Final Project: Clouds
John Murphy
6/25/2021
Reading in the data
Also creating two subsets to view the data based on seeding
library(ggplot2)## Warning: package 'ggplot2' was built under R version 4.0.5clouds = read.csv("clouds.csv")
clouds## X seeding time sne cloudcover prewetness echomotion rainfall
## 1 1 no 0 1.75 13.4 0.274 stationary 12.85
## 2 2 yes 1 2.70 37.9 1.267 moving 5.52
## 3 3 yes 3 4.10 3.9 0.198 stationary 6.29
## 4 4 no 4 2.35 5.3 0.526 moving 6.11
## 5 5 yes 6 4.25 7.1 0.250 moving 2.45
## 6 6 no 9 1.60 6.9 0.018 stationary 3.61
## 7 7 no 18 1.30 4.6 0.307 moving 0.47
## 8 8 no 25 3.35 4.9 0.194 moving 4.56
## 9 9 no 27 2.85 12.1 0.751 moving 6.35
## 10 10 yes 28 2.20 5.2 0.084 moving 5.06
## 11 11 yes 29 4.40 4.1 0.236 moving 2.76
## 12 12 yes 32 3.10 2.8 0.214 moving 4.05
## 13 13 no 33 3.95 6.8 0.796 moving 5.74
## 14 14 yes 35 2.90 3.0 0.124 moving 4.84
## 15 15 yes 38 2.05 7.0 0.144 moving 11.86
## 16 16 no 39 4.00 11.3 0.398 moving 4.45
## 17 17 no 53 3.35 4.2 0.237 stationary 3.66
## 18 18 yes 55 3.70 3.3 0.960 moving 4.22
## 19 19 no 56 3.80 2.2 0.230 moving 1.16
## 20 20 yes 59 3.40 6.5 0.142 stationary 5.45
## 21 21 yes 65 3.15 3.1 0.073 moving 2.02
## 22 22 no 68 3.15 2.6 0.136 moving 0.82
## 23 23 yes 82 4.01 8.3 0.123 moving 1.09
## 24 24 no 83 4.65 7.4 0.168 moving 0.28seedy = subset(clouds, seeding == "yes")
seedy## X seeding time sne cloudcover prewetness echomotion rainfall
## 2 2 yes 1 2.70 37.9 1.267 moving 5.52
## 3 3 yes 3 4.10 3.9 0.198 stationary 6.29
## 5 5 yes 6 4.25 7.1 0.250 moving 2.45
## 10 10 yes 28 2.20 5.2 0.084 moving 5.06
## 11 11 yes 29 4.40 4.1 0.236 moving 2.76
## 12 12 yes 32 3.10 2.8 0.214 moving 4.05
## 14 14 yes 35 2.90 3.0 0.124 moving 4.84
## 15 15 yes 38 2.05 7.0 0.144 moving 11.86
## 18 18 yes 55 3.70 3.3 0.960 moving 4.22
## 20 20 yes 59 3.40 6.5 0.142 stationary 5.45
## 21 21 yes 65 3.15 3.1 0.073 moving 2.02
## 23 23 yes 82 4.01 8.3 0.123 moving 1.09seedn = subset(clouds, seeding == "no")
seedn## X seeding time sne cloudcover prewetness echomotion rainfall
## 1 1 no 0 1.75 13.4 0.274 stationary 12.85
## 4 4 no 4 2.35 5.3 0.526 moving 6.11
## 6 6 no 9 1.60 6.9 0.018 stationary 3.61
## 7 7 no 18 1.30 4.6 0.307 moving 0.47
## 8 8 no 25 3.35 4.9 0.194 moving 4.56
## 9 9 no 27 2.85 12.1 0.751 moving 6.35
## 13 13 no 33 3.95 6.8 0.796 moving 5.74
## 16 16 no 39 4.00 11.3 0.398 moving 4.45
## 17 17 no 53 3.35 4.2 0.237 stationary 3.66
## 19 19 no 56 3.80 2.2 0.230 moving 1.16
## 22 22 no 68 3.15 2.6 0.136 moving 0.82
## 24 24 no 83 4.65 7.4 0.168 moving 0.28Viewing the subests
summary(seedy)## X seeding time sne
## Min. : 2.00 Length:12 Min. : 1.00 Min. :2.050
## 1st Qu.: 8.75 Class :character 1st Qu.:22.50 1st Qu.:2.850
## Median :13.00 Mode :character Median :33.50 Median :3.275
## Mean :12.83 Mean :36.08 Mean :3.330
## 3rd Qu.:18.50 3rd Qu.:56.00 3rd Qu.:4.032
## Max. :23.00 Max. :82.00 Max. :4.400
## cloudcover prewetness echomotion rainfall
## Min. : 2.800 Min. :0.0730 Length:12 Min. : 1.090
## 1st Qu.: 3.250 1st Qu.:0.1237 Class :character 1st Qu.: 2.683
## Median : 4.650 Median :0.1710 Mode :character Median : 4.530
## Mean : 7.683 Mean :0.3179 Mean : 4.634
## 3rd Qu.: 7.025 3rd Qu.:0.2395 3rd Qu.: 5.468
## Max. :37.900 Max. :1.2670 Max. :11.860mean(seedy$rainfall)## [1] 4.634167sd(seedy$rainfall)## [1] 2.776841summary(seedn)## X seeding time sne
## Min. : 1.00 Length:12 Min. : 0.00 Min. :1.300
## 1st Qu.: 6.75 Class :character 1st Qu.:15.75 1st Qu.:2.200
## Median :11.00 Mode :character Median :30.00 Median :3.250
## Mean :12.17 