# MATH SL Internal Assessment (IA) 2015 Correlation

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### Date of Submission: 16 January 2015

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INTRODUCTION

Exchange rate is commonly understood as the value of one currency in terms of another currency in the floating or fixed exchange market. Floating exchange market refers to the value of one currency determined by the supply and demand of the currency in the foreign exchange market; meanwhile on the fixed exchange market, the currency value is determined by the government ("Fixed and Floating Exchange Rates."). Exchange rates can quote a country’s currency to any other foreign currency; however, the most commonly used foreign currency is the United States Dollar (USD) as it has become the standard currency for most commodities and used in most international transactions. No exception in Indonesia, Indonesia Rupiah (IDR) is commonly paired with USD and directly quoted as USD relative to IDR. An example of this shall be 1 USD = 12,478.55 IDR.

Exchange rate is endlessly monitored by people having interests in the economic and financial sectors. Many sources have explained the factors that can influence a country’s exchange rate, including factors such as differentials in inflation, interest rates, current-account deficits, public debt, the terms of trade, and political stability and economic performance (Bergen, Jason. "Factors That Influence Exchange Rates."). Relying on those factors, people have created predictions in the foreign exchange market; some predict with thorough and profound analysis of all factors and some predict by judging the movement of a single or certain factors. Both ways have their advantages and disadvantages. Judging a single factor, instead of creating a complete analysis, helps in making the rapid prediction, but with dubious accuracy. It has become important then to recognize which factor would be the best in predicting the exchange rates.

Terms of Trade (TOT) is one of the factors suspected to have a momentous impact of the change in exchange rates. TOT is commonly understood as “the ratio of an index of a country’s export prices to an index of its import prices.” This refers to when a country's TOT is less than 100%; a country experiences fewer exports than imports. On the contrary, when the TOT is more than 100%, a country experiences more exports than imports ("Terms of Trade (TOT).").

The assumption is that export and import values would determine the strength of the currency of a country. When the export values are greater than import values, a country will experience appreciation. Appreciation is commonly understood as an increase in value of one currency against another currency. On the contrary, when the export values are less than import

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values, a country will experience depreciation. Depreciation is commonly understood as a decrease in value of one currency against another currency.

Until now, nevertheless, very limited researches are available that observe the correlation between TOT of Indonesia and the currency value of USD relative to IDR. Knowing the significance of understanding their correlation, especially as an observer in the financial sector, it becomes valuable to find out the answer through this report.

RATIONALE

The rationale of this report is to recognize the correlation between Indonesia’s TOT and the exchange rate of USD relative to IDR, as well as using the Indonesia’s TOT as a predictor of the exchange rate. When there is a potent correlation between the variables, it indicates that when the TOT changes, the strength of IDR value changes as well. Similarly, when there is no potent correlation, the change in terms of TOT does not mean there will be a change in the strength of IDR value. In another way of seeing it, this shall also test the assumption whether the export and import values have any correlation with the value of a country’s currency.

Having gained the result, it will be worthwhile for me to provide some advices to my surroundings in determining their investments chiefly into the foreign exchange market. The reason I chose the USD relative to IDR as a variable is because many people actively have transactions in foreign trading between IDR and USD; and the reason I chose to use TOT as a variable is, aside because it is commonly suspected to have a correlation with exchange rates, is because the data are reasonably accessible.

My personal reason of choosing this topic is because this will be my early step and valuable experiences in learning more about the financial sector and the foreign exchange market in which I have a profound interest in for the future.

AIM

The aim of this report is to find the correlation between Indonesia’s TOT and the exchange rate of USD relative to IDR by a building linear regression model between those variables by using available data in reliable sources. This report also interprets and analyzes the model and discusses its implication in real life.

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DISCUSSION

This report takes several general steps, starting with data collection and calculation continued to mapping the data in the scatter diagram to understand the data spreading. Next is to build the linear regression model using Ms. Excel software which then compared with the model built by hand using mathematical equations. Having the model, it is then continued with drawing a linear line to fit in the data and analyzing the model (including the use of the Pearson correlation to check the strength of the correlation). At the end, the error resulted by the model is then checked to test the reliability of the model.

