentration. When determining means and medians for indoor variables, because the study focuses on naturally ventilated classrooms with manual window (blinds) opening/closing, periods with no classes were removed. Missing records and univariate outliers present in the resulting dataset were dealt with considering listwise deletion [73]. The classrooms' daily air change rates were derived from class records of CO\({}_{2}\) concentration and of metabolic CO\({}_{2}\) production rate (\(c\) and \(S_{c}\), respectively) using the solution of the decay equation [74; 75; 76]. Figure 3: Data for two consecutive academic years, showing time series of the outdoor and of indoor variables for the monitored classroom on the second floor of the east wing. The time series for the outdoor variables are continuous, while those for the indoor variables exclude weekends as well as Bank, Christmas, February half-term (Carnival), Easter, and summer holidays. To improve the efficacy of the path model analysis, values of the daily metabolic CO2 production rate \(\overline{S}_{c}\) were scaled by \(10^{-1}\), reducing the variance range in the sample dataset. To ensure normal distribution of the studied variables, the daily total precipitation and daily air change rate required logarithmic transformation (see notes to Table 3 below). Table 3 presents statistics for the variables used in this paper, including the correlation, mean, standard deviation (SD), skewness, and kurtosis. The values of skew and kurtosis did not exceed 1.25 and, with the exception of precipitation, \(|skewness|<1\) and \(|kurtosis|<1\), suggesting that the assumption of multivariate normality applies when using the maximum likelihood method to estimate a path model from sample data. Regarding the correlations, Table 3 shows these are lower than 0.9 and that most are statistically significant considering \(p<0.01\). The correlations with \(p>0.01\) are those relating daily metabolic CO2 production rate with daily outdoor and indoor environmental variables and those relating daily values of wind speed with relative humidity and solar energy. The fairly stable time series for daily values of metabolic CO2 production rate (\(\overline{S}_{c}\)) and wind speed (\(\overline{WS}\)) presented in Figure 3 justify these nonsignificant correlations. Despite being lower than 0.9, the strong correlation between daily outdoor and indoor air temperature (0.8821) must be noted; indeed, Figure 3 shows that despite differences in amplitude, the time series of daily outdoor and indoor air temperature (\(\overline{T}_{\text{out}}\) and \(\overline{T}_{\text{in}}\)) have similar trends, with both showing similar frequencies and no meaningful phase shift. This strong correlation between outdoor and indoor air temperatures has previously been reported by researchers studying room airing with window opening/closing [77; 78]. Using the Variance Inflation Factor (VIF) to check sample data multivariate collinearity shows that the VIF values are lower than 5, suggesting the absence of multicollinearity problems [42]. Because our subsequent analysis always considers daily statistics, the term \"daily\" is omitted when referring to mean or total sample variables.