#Data analysis
# Daily Food Budget of BSS students
X = c(65,70,150,200,75,155,145,50,85,60,95,80,100,45,60,150,80,160,45,60,45,55,60,45,50,
150,65,80,145,60,85,100,60,45,55,50,65,60,80,150,50,50,35,150,100,100,100,85,100,
100,150,200,150,100,50,45,150,100,150,85,45,65)
# Individual Satisfaction on VSU Food Pricing
Y = c(5,5,6,6,5,6,6,4,5,5,6,6,5,4,5,8,5,6,4,5,4,4,5,4,4,7,5,5,7,6,5,5,5,4,5,5,5,5,6,7,5,
5,4,6,6,6,5,5,6,6,6,5,5,5,4,4,6,5,5,5,4,6)
DATA = cbind(X,Y)
DATA## X Y
## [1,] 65 5
## [2,] 70 5
## [3,] 150 6
## [4,] 200 6
## [5,] 75 5
## [6,] 155 6
## [7,] 145 6
## [8,] 50 4
## [9,] 85 5
## [10,] 60 5
## [11,] 95 6
## [12,] 80 6
## [13,] 100 5
## [14,] 45 4
## [15,] 60 5
## [16,] 150 8
## [17,] 80 5
## [18,] 160 6
## [19,] 45 4
## [20,] 60 5
## [21,] 45 4
## [22,] 55 4
## [23,] 60 5
## [24,] 45 4
## [25,] 50 4
## [26,] 150 7
## [27,] 65 5
## [28,] 80 5
## [29,] 145 7
## [30,] 60 6
## [31,] 85 5
## [32,] 100 5
## [33,] 60 5
## [34,] 45 4
## [35,] 55 5
## [36,] 50 5
## [37,] 65 5
## [38,] 60 5
## [39,] 80 6
## [40,] 150 7
## [41,] 50 5
## [42,] 50 5
## [43,] 35 4
## [44,] 150 6
## [45,] 100 6
## [46,] 100 6
## [47,] 100 5
## [48,] 85 5
## [49,] 100 6
## [50,] 100 6
## [51,] 150 6
## [52,] 200 5
## [53,] 150 5
## [54,] 100 5
## [55,] 50 4
## [56,] 45 4
## [57,] 150 6
## [58,] 100 5
## [59,] 150 5
## [60,] 85 5
## [61,] 45 4
## [62,] 65 6DATA CALCATIONS
Summations= read.csv("Pearsons R Summations.csv", header = T, sep = ",")
as.data.frame(Summations)## X Y X.2 Y.2 XY
## 1 65 5 4225 25 325
## 2 70 5 4900 25 350
## 3 150 6 22500 36 900
## 4 200 6 40000 36 1200
## 5 75 5 5625 25 375
## 6 155 6 24025 36 930
## 7 145 6 21025 36 870
## 8 50 4 2500 16 200
## 9 85 5 7225 25 425
## 10 60 5 3600 25 300
## 11 95 6 9025 36 570
## 12 80 6 6400 36 480
## 13 100 5 10000 25 500
## 14 45 4 2025 16 180
## 15 60 5 3600 25 300
## 16 150 8 22500 64 1200
## 17 80 5 6400 25 400
## 18 160 6 25600 36 960
## 19 45 4 2025 16 180
## 20 60 5 3600 25 300
## 21 45 4 2025 16 180
## 22 55 4 3025 16 220
## 23 60 5 3600 25 300
## 24 45 4 2025 16 180
## 25 50 5 2500 25 250
## 26 150 7 22500 49 1050
## 27 65 5 4225 25 325
## 28 80 5 6400 25 400
## 29 145 7 21025 49 1015
## 30 60 6 3600 36 360
## 31 85 5 7225 25 425
## 32 100 5 10000 25 500
## 33 60 4 3600 16 240
## 34 45 4 2025 16 180
## 35 55 5 3025 25 275
## 36 50 5 2500 25 250
## 37 65 5 4225 25 325
## 38 60 5 3600 25 300
## 39 80 6 6400 36 480
## 40 150 7 22500 49 1050
## 41 50 5 2500 25 250
## 42 50 5 2500 25 250
## 43 35 4 1225 16 140
## 44 150 6 22500 36 900
## 45 100 6 10000 36 600
## 46 100 6 10000 36 600
## 47 100 5 10000 25 500
## 48 85 5 7225 25 425
## 49 100 6 10000 36 600
## 50 100 6 10000 36 600
## 51 150 6 22500 36 900
## 52 200 5 40000 25 1000
## 53 150 5 22500 25 750
## 54 100 5 10000 25 500
## 55 50 4 2500 16 200
## 56 45 4 2025 16 180
## 57 150 6 22500 36 900
## 58 100 5 10000 25 500
## 59 150 5 22500 25 750
## 60 85 5 7225 25 425
## 61 45 4 2025 16 180
## 62 65 6 4225 36 390
## 63 SUM_X SUM_Y SUM_X^2 SUM_Y^2 SUM_XY
## 64 5595 324 616775 1740 30800#Manual Computation: Using Pearson’s R correlation Analysis
\(n=62\)
\[r=\frac{n\Sigma(xy)-\Sigma(x)\Sigma(y)}{\sqrt([n(\Sigma(x^2)-(\Sigma(x)^2][n(\Sigma(y^2)-(\Sigma(y)^2])}\] \[r=\frac{62(30800)-(5595)(324)}{\sqrt([62(616775)-(5595)^2][62(1740)-(324)^2])}\]
\[=\frac{96820}{144923.3}\]
\[=0.6821995\] #R COdes Computation
#library(tidyverse)
Pearson_Correlation = cor.test(X,Y)
Pearson_Correlation##
## Pearson's product-moment correlation
##
## data: X and Y
## t = 7.2272, df = 60, p-value = 1.024e-09
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.5212477 0.7962870
## sample estimates:
## cor
## 0.6821996HYPOTHESIS TESTING
Alternative and Null Hypothesis
\(H_{0}:p = 0\) : There is no significant linear relationship between BSS student’s daily food budget and satisfaction on the VSU food prices
\(H_{1}:p \neq 0\) : There is a significant linear relationship between BSS student’s daily food budget and satisfaction on the VSU food prices
Alpha:
\(a = 0.01\)
Test Statistics : T-TEST
\[t = \frac{r}{\sqrt(\frac{1-r^2}{n-2})}= t = \frac{0.6821996 }{\sqrt(\frac{1-(0.6821996 )^2}{62-2})}= 7.227215158\]
Decision Rule
qt(0.005,60, lower.tail = FALSE)## [1] 2.660283Reject \(H_{0}\) if \(|t_{c}|\ge t_{(0.005,60)} = 2.660283\), otherwise, do not reject \(H_{0}\).
Decision
We will reject \(H_{0}\) since \(t_{c}=7.227215158 \ge t_{(0.005,60)}= 2.660283\).
Conclusion
Therefore at 1% level of significance, we can say that the data is sufficient to conclude that there is a significant linear relationship between students daily food budget and their satisfaction on the food pricing at Visayas State University.
Generally, the result shows that as the BSS students allocated a greater amount of daily food budget, it indicates that their satisfaction on the pricing of food products also increases,since they can afford to buy their necessities and they have extra money to satisfy their cravings.
However, when they allocate smaller amount of daily food budget it means their satisfaction also decreases because due to the high prices of some food products, their budget is not sufficient to buy those products, thus they often buy affordable foods that serve as alternative to satisfy their hunger.