Mean :34.58 Mean :3.008
## 3rd Qu.:17.50 3rd Qu.:53.75 3rd Qu.:3.837
## Max. :24.00 Max. :83.00 Max. :4.650
## cloudcover prewetness echomotion rainfall
## Min. : 2.200 Min. :0.0180 Length:12 Min. : 0.280
## 1st Qu.: 4.500 1st Qu.:0.1875 Class :character 1st Qu.: 1.075
## Median : 6.050 Median :0.2555 Mode :character Median : 4.055
## Mean : 6.808 Mean :0.3362 Mean : 4.172
## 3rd Qu.: 8.375 3rd Qu.:0.4300 3rd Qu.: 5.832
## Max. :13.400 Max. :0.7960 Max. :12.850mean(seedn$rainfall)## [1] 4.171667sd(seedn$rainfall)## [1] 3.519196The means and standard deviations are relatively close with more variability in the clouds with no seeding.
Boxplots of data
ggplot(seedy, aes(x=seeding, y=rainfall)) + geom_boxplot()
ggplot(seedn, aes(x=seeding, y=rainfall)) + geom_boxplot()
Based on the boxplots above, the medians are very close to eachother. We also see the affect of the deviation in the clouds that don’t have seeding vs. the clouds that are seeded and appear to have a much more controlled rainfall with one major outlier.
t.test
t.test(seedy$rainfall, seedn$rainfall, alternative = "two.sided")##
## Welch Two Sample t-test
##
## data: seedy$rainfall and seedn$rainfall
## t = 0.3574, df = 20.871, p-value = 0.7244
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -2.229691 3.154691
## sample estimates:
## mean of x mean of y
## 4.634167 4.171667We have a signifcant P-Value that indicates the seeded and non-seeded rainfalls are very similar to eachother which is reflected in the closeness of the means and the similar spread to the boxplots
Linear Regression Model
cloudslm = lm(rainfall ~ seeding + cloudcover + prewetness +
echomotion + sne, data = clouds)cloudslm##
## Call:
## lm(formula = rainfall ~ seeding + cloudcover + prewetness + echomotion +
## sne, data = clouds)
##
## Coefficients:
## (Intercept) seedingyes cloudcover
## 6.37680 1.12011 0.01821
## prewetness echomotionstationary sne
## 2.55109 2.59855 -1.27530summary(cloudslm)##
## 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: 0.1524anova(cloudslm)## Analysis of Variance Table
##
## Response: rainfall
## Df Sum Sq Mean Sq F value Pr(>F)
## seeding 1 1.283 1.2834 0.1575 0.69613
## cloudcover 1 15.738 15.7377 1.9313 0.18157
## prewetness 1 0.003 0.0027 0.0003 0.98557
## echomotion 1 29.985 29.9853 3.6798 0.07108 .
## sne 1 28.649 28.6491 3.5158 0.07711 .
## Residuals 18 146.677 8.1487
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Based on the F-Value we see that there are 3 potential impacts to rainfall: Cloud cover, echo motion, and suitability criterion (sne)
Creating LRM based in relation to sne based on seeding
cloudslmy = lm(rainfall ~ sne, data = seedy)
cloudslmy##
## Call:
## lm(formula = rainfall ~ sne, data = seedy)
##
## Coefficients:
## (Intercept) sne
## 12.020 -2.218summary(cloudslmy)##
## Call:
## lm(formula = rainfall ~ sne, data = seedy)
##
## 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: 0.02921cloudslmn = lm(rainfall ~ sne, data = seedn)
cloudslmn##
## Call:
## lm(formula = rainfall ~ sne, data = seedn)
##
## Coefficients:
## (Intercept) sne
## 7.319 -1.046summary(cloudslmn)##
## Call:
## lm(formula = rainfall ~ sne, data = seedn)
##
## 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: 0.3177Plots of the models
x1 = ggplot(cloudslmy, aes(x = sne, y = rainfall)) + geom_point()
x1 = x1 + geom_abline(slope = coef(cloudslm)[4], intercept = coef(cloudslm)[6])
x2 = ggplot(cloudslmn, aes(x = sne, y = rainfall)) + geom_point()
x2 = x2 + geom_abline(slope = coef(cloudslm)[4], intercept = coef(cloudslm)[6])
x1
x2