Data Collection and Calculation

The data is collected online with BPS (Badan Pusat Statistik) Indonesia as the main source. The data collected range from January 2011 to September 2014, including data as below:

 Indonesia Cumulative Export Values by Month  Indonesia Cumulative Import Values by Month

 Average Exchange Rate USD relative to IDR by Month

The reason data range for more than three years because the more data used, the more accurate the result will be in describing the actual condition. Nevertheless, the percentage error will be higher than the fewer data used. The TOT Index is then calculated with the below formula. The TOT index by Month can be seen in Appendix II.

Scatter Diagram

From the data collection, there are two sets of data: 1) TOT index by Month and 2) average exchange rate USD relative to IDR by Month. TOT is the independent variable because the change in TOT is suspected to affect the exchange rate. Meanwhile, the exchange rate is the dependent variable because it becomes my interest to have an observation regarding whether TOT affects the exchange rate. These two sets of data are related one to another based on the Month. For instance, in January 2012, the TOT index is: 106.98 and the average exchange rate is: 9049.0065; this is then noted as (106.98, 9049.0065). All data are mapped in the scatter diagram, in this case, this made with Graphmatica as GDC.

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Figure 1. Scatter Diagram TOT vs Exchange Rate (USD-IDR).

Linear Regression Model

The data are then inserted into Ms. Excel to calculate the y², x², and xy; where x is the TOT and y is the exchange rate (USD-IDR). The scatter plot and the linear regression line are depicted using the software, which resulted in a linear regression model as the following:

To prove the reliability of the equation that is given by Ms. Excel, a manual calculation is calculated by using the formula below (Stephanie."Find a Linear Regression Equation by Hand."):

;

Where a is the intercept and b is the slope of the line

Where is the sum of TOT

Where is the sum of the exchange rate (USD-IDR) n is the total months in the data collection

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From data collection of January 2011 to September 20141, all variables are given in the formula above. Then, the calculation of the linear regression of TOT relative to the exchange rate (USD-IDR) can be revealed. The calculations are below:

The calculation above indicates a very similar linear equation with the one provided by Ms. Excel. Hence, it can be said that the model is correct. For the way forward, the model used is the one resulted from Ms. Excel, that is: y = -56.454x + 15777. The scatter plot with the linear regression line is pictured as in the below figure.

Figure 2. Scatter Diagram with Linear Regression line.

The linear regression model is analyzed for its characteristics such as: directions, strength, outliers, and linearity.

Direction - This linear regression line indicates a negative gradient or said a downward

trend (Haese, R. C, “Mathematics for the International Student: Mathematics SL.”), which determines the two variables have a negative or inverse correlation during 2011 until 2014. When the TOT

1 See Appendix III

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index increases, then the exchange rate decreases; in other words, IDR becomes stronger relative to the USD (USD becomes weaker relative to IDR) and vice versa.

Strength - Judging from the diagram in Figure 2, the strength of the correlation between

the two variables is moderate to weak because the points fall not so close to the linear line, especially the points at the top side of the line. To strengthen the confidence in judging the strength, a Pearson’s correlation coefficient is calculated as well. The formula and calculations are given below2:

The Pearson correlation coefficient is also acquired using Ms. Excel by using a formula which is “= Pearson (data 1, data 2)”. The result from Excel is (-0.446154935) which is similar with the result calculated manually by hand. From this result, the strength of the correlation is weak negative correlation since it is in the between of -0.5 and -0.1 which is the range of weak negative correlation (Haese, R. C. “Mathematics for the International Student: Mathematics SL.”).

Outliers – As seen in Figure 2, some outliers appeared especially data located far top of

the linear line, but they prove to be an authentic data, not caused by any error. Therefore, they are appropriate to be kept.

The curve fit is accurate since the manual calculation and Excel are almost similar which is y= -56.4542x+ 15777.49 and y = -56.454x + 15777.

Linearity - Based on the data spreading, it is suggested that the more appropriate result

that would fit with the data collections is polynomial instead of linear. Linear regression line method was used to have an easy assumption and more focused into the trend direction. However, it leads to inaccurate results because other factors that affect the two variables are being ignored. Using the polynomial method is supported by the graph with a curve fit line which is made by mathematical software called “Graphmatica”.

2 See Appendix III

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Figure 3. Polynomial line TOT vs Exchange Rate (USD-IDR).

From this graph, not only the linear regression line can be relied on, but also the polynomial regression should be relied on for further analysis. It is reasonable since the exchange rates are affected by other factors that mentioned earlier in the rationale. Therefore, TOT may affect the exchange rates, but other factors may be more influential.

