Caribbean Advanced Proficiency Examination
Integrated Mathematics Statistical analysis
Name of candidates: Hadiya Victorine Mark Anthony Henry Orwin Austin Kelston Shipley Jehu West Centre Number: 090041
School: Queens College
Projec t Title
To investigate the relationship between the quantity of rice exported (metric tonnes) and the time period (years) 2006-2015
Introd uction
Agriculture is a vital component in all developing countries. Of all the agriculture products produced by the countries, rice is the second most major crop grown by Guyana and it contributes to 13% of the country’s GDP, second best to sugar. Most of the rice industry is owned by the private sector collectively managed by a board of directors called the Guyana Rice Development Board (GRBD). Over the years, export of rice commodities has been quite unstable with both positive and negative effects. Being the second major crop grown, if Guyana cannot meet its demand of its foreign exchange-partners, Guyana’s economy has a chance of being crippled. Therefore, the purpose is to investigate the relationship between the amount of rice production exported between the years 2006-2015. The investigation identifies and evaluates the factors affecting the quantity of rice exported. With the results obtained, the Guyana Rice
Development Board can predict how future exportation rates may fluctuate and how it can be minimized, avoided and possibly, handled.
Mathe matic al Formu lation
The amount of rice exported annually depends on the amount produced in Guyana which is dependent on climatic conditions throughout each year. Being a less developed country, agriculture is one of the most integral elements of Guyana’s economy. This project seeks to analyse the quantity of rice exported in Guyana from the year 2006 to 2015.
The analytical technique which will be used in this research is Correlation and Linear Regression. Correlation tends to show the strength of the relationship between the two variables whereas regression seeks to plot this relationship on a line. Therefore, in this project the way in which the amount of rice produced vary as the years go by will be analysed in detail, posing reasons for the increase, decrease or stagnation of the production as well as suggesting ways in which the production can be improved.
Time period (year)
2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Presen tation of data
Quantity of rice production exported (metric tonnes) 204 576 269 436 196 233 260 815 336 313 305 382 334 141 394 989 501 208 537 334
Total revenues earned (US $) 54 622 559 75 251 464 118 032 802 114 120 324 151 321 890 173 239 722 196 226 960 239 826 389 249 504 955 220 850 000
Fig 1 Figure 1 showing the amount of rice production exported and total revenues earned on the exported commodity during (and including) the years 2006-2015. The table shows a general increase in revenues earned on exportations as the rice industry aged and more significantly, as the total metric tonnes of rice exported increased.
Quantity of rice exported (metric tonnes) 600000
500000 Quantity of rice exported (metric tonnes) 400000
Quantity of rice exported (metric tonnes)
300000
200000 Linear (Quantity of rice exported (metric tonnes)) 100000
0 2004 2006 2008 2010 2012 2014 2016
Time (years)
Fig 2 Figure 2 showing a scatter plot of the quantity of rice exported in metric tonnes against time (years). The regression line (identified by the linear label) equation is: y = -70338724.31 + 35151.83636x
Quantity of rice exported
Total revenue earned x 1000 (US $)
600000 500000 400000 300000 200000 100000 0 2006
2007
2008
2009
2010
2011
Time (years)
Fig 3
2012
2013
2014
2015
Figure 3 shows a line graph comparing the revenue earned and the metric tonnes of rice exported during the period 2006-2015. It should be noted that the total revenue was scaled to ‘a value’ x 1000, to facilitate better comparison.
Calculati Summary Statistics
ons
x- Time (in years) y- Quantity of rice exported (metric tonnes) n = 10 ´x = 2,010.5
x = 20,105
´y
= 3,340,427
y = 3,340,427
xy = 6,718,828,510
x2 = 40,421,185
y2 = 1.234947357 x 1012
Sxy = 290002.65
Sxx = 8.25
Syy = 1.191021029 x 1010
Sy = 109133.9099
Sx = 2.872281323
General Equation for the Least Squares Regression Line of y on x y = a + bx b = 35151.83636 a = -70338724.31
Equation: y = -70338724.31 + 35151.83636x r = 0.9252 (to 4 significant figures)
Analysis of data
Over the period 2006-2015, an overall increase in the quantity of rice exported was observed (as illustrated in Figure 3). In the year 2008, the rice industry experienced one of its highest export earnings in a long while. In contrast however, the quantity of rice exported that year was actually the lowest over the 10 year period. According to the Guyana Rice Development Board (GRDB), this increased revenue was attributed to the high prices being offered by the European Union (EU) market. At that time however, there were rice quotas and levy restrictions on the importation of rice by the EU which accounted for the low quantity of rice exported in that year. After the removal of the rice quota in the year 2010, the quantity of rice exported to the European Union began to rise. In addition, an agreement was signed between Jamaica and several other markets in the Caribbean Community that allowed for the export of 60,000 metric tonnes of rice yearly. As a result, not only was there an increase in the quantity of rice exported but also the total revenue earned from the exported commodity. It is worth highlighting that in the year 2015, there was a drop in the revenue earned compared to previous years. According to the head of the Guyana rice development bank, the major contributing factor for this was the drop in the price offered by the Venezuelan market (from US$760 per tonne to US$340-400 per tonne).
