Published on February 18, 2014
Statistics and Research methodologies Assignment 1. On June 14, 2013 the finance minister, P. Chidambaram urged Indians to not buy too much of gold for at least 1 year as it caused the country’s current account deficit to rise which in turn leads to country’s imports to rise which in turn leads to rupee’s devaluation and it becoming weaker as compared to other currencies. The finance minister made the above statement because he knows there’s a link that exists between the amounts of gold a country consumes and the value of the nation’s currency. Above statement makes it clear that there’s a correlation between consumption of gold and the forex rate of a currency. As the price is a function of consumption there also must exist a relation between price of gold and the currency exchange rate. The relation is: as more gold would be imported, more would be its price, and more price would lead to current account deficit being larger which in turn would finally lead to a weaker currency. More import Price of gold Rupee devaluation and increase in forex rate Thus we can say that in the above case price of gold is an independent variable (X) and the foreign exchange rate (Y) is the dependent variable. Let us analyze the above theory with the statistical tools of regression and correlation. (From now on the independent variable i.e. the price of gold and the dependent variable i.e. the forex rate of currency would be called as X and Y respectively.) Above variables X and Y would be said to be correlated if the change in one affects or induces a change in another. If they incidentally are correlated then there must be some relation between them that we can use to predict or estimate the value of unknown variable from the value of known variable. This prediction can be done by the process of regression analysis.
Data * End of Introduction * Date gold price/gm (X) Rupee exchange rate (Y) 24-Oct 3,180.00 61.4550 22-Oct 3,156.00 61.1950 21-Oct 3,129.00 60.6250 18-Oct 3,119.00 61.2500 17-Oct 3,103.00 61.1050 16-Oct 3,053.00 61.4550 15-Oct 3,022.00 61.8350 14-Oct 3,020.00 61.4350 11-Oct 2,994.00 61.0400 10-Oct 3,014.00 61.6150 09-Oct 2,997.00 61.8600 08-Oct 2,998.00 62.0800 07-Oct 2,968.00 61.6050 06-Oct 2,951.00 61.3850 04-Oct 2,961.00 61.3860 03-Oct 2,940.00 61.9650 01-Oct 2,975.00 62.6150 30-Sep 2,985.00 62.5850 27-Sep 2,970.00 61.9150 26-Sep 2,983.00 61.7350 25-Sep 2,983.00 62.4350 24-Sep 3,029.00 62.7350 Q.1 Source: http://www.investing.com/currencies/usd-inr-historical-data http://www.gold-silver-india.com/ Above is the data for variables X and Y. The scatter chart would be as follows: Q.2 Scatter graph 63.0000 Forex rate 62.5000 62.0000 61.5000 61.0000 y = -0.0039x + 73.635 R² = 0.2482 60.5000 2,900.00 2,950.00 3,000.00 3,050.00 Gold Price 3,100.00 3,150.00 3,200.00
There are two types of correlation: positive correlation and negative correlation. Positive correlation is seen when value of two variables involved deviate in the same direction i.e. if value of one increase (or decrease) the value of other also simultaneously increase (or decrease). Generally scatter chart of a positive correlation resembles the figure below: Negative correlation is seen when value of two variables involved deviate in the opposite direction i.e. if value of one increase (or decrease) the value of other also simultaneously decrease (or increase). Generally scatter chart of a positive correlation resembles the figure below:
All the charts other than two above represents partial correlation meaning it’s not always possible that if the value of X will increase, necessarily the value of Y will also increase and vice-versa. Analysis: Our chart resembles more to that of Negative correlation although it’s not perfectly negative but is tending towards negative i.e. most of the time if X, the independent variable increases, Y decreases. We can also say that if the price of gold increases the currency exchange rate decreases (i.e. the currenncy becomes stronger – opposite of what we have assumed in the theory) Secondly the scatter of points also tells a good story about the correlation between the variables. If the points are widely scattered then we can say that the variables are poorly correlated and vice versa. In our case the points are neither highly scattered nor highly narrow and tight. There exists a reasonable amount of correlation between the two variables X and Y. Q.3 Mean, standard deviation of variables X and Y is a follows: Variable X Variable Y Mean 3024.091 61.69595 Standard deviation 69.36165 0.549656 Analysis: Standard deviation of Variable X is noticeably very high because of ever-rising gold prices and each day there’s a new value of gold which is very much deviated from the previous value. On the other hand, Standard deviation of variable Y is too low because even a small fluctuation iin currency is a result of many factors. A drastic change in price of gold is still not enough to induce a big change in the forex rate. Q.4 The Value of Co-variance between the two variables can be found out in excel by using the function “=COVARIANCE.S(array1, array2)”. It comes out to be -18.9945. Analysis: Covariance and correlation both shows the relationship between two variables but covariance takes the units of the variables in consideraion while correlation does not.
