X seeding time sne
Min. : 1.00 Length :24 Min. : 0.00 Min. :1.300
1st Qu.: 6.75 N.unique : 2 1st Qu.:15.75 1st Qu.:2.612
Median :12.50 N.blank : 0 Median :32.50 Median :3.250
Mean :12.50 Min.nchar: 2 Mean :35.33 Mean :3.169
3rd Qu.:18.25 Max.nchar: 3 3rd Qu.:55.25 3rd Qu.:3.962
Max. :24.00 Max. :83.00 Max. :4.650
cloudcover prewetness echomotion rainfall
Min. : 2.200 Min. :0.0180 Length :24 Min. : 0.280
1st Qu.: 3.750 1st Qu.:0.1405 N.unique : 2 1st Qu.: 2.342
Median : 5.250 Median :0.2220 N.blank : 0 Median : 4.335
Mean : 7.246 Mean :0.3271 Min.nchar: 6 Mean : 4.403
3rd Qu.: 7.175 3rd Qu.:0.3297 Max.nchar:10 3rd Qu.: 5.575
Max. :37.900 Max. :1.2670 Max. :12.850
# 1. Split data into Seeding and Non-Seeding groupsseed_yes <-subset(clouds, seeding =="yes")seed_no <-subset(clouds, seeding =="no")# 2. Summary statistics (Mean and Standard Deviation)mean(seed_yes$rainfall)
[1] 4.634167
sd(seed_yes$rainfall)
[1] 2.776841
mean(seed_no$rainfall)
[1] 4.171667
sd(seed_no$rainfall)
[1] 3.519196
# 3. Visualization: Boxplotboxplot(rainfall ~ seeding, data = clouds, main ="Rainfall Distribution by Seeding Status",xlab ="Seeding", ylab ="Rainfall", col =c("lightcoral", "lightskyblue"))
Welch Two Sample t-test
data: rainfall by seeding
t = -0.3574, df = 20.871, p-value = 0.7244
alternative hypothesis: true difference in means between group no and group yes is not equal to 0
95 percent confidence interval:
-3.154691 2.229691
sample estimates:
mean in group no mean in group yes
4.171667 4.634167
The seeding group had a slightly higher mean rainfall (4.63) than the non-seeding group (4.17), while the non-seeding group showed greater variability (SD = 3.52 vs. 2.78). The boxplot revealed substantial overlap between the two distributions. A t-test found no significant difference in rainfall between the groups (t = -0.357, p = 0.724). Therefore, the data do not provide evidence that cloud seeding significantly increases rainfall.
2. Multiple Linear Regression Model
# 1. Build the Multiple Linear Regression Modelmodel_clouds <-lm(rainfall ~ seeding + cloudcover + prewetness + echomotion + sne, data = clouds)# 2. Check Coefficients and Model Fitsummary(model_clouds)
Call:
lm(formula = rainfall ~ seeding + cloudcover + prewetness + echomotion +
sne, data = clouds)
Residuals:
Min 1Q Median 3Q Max
-5.1158 -1.7078 -0.2422 1.3368 6.4827
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.37680 2.43432 2.620 0.0174 *
seedingyes 1.12011 1.20725 0.928 0.3658
cloudcover 0.01821 0.11508 0.158 0.8761
prewetness 2.55109 2.70090 0.945 0.3574
echomotionstationary 2.59855 1.54090 1.686 0.1090
sne -1.27530 0.68015 -1.875 0.0771 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2.855 on 18 degrees of freedom
Multiple R-squared: 0.3403, Adjusted R-squared: 0.157
F-statistic: 1.857 on 5 and 18 DF, p-value: 0.1524
# 3. Sequential ANOVA to check variable importanceanova(model_clouds)
The multiple regression model explains about 34% of the variation in rainfall (R² = 0.3403), but the overall model is not statistically significant (p = 0.152). According to both the coefficient table and the ANOVA results, echomotion and sne appear to be the most important predictors of rainfall, with the largest F-values and sums of squares. Seeding, cloudcover, and prewetness show little evidence of influencing rainfall. Therefore, echomotion and sne appear to have the strongest effects on rainfall, while cloud seeding itself does not appear to significantly increase rainfall in this dataset.
3. Suitability Index (sne) Models
# 1. Build separate models for Seeding (Yes) and No Seeding (No)model_yes <-lm(rainfall ~ sne, data = seed_yes)model_no <-lm(rainfall ~ sne, data = seed_no)# 2. Check the coefficients of both modelssummary(model_yes)
Call:
lm(formula = rainfall ~ sne, data = seed_yes)
Residuals:
Min 1Q Median 3Q Max
-3.0134 -1.3297 -0.3276 0.6171 4.3867
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 12.0202 2.9774 4.037 0.00237 **
sne -2.2180 0.8722 -2.543 0.02921 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2.27 on 10 degrees of freedom
Multiple R-squared: 0.3927, Adjusted R-squared: 0.332
F-statistic: 6.467 on 1 and 10 DF, p-value: 0.02921
summary(model_no)
Call:
lm(formula = rainfall ~ sne, data = seed_no)
Residuals:
Min 1Q Median 3Q Max
-5.4892 -2.1762 0.2958 1.4902 7.3616
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.319 3.160 2.317 0.043 *
sne -1.046 0.995 -1.052 0.318
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.502 on 10 degrees of freedom
Multiple R-squared: 0.09957, Adjusted R-squared: 0.009528
F-statistic: 1.106 on 1 and 10 DF, p-value: 0.3177
# 3. Produce a figure showing the two models togetherplot(rainfall ~ sne, data = clouds, col =ifelse(seeding =="yes", "blue", "red"), pch =16, main ="Rainfall vs SNE by Seeding Status",xlab ="SNE (Suitability Criterion)", ylab ="Rainfall")# Add the regression lines for each modelabline(model_yes, col ="blue", lwd =2) # Seeding Yes Lineabline(model_no, col ="red", lwd =2) # Seeding No Line# Add a simple legendlegend("topright", legend =c("Seeding (Yes)", "No Seeding (No)"), col =c("blue", "red"), lwd =2)
Both models show a negative relationship between SNE and rainfall. The seeding model has a steeper slope (−2.22) than the non-seeding model (−1.05), indicating a stronger effect of SNE on rainfall when cloud seeding is used. The SNE coefficient is statistically significant in the seeding model (p = 0.029) but not in the non-seeding model (p = 0.318). This suggests that rainfall is more sensitive to changes in SNE during seeded experiments than during non-seeded experiments.