Model Reliability Testing

Using a percentage error is the best way to look for the reliability of the data collection. It compares the approximate value with the exact value by inserting the x value or TOT into the regression line function, to find the y value, the USD-IDR exchange rate. Consequently, the formula for the percentage error and the calculation is:

Below is the example of the error calculation for the year 2011. The detail calculation for the other years can be seen in Appendix IV:

Year - 2011 TOT Index (x) Approximate USD/IDR (y) y = -56.454x + 15777 Exact Value USD/IDR (y) Percentage error (%) January 116.303886 9211.18042 9034.175564 2% February 122.6846566 8850.960397 8909.759526 1% March 112.9758688 9399.060304 8758.671892 7% April 111.1901162 9499.873183 8648.658414 10%

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May 123.3481554 8813.503236 8562.544668 3% June 121.9930352 8890.005191 8560.837126 4% July 107.4731605 9709.710199 8526.018929 14% August 123.697302 8793.792511 8526.354327 3% September 115.6521499 9247.973529 8731.185577 6% October 109.1697004 9613.933731 8860.814772 8% November 111.9629658 9456.242729 9003.017429 5% December 103.6546442 9925.280714 9051.310131 10%

Average Percentage Error for 2011 (%) 6%

Table 1. Average Percentage Error (%) in 2011

The summary of Average Percentage Error for each year is as below. It can be seen that the average percentage error ranges from lowest 6% to highest 13%. The overall average is 9%. There might be possibility that the 13% error of 2014 could be lower considering the data collected is not for a complete year, but only until September 2014. Regardless, the percentage error overall is somewhat around 9% is considered at an acceptable level. It is considerably acceptable because it only depends on the level of risk that someone is willing to absorb. If someone is a risk taker, 9 % is acceptable for them. The equation of linear regression closely behaves in real life with only 9% error per year. In addition, with small variations of percentage error between the years, it can also be concluded that the model fit quite good for each of the years.

Year Average Percentage Error (%)

2011 6% 2012 9% 2013 8% 2014 13% Average overall 9%

Table 1. Average Percentage Error (%)

However, it is also worth considering, for a specific month, the percentage error can reach up to 20% percentage error (see Appendix IV). This may also give an indication that the model sometime may not be the best model for predicting, especially considering there are also other factors aside of the TOT or export-import activities that may influence the fluctuation of the exchange rate, such as political factor and economic performance of Indonesia. It can be said that, the appropriateness of using the model depends also on the level of risk someone is willing to take.

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CONCLUSION

In conclusion, having tested the correlation between TOT index and exchange rate (USD-IDR) using a linear regression model, it can be said that the two variables have a negative correlation with weak to moderate strength. When the TOT index increases, then the exchange rate decreases. Through the Pearson Correlation Coefficient, the weak to moderate strength is confirmed as the r value is in between -0.5 and -0.1. It was also found that linear assumption may not be the best assumption in judging their relationship, as polynomial may fit better.

The linear model that is found in this report is y = -56.454x + 15777. This model can be used to predict the value of the exchange rate (USD-IDR) by inputting the value of TOT index. This model has been tested for its percentage error using the data collected from January 2011 to September 2014. The result indicates that the model gives results in a total average of percentage error of 9%. This percentage error is considered acceptable since it depends on someone who is willing to take the risks. Therefore, it can be said that this model represents the actual condition quite well.

However, on the other side, one shall be aware that TOT and the exchange rate (USD-IDR) is correlated but does not mean both variables have causation. There are still other factors out there that have influences or impacts to the exchange rate (USD-IDR).

REFLECTION

From this report, I understood that linear regression can be used to build a model and have predictions for exchange rates. Nevertheless, there is a lack of confidence to determine the terms of trade have a huge impact on exchange rates. It is plausible, as the strength of the trend is a weak to moderate negative correlation which means although there is a correlation, it may not potentially affect the exchange rates. Furthermore, the correlation of both variables doesn’t mean they have causation. Consequently, other factors still have more impacts to exchange rates.

The equation of the linear equation is reliable because it is found by using Ms. Excel calculation which is trusted as a technology that has a high accuracy. Manual calculation can be said to have an important role to prove the calculation result of Ms. Excel. Eventually, both calculation results are similar which proved that they are correct to be used.

