Table 3 Regression model specifications.

1A

x_t = β₀ + β₁t + β₂TS1 + β₃TS2 + β₄TS3 + β₅TS4 + β₆TS5 + e_t

x_t is the un-aggregated value of WQ parameter which occurred in t-week; y_t is the cumulative diarrheal disease count for t-week.

1B

y_t = exp{β₀ + β₁t + β₂TS1 + β₃TS2 + β₄TS3 + β₅TS4 + β₆TS5 + e_t}

TS1 through TS5 are binary variables for Tamil season (Table 2); β₁ regression coefficient reflects the trend over the study period; β₂ through β₆ reflect the change in the study parameter as compared to the season-specific reference category (TS6).

2A

x_t = β₀ + β₁t + β_LS + e_t

x_t is the un-aggregated value of WQ parameter which occurred in t- week; y_t is the cumulative diarrheal disease count for t-week.

2B

y_t = exp{β₀ + β₁t + β_LS + e_t}

β₁ regression coefficient reflects the trend and β_L (β₂ through β₅) is the vector of coefficients for a seasonal pattern (S) represented by two harmonics^#; a period ω = 365.25 is used to adjust for the effect of a leap year.

3A

x_t = β₀ + β₁t + β_LS + β₆ Temp + β₇Rain + e_t

x_t is the value of un-aggregated WQ parameter which occurred in t-week; y_t is the cumulative diarrheal disease count for t-week.

3B

y_t = exp{β₀ + β₁t + β_LS + β₆ Temp + β₇Rain + e_t}

Interpretation of β₁ and β_Lis similar to Model 2; β₆ and β₇are effects of weekly average temperature and weekly cumulative rainfall (log₁₀ transformed).

y_t is the cumulative diarrheal disease count for t-week.

Interpretation of β₁, β_L, β₆ and β₇are similar to Model 3; β₈ through β₁₂are effects of private domain weekly median water quality parameters (TC and FC were log₁₀ transformed).