The scatter plot in Figure 2 shows a positive linear correlation between the bivariate data. As time increased, the quantity of rice exported also increased. A value of 0.9252 (to 4 significant figures) was obtained for the Pearson’s Product Moment Correlation Coefficient. This value being extremely close in range to +1 indicated strong positive linear correlation, thus supporting the above claim. The regression coefficient (b) of the least squares regression line of y on x was found to be 35151.83636. This value represents the slope of the regression line or the rate of change of the two variables. It can be said therefore that for the period 2006-20015, that as the years increased, the quantity of rice exported also increased by approximately 35,152 metric tonnes.
Discu ssion of findin gs
The data obtained established that there was a strong relationship between the rice exported (in metric tonnes) and years (from 2006 to 2015) i.e. an increase in the rice production exported caused an increase in exportation of rice commodities. Therefore, we can interpret that as the rice industry grew in age and experience, their capacity for increasing rice exports generally increased. However, this was not a stable increase in rice exportation. During the years 2007-2008 and 2010-2011, there was a drastic fall in the metric tonnes of rice exported. One reason for this was because of the extreme weather conditions (such as heavy rainfall) during these years which severely affected the rice yield of the second crop grown. Nevertheless, after these two-time periods, there was an explosion of metric tonnes of rice exported, mainly because of the entry of private rice producers in the rice industry. The revenues earned also showed a general increase. From the findings, we can interpret that the metric tonnes of rice exported or the revenue earned on the exported commodity did not fluctuated as was thought. Thought the rice industry may have its reported success and failure, it is still a young commodity that can only grow and increase in both production and revenue as the years increases.
Assumptions:
The statistical data provided by the Guyana rice board was completely accurate. Any loss of rice owing to transport or other factors was accounted for in the data provided. All weather conditions and the effect they had on production were taken into consideration by the Guyana
Rice Board. GDP data was attained from credible sources and are accurate.
Recommendation:
1. To further develop the rice industry to achieve maximum production. In order to facilitate this, there must be investment towards major technological advancement in term of meteorology. Predicting the weather and establishing trends of the climate will greatly benefit the rice industry and Guyana in the future.
Limitations: 1. There was great effort in gathering primary information but it was very difficult to interview any members of the Guyana Rice Board. The members of the board were unable to be contacted or could not insert us in their busy schedule. An interview would have aided in giving answer to some unanswered questions which made the research more difficult.
Conclusion: The rice industry has both its successes and failures. As the rice industry progresses and gathers experience, the production value can only increase. This was seen by the general increase in metric tonnes of rice production exported as the as the years increased (from 2006-2015). The relationship between the rice exported and the years sampled is a positive linear relationship.
References (2016). Retrieved from http://www.inewsguyana.com/687784-tonnes-of-rice-produced-in-2015/ Annual Report. (2017). Retrieved from Guyana Rice Development Board: http://grdb.gy/category/annual-reports/ Guyana Rice Development Board . (2014). Retrieved from http://grdb.gy/wpcontent/uploads/2016/10/GRDB-Annual-Report-2014.pdf
(2016). Retrieved from http://www.inewsguyana.com/687784-tonnes-of-rice-produced-in-2015/ Bryan, J. (2015, December 24). Guyana earns less from rice exports in 2015. Retrieved from Kaieteure News: http://www.kaieteurnewsonline.com/2015/12/24/guyana-earns-less-fromrice-exports-in-2015-despite-increased-exports/
Appendix b- Regression coefficient of y on x b= a=
where
Sxy = xy/n -
´y - b x´ where
´y
´x ´y
= y/n
Sxx = x2/n ´x
´x
= x/n
r- Pearson’s Product Moment Correlation Coefficient (PMCC)
Sxy Sx Sy r=
√ S yy where Sy =
√ S xx Sx =
2