The reliability of the data can be seen through at the percentage error. The average percentage error of my data is somewhat around 9%, which indicates it is at an acceptable level. An acceptable level means my percentage error only depends on the level of risk that someone,

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who is using this model, is willing to take. That average percentage error is not determined as either low or high degree of reliability. Therefore, someone who is a risk-taker can rely on this model since they need to accept any possible results (either bad or good) that they may have by using this model. This model can be used either in short-term or long-term because it is proven by inputting data range for more than three years which indicate a better accuracy.

The model of linear equation may not reveal the best results for showing the impact of exchange rates; instead, the polynomial regression line would be more vigorous with the data. Linear regression line method was used to have a simple assumption and more focused into the trend direction. However, it leads to inaccurate results because other factors that affect the two variables are being ignored. Therefore, other methods of regression are recommended to be further investigated.

I have increased awareness regarding the use of correlation in real life context. This application of correlation in real life is based on the math SL syllabus and it is very beneficial in the field of economics and business. Correlation can improve the confidence of every individual to decide decisions as it increases certainty. In real life, investments are significantly vital for every individual since they become as the part of the additional or even main source of incomes. Hence, in order to be thriving in investments, especially in exchange markets, more data

collection is required in order to have more certainty and accurate results.

Most importantly, using a linear regression might be the basic step to reveal the meaning of the data collection. Even though it is the basic, it requires efforts such as calculating Pearson Correlation Coefficient and finding the regression line. Fortunately, Ms. Excel can be relied on. However, it needs to be proved by using a manual way since it may lead to inaccuracy. Proving can be reliable since it is used by a computer and calculator. Furthermore, proving needs to be thorough since a mistake calculation can lead to a disaster. The data should be calculated multiple times with the formulas that are familiar.

From this report, some critical questions may arise such as; What if I used polynomial line best fit instead of linear best fit to analyze further the data collection? What if I used interpolation and extrapolation method for the graph to have more accurate predictions?

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Bibliography

Bergen, Jason. "Factors That Influence Exchange Rates." FInvestopedia, 04 May 2004. Web. 05 Jan. 2015. < http://www.investopedia.com/articles/basics/04/050704.asp>.

"Converter USD in Terms of IDR Exchange Rate." X-rates.com, n.d. Web. 06 Jan. 2015. <http://www.x-rates.com/>.

"Fixed and Floating Exchange Rates." Tutor2u, n.d. Web. 06 Jan. 2015. <http://tutor2u.net/>. Haese, R. C. “Mathematics for the International Student: Mathematics SL.”Adelaide Airport, S.

Aust.: Haese Mathematics, 2012. Print.

"Indonesia Exports-Imports." Badan Pusat Statistik, n.d. Web. 6 Jan. 2015. <http://www.bps.go.id/>.

Stephanie. "Find a Linear Regression Equation by Hand." StatisticsHowTo, n.d. Web. 09 Jan. 2015. <http://www.statisticshowto.com/how-to-find-a-linear-regression-equation/>. "Terms of Trade (TOT)." Investopedia, 24 Feb. 2010. Web. 06 Jan. 2015.

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## APPENDIX:

