DataSet A

library(readxl)
library(ggpubr)
## Loading required package: ggplot2
DatasetA <- read_excel("/Users/srikarthikeya/Downloads/DatasetA.xlsx")
mean(DatasetA$StudyHours) 
## [1] 6.135609
sd(DatasetA$StudyHours)
## [1] 1.369224
mean(DatasetA$ExamScore) 
## [1] 90.06906
sd(DatasetA$ExamScore)
## [1] 6.795224
hist(DatasetA$StudyHours,
     main = "StudyHours",
     breaks = 20,
     col = "blue",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

hist(DatasetA$ExamScore,
     main = "ExamScore",
     breaks = 20,
     col = "green",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

The variable StudyHours appears normally distributed. The data looks symmetrical (most data is in the middle). The data also appears to have a proper bell curve. The variable ExamScore appears normally distributed. The data looks symmetrical (most data is in the middle). The data also appears to have a proper bell curve.

shapiro.test(DatasetA$StudyHours) 
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetA$StudyHours
## W = 0.99388, p-value = 0.9349
shapiro.test(DatasetA$ExamScore)
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetA$ExamScore
## W = 0.96286, p-value = 0.006465

The Shaprio-Wilk p-value for StudyHours normality test is greater than .05 (.9349), so the data is normal. The Shapiro-Wilk p-value for the ExamScore normality test is less than .05 (.0064), so the data is not normal.

cor.test(DatasetA$StudyHours, DatasetA$ExamScore, method = "spearman")
## Warning in cor.test.default(DatasetA$StudyHours, DatasetA$ExamScore, method =
## "spearman"): Cannot compute exact p-value with ties
## 
##  Spearman's rank correlation rho
## 
## data:  DatasetA$StudyHours and DatasetA$ExamScore
## S = 16518, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##       rho 
## 0.9008825

The Spearman Correlation test was selected because both variables were not normally distributed according to the histograms and the Shapiro-Wilk tests. The p-value is 2.2e-16 is below .05. This means the results are statistically significant. The alternate hypothesis is supported. The correlation value is 0.9008. The correlation is positive, which means as StudyHours increases, ExamScore increases. The correlation value is greater than 0.50 which means the relationship is strong.

ggscatter(
  DatasetA,
  x = "StudyHours",
  y = "ExamScore",
  add = "reg.line",
  xlab = "StudyHours",
  ylab = "ExamScore",
  col="red"
)

The line of best fit is pointing to the top right. This means the diretion of the data is positive. As StudyHours increases, Examscore increases. The dots closely hug the line. This means there is a strong relationship between the variables. The dots form a straight-line pattern. This means the data is linear. There is possibly no outlier

StudyHours (M = 6.13, SD = 1.369) was correlated with ExamScore (M = 90.06, SD = 6.79), r.ho = 0.9008, p = 2.2e-16. The relationship was positive and strong. As the StudyHours increased, the ExamScore increased.

Dataset B

DatasetB <- read_excel("/Users/srikarthikeya/Downloads/DatasetB.xlsx")
mean(DatasetB$ScreenTime) 
## [1] 5.063296
sd(DatasetB$ScreenTime)
## [1] 2.056833
mean(DatasetB$SleepingHours) 
## [1] 6.938459
sd(DatasetB$SleepingHours)
## [1] 1.351332
hist(DatasetB$ScreenTime,
     main = "ScreenTime",
     breaks = 20,
     col = "yellow",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

hist(DatasetB$SleepingHours,
     main = "SleepingHours",
     breaks = 20,
     col = "red",
     border = "white",
     cex.main = 1,
     cex.axis = 1,
     cex.lab = 1)

The variable “ScreenTime” appears normally distributed. The data looks symmetrical (most data is in the middle). The data also appears to have a proper bell curve. The variable “SleepingHours” appears normally distributed. The data looks symmetrical (most data is in the middle). The data also appears to have a proper bell curve.

shapiro.test(DatasetB$ScreenTime) 
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetB$ScreenTime
## W = 0.90278, p-value = 1.914e-06
shapiro.test(DatasetB$SleepingHours)
## 
##  Shapiro-Wilk normality test
## 
## data:  DatasetB$SleepingHours
## W = 0.98467, p-value = 0.3004

The Shaprio-Wilk p-value for ScreenTime normality test is less than .05 (1.914e-06[0.000001914]), so the data is not normal. The Shapiro-Wilk p-value for the SleepingHours normality test is greater than .05 (0.3004), so the data is normal.

cor.test(DatasetB$ScreenTime, DatasetB$SleepingHours, method = "spearman")
## 
##  Spearman's rank correlation rho
## 
## data:  DatasetB$ScreenTime and DatasetB$SleepingHours
## S = 259052, p-value = 3.521e-09
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## -0.5544674

The Spearman Correlation test was selected because both variables were not normally distributed according to the histograms and the Shapiro-Wilk tests. The p-value is 3.521e-09 is below .05. This means the results are statistically significant. The alternate hypothesis is supported. The correlation value is -0.5544674 . The correlation is negative, which means as ScreenTime increased, the SleepingHours decreases. The correlation value is greater than 0.50 which means the relationship is strong.

ggscatter(
  DatasetB,
  x = "ScreenTime",
  y = "SleepingHours",
  add = "reg.line",
  xlab = "ScreenTime",
  ylab = "SleepingHours",
  col="orange"
)

The line of best fit is pointing to the bottom right. This means the diretion of the data is positive. As ScreenTime Decrease, SleepingHours increases. The dots closely hug the line. This means there is a strong relationship between the variables. The dots form a straight-line pattern. This means the data is linear. There is possibly no outlier .

ScreenTime (M = 5.06, SD = 2.056) was correlated with SleepingHours (M = 6.93, SD = 1.35), r.ho = -0.5544, p = 3.521e-09. The relationship was negative and strong. As the ScreenTime increased, the SleepingHours decreases.