Covariance shows the strenght of the relation between two variables. Correlation does the same thing but on a scale of -1 to +1 and does not take units of the variables into consideration. In our case there’s negative covariance which shows the relationship between X and Y is inverse in nature i.e. if X decreases, Y increases and vice-versa. Negative covariance in our case also shows that higher than average (or mean) values of X are paired with lower than average (or mean) values of Y. Covariance is generally not used to interpret how two variables vary with each other because its magnitude is hard to interpret. Correlation is much more used for this purpose. Q.5 Correlation coeffeicient as stated above is scaled version of the covariance. It can be obtained by CORREL function in excel. Inputting the values of X and Y in function gives us a correlation coeffeicient of -0.498216 Analysis: The value is in negative, this means there’s negative correlation between X and Y. -1 being the correlation for perfectly negative correlated variables tell us that in our case by almost half the strength of perfectly negative correlation the variable varies with each other. Generally it’s considered that absolute value of correlation coefficient above 0.8 is considered as strong and absolute value below 0.5 is considered as weak. So In our case the variables are at the verge of being poorly correlated but are actually not. Q.6 Regression coefficient can be calculated by using Data analysis tool of excel. Regression coefficient of Y on X comes out to be -0.003948112. Regression coefficient of Y on X is basically covariance of X and Y divides by the variance of X. Regression coefficient is also the slope of the line that we got in the scatter graph. The basic difference between correlation coefficient and regression coefficient is that correlation coefficient gives us how strong a relationship exists between the variables while on the other hand regression coefficient allows us to estimate change in value of Y for a unit increase in X. Analysis: In our case the regression coefficient is negative with a value of 0.0039, this means that there’s decrease of 0.0039 for each additional percentage increase in X. i.e. for each percent rise in the price of gold the forex rate decreases, again going against our theory.
Q.7 Linear regression equation is given by Y = aX + b, where Y is the dependent variable and X is the independent variable, a is the regression coefficient or the slope of the line, b is the intercept cut by the line on X axis. The linear regression equation also describes how well the line describes the data. It’s also called the line of best fit. So the equation will come out to be: Y = -0.0039X + 73.635 Unless X is 0, the intercept in the above equation has no specific meaning. Q.8 The equation of X on Y can be found out by reversing the variables and inputting their value in excel. It gives us the equations as: Y = -62.87X + 6902.9 Q.9 Graph for the above equation would be as follows: Regression equation of X on Y 3,200.00 Gold prices 3,150.00 y = -62.87x + 6902. R² = 0.248 3,100.00 3,050.00 Series1 3,000.00 Linear (Series1) 2,950.00 2,900.00 60.5000 61.0000 61.5000 62.0000 62.5000 63.0000 Forex rates Q.10 Suppose the price of gold suddenly rises to 5000 Rs/gram, what would be the impact on the forex rates i.e. the dependent variable. The value of the dependent variable can be found by putting the value of X in the linear regression equation we got in Question no. 7
The original equation is: y = -0.0039x + 73.635 Substituting X=5000in above, we get: +54.135 It means if gold prices rise to 5000 the forex rate would go down to 54.135 Q.11 Correlation and regression are the two most widely used statistical methods for determining the strength between two variables and how they vary with one another. Correlation is very useful in hypothesis testing where it’s necessary to establish cause-effect relationship. Correlation and regression plays a crucial role in medical as well as scientific experiments. For example if one wants to observe the effect of a drug on the blood pressure of a patient, correlation and regression analysis can be used to determine the level of blood pressure compared amount of drug given. Recently the very method of regression and correlation analysis was used to determine the lentic water quality of the important religious Brahmasarovar water tank at kurukshetra, Haryana. A positive correlation was found between the dissolved oxygen and the population of plankton and phytoplankton (the good bacteria that reduced carbon dioxide and increases the amount of oxygen that helps sustain the aquatic web of life) Correlation and regression analysis has also been extensively used by business analysts in order to project the future stock prices and financial condition of the company. Correlation and regression is also used by researchers of NASA and other space agencies to calculate the solar maximum that will occur (which is a 11 year period when number of sun spots appear on the sun when the irradiance of sun increase thus altering earth’s climate and increasing the temperature) CONCLUSION In the assignment we tried to test the theory whether gold price really affect the forex rates. In some case we found that yes there’s a direct correlation between the price of gold and forex rates and in other questions we found inverse of it. Thus we can say that this variation is due to plethora of various other factors that play a role in determining exchange rate such as state of international economy, economy, economic decisions taken by government etc. i.e. the forex rate along with being dependent on gold is also dependent on other variables, Hence the variation.
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