I: DATA OF INDONESIA CUMMULATIVE EXPORT AND IMPORT IN 2011-2014 AND IDR EXCHANGE RATE

No Year Month Value of Export (US\$) Value of Import (US\$) USD/IDR 1 2011 January 14,606,249,454 12,558,694,259 9034.1756 2 February 14,415,278,398 11,749,862,451 8909.7595 3 March 16,365,953,469 14,486,238,209 8758.6719 4 April 16,554,240,767 14,888,230,483 8648.6584 5 May 18,287,435,825 14,825,868,915 8562.5447 6 June 18,386,855,403 15,072,053,394 8560.8371 7 July 17,418,472,565 16,207,276,766 8526.0189 8 August 18,647,825,151 15,075,369,345 8526.3543 9 September 17,543,408,243 15,169,115,540 8731.1856 10 October 16,957,743,283 15,533,378,964 8860.8148 11 November 17,235,463,273 15,393,896,679 9003.0174 12 December 17,077,694,229 16,475,570,731 9051.3101 13 2012 January 15,570,069,320 14,554,618,780 9049.0065 14 February 15,695,443,242 14,866,785,109 9008.1915 15 March 17,251,519,437 16,325,662,478 9140.8020 16 April 16,173,190,978 16,937,875,721 9158.9418 17 May 16,829,545,550 17,036,735,320 9268.8984 18 June 15,441,457,938 16,727,521,763 9415.9986 19 July 16,090,595,299 16,354,450,283 9433.9247 20 August 14,047,007,385 13,813,875,810 9488.2893 21 September 15,898,115,717 15,348,557,469 9548.5414 22 October 15,324,042,715 17,207,931,360 9597.6121 23 November 16,316,911,273 16,935,009,726 9617.1683 24 December 15,393,946,390 15,581,977,290 9642.3812 25 2013 January 15,375,487,902 15,450,235,320 9656.7843 26 February 15,015,627,735 15,313,286,233 9682.5440 27 March 15,024,577,683 14,887,075,645 9706.4351 28 April 14,760,892,129 16,463,468,844 9722.8320 29 May 16,133,358,194 16,660,559,292 9752.2900 30 June 14,758,819,151 15,636,019,963 9875.2500 31 July 15,087,863,565 17,416,991,671 10087.4700 32 August 13,083,707,039 13,012,045,835 10601.1300 33 September 14,706,775,080 15,509,774,940 11309.2400 34 October 15,698,330,394 15,674,021,743 11141.3600 35 November 15,938,557,641 15,149,325,413 11473.0700 36 December 16,967,798,188 15,455,864,981 12020.9700 37 2014 January 14,472,285,648 14,916,227,693 12044.6281 38 February 14,634,090,390 13,790,661,990 11832.5100 39 March 15,192,634,701 14,523,719,412 11420.1139 40 April 14,292,472,554 16,254,976,317 11433.3900 41 May 14,823,602,661 14,770,336,777 11523.6116 42 June 15,409,451,765 15,697,742,441 11888.9032

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43 July 14,124,129,298 14,081,710,235 11687.5300 44 August 14,481,642,319 14,793,236,965 11721.2600 45 September 15,275,846,089 15,546,096,309 11918.3900

II: TERMS OF TRADE (EXPORT PRICES/IMPORT PRICES) X 100 No Year Month Terms of Trade Index

1 2011 January 116.30 2 February 122.68 3 March 112.98 4 April 111.19 5 May 123.35 6 June 121.99 7 July 107.47 8 August 123.70 9 September 115.65 10 October 109.17 11 November 111.96 12 December 103.65 13 2012 January 106.98 14 February 105.57 15 March 105.67 16 April 95.49 17 May 98.78 18 June 92.31 19 July 98.39 20 August 101.69 21 September 103.58 22 October 89.05 23 November 96.35 24 December 98.79 25 2013 January 99.52 26 February 98.06 27 March 100.92 28 April 89.66 29 May 96.84 30 June 94.39 31 July 86.63 32 August 100.55 33 September 94.82 34 October 100.16 35 November 105.21 36 December 109.78 37 2014 January 97.02 42 June 98.16 38 February 106.12 43 July 100.30 39 March 104.61 44 August 97.89 40 April 87.93 45 September 98.26 41 May 100.36

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### IN 2011-2014

No Year Month Terms of Trade Index (x) USD/IDR (y) y^2 x^2 x*y

1 2011 January 116.303886 9034.175564 81616328.12 13526.59 1050709.72 2 February 122.6846566 8909.759526 79383814.81 15051.52 1093090.79 3 March 112.9758688 8758.671892 76714333.31 12763.55 989518.566 4 April 111.1901162 8648.658414 74799292.36 12363.24 961645.334 5 May 123.3481554 8562.544668 73317171.19 15214.77 1056174.09 6 June 121.9930352 8560.837126 73287932.3 14882.3 1044362.5 7 July 107.4731605 8526.018929 72692998.78 11550.48 916318.2 8 August 123.697302 8526.354327 72698718.11 15301.02 1054687.03 9 September 115.6521499 8731.185577 76233601.58 13375.42 1009780.38 10 October 109.1697004 8860.814772 78514038.42 11918.02 967332.494 11 November 111.9629658 9003.017429 81054322.83 12535.71 1008004.53 12 December 103.6546442 9051.310131 81926215.09 10744.29 938210.332 13 2012 January 106.9768268 9049.006473 81884518.15 11444.04 968033.998 14 February 105.5738892 9008.191501 81147514.12 11145.85 951029.812 15 March 105.6711754 9140.802029 83554261.73 11166.4 965919.295 16 April 95.48535628 9158.941819 83886215.24 9117.453 874544.823 17 May 98.7838646 9268.898428 85912478.07 9758.252 915617.607 18 June 92.31168942 9415.998636 88661030.31 8521.448 869206.742 19 July 98.38664719 9433.924691 88998935.08 9679.932 928172.22 20 August 101.6876623 9488.289321 90027634.24 10340.38 964841.96 21 September 103.5805205 9548.541376 91174642.41 10728.92 989042.886 22 October 89.05220735 9597.612058 92114157.22 7930.296 854688.539 23 November 96.35017362 9617.168279 92489925.71 9283.356 926615.833 24 December 98.79327959 9642.381192 92975515.05 9760.112 952602.461 25 2013 January 99.51620531 9656.784295 93253482.92 9903.475 961006.529 26 February 98.05620757 9682.543998 93751658.27 9615.02 949433.544 27 March 100.9236336 9706.4351 94214882.35 10185.58 979608.7 28 April 89.65845697 9722.832019 94533462.47 8038.639 871734.116 29 May 96.83563385 9752.29 95107160.24 9377.14 944369.184 30 June 94.3898715 9875.25 97520562.56 8909.448 932123.579 31 July 86.6272652 10087.47 101757051 7504.283 873849.939 32 August 100.5507297 10601.13 112383957.3 10110.45 1065951.36 33 September 94.82262081 11309.24 127898909.4 8991.329 1072371.78 34 October 100.1550888 11141.36 124129902.6 10031.04 1115863.9

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35 November 105.2096856 11473.07 131631335.2 11069.08 1207078.09 36 December 109.782262 12020.97 144503719.7 12052.15 1319689.28 37 2014 January 97.02376463 12044.62807 145073065.2 9413.611 1168615.16 38 February 106.1159385 11832.51 140008292.9 11260.59 1255617.9 39 March 104.6056748 11420.11391 130419001.7 10942.35 1194608.72 40 April 87.92675102 11433.39 130722406.9 7731.114 1005300.84 41 May 100.3606274 11523.61156 132793623.5 10072.26 1156516.89 42 June 98.16348958 11888.90322 141346019.7 9636.071 1167056.23 43 July 100.3012352 11687.53 136598357.5 10060.34 1172273.7 44 August 97.89366826 11721.26 137387936 9583.17 1147437.14 45 September 98.26162006 11918.39 142048020.2 9655.346 1171120.31 Sum 4639.939364 448042.8163 4522148402 482245.8 45981777 Average 103.1097636 9956.507029 Pearson -0.446154935

### IV. Percentage Error in 2012-2014

y = -56.454x + 15777

Index (x) Approximate USD/IDR (y)

Exact Value

USD/IDR (y) Percentage error (%)

2012 January 106.9768268 9737.730221 9049.006473 8% February 105.5738892 9816.931658 9008.191501 9% March 105.6711754 9811.439462 9140.802029 7% April 95.48535628 10386.4697 9158.941819 13% May 98.7838646 10200.25571 9268.898428 10% June 92.31168942 10565.63589 9415.998636 12% July 98.38664719 10222.68022 9433.924691 8% August 101.6876623 10036.32471 9488.289321 6% September 103.5805205 9929.465295 9548.541376 4% October 89.05220735 10749.64669 9597.612058 12% November 96.35017362 10337.6473 9617.168279 7% December 98.79327959 10199.72419 9642.381192 6% Average 99.38777436 10166.16259 9364.146317 9% 2013 January 99.51620531 10158.91215 9656.784295 5% February 98.05620757 10241.33486 9682.543998 6% March 100.9236336 10079.45719 9706.4351 4% April 89.65845697 10715.42147 9722.832019 10% May 96.83563385 10310.24113 9752.29 6% June 94.3898715 10448.31419 9875.25 6% July 86.6272652 10886.54437 10087.47 8%

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August 100.5507297 10100.5091 10601.13 5% September 94.82262081 10423.88376 11309.24 8% October 100.1550888 10122.84462 11141.36 9% November 105.2096856 9837.492408 11473.07 14% December 109.782262 9579.352181 12020.97 20% Average 98.04397175 10242.02562 10419.11462 8% 2014 January 97.02376463 10299.62039 12044.62807 14% February 106.1159385 9786.33081 11832.51 17% March 104.6056748 9871.591233 11420.11391 14% April 87.92675102 10813.1832 11433.39 5% May 100.3606274 10111.24114 11523.61156 12% June 98.16348958 10235.27836 11888.90322 14% July 100.3012352 10114.59407 11687.53 13% August 97.89366826 10250.51085 11721.26 13% September 98.26162006 10229.7385 11918.39 14% Average 98.96141882 10190.23206 11718.92631 13%

References

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