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Discussion of coefficients

Categories: FinanceMath

In simple or multiple linear regression, the size of the coefficient for each independent variable gives you the size of the effect that variable is having on your dependent variable, and the sign on the coefficient (positive or negative) gives you the direction of the effect. The regression equation which has a single independent variable, the coefficient tells you how much the dependent variable is expected to increase (if the coefficient is positive) or decrease (if the coefficient is negative) when that independent variable increases by one.

In regression equation where there are multiple independent variables, the coefficient tells you how much the dependent variable is expected to increase when that independent variable increases by one, holding all the other independent variables constant. Regression analysis: A statistical technique used to explain or predict the behavior of a dependent variable. Generally, a regression equation takes the form of Y=a+bx+c, where Y is the dependent variable that the equation tries to predict, X is the independent variable that is being used to predict Y, a is the Y-intercept of the line, and c is a value called the regression residual.

The values of the coefficients a and b are selected in such a way so that the square of the regression residuals is minimized. Standard error: The standard error of a correlation coefficient is used to determine the confidence intervals around a true correlation of zero. If the correlation coefficient falls outside of this range, then it is significantly different than zero.

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The standard error can be calculated for interval or ratio-type data The equation for RSS and TSS is:

Total sum of squares = explained sum of squares + residual sum of squares RSS: (residual sum of square) here is 1. 299, 1. 531 and 1. 914 for large companies, medium companies and small companies respectively The residual sum of squares (RSS) is the sum of squares of residuals. RSS can be said to be the discrepancy between the data and our estimation model. RSS is a measure for how well a line fits the points, the smaller RSS, the better the fit hence the smaller this discrepancy is, the better the estimation will be.

TSS: The value of the total sum of squares (TSS) depends on the data being analyzed and the test that is being done. In statistical linear models, (particularly in standard regression models), the TSS is the sum of the squares of the difference of the dependent variable and its grand mean In analysis of variance (ANOVA) the total sum of squares is the sum of the so-called “within-samples” sum of squares and “between-samples” sum of squares, i. e.

, partitioning of the sum of squares. C: is the intercept of the regression equation with the y-axis that is it is the intersection point of the dependent variable and the line of regression. DLPI: is the dependent Variable and is determined by the regression equation once the independent variable is identified in this case it is the rate of return of the company or industry defined as the difference of the natural logarithm of stock market price.

Natural Logarithm: The natural logarithm of a number x is the power to which e would have to be raised to equal x — for example the natural log of e itself is 1 because e1 = e, while the natural logarithm of 1 would be 0, since e0 = 1, The natural logarithm can be defined for all positive real numbers x as the area under the curve y = 1/t from 1 to x, and can also be defined for non-zero complex numbers Compare the regression with estimated results:

As we compare the regression with the estimated results we find that the results are close to the estimation with the large cap companies having more relation with the fluctuations in the exchange rates than the small cap companies, although the relationship is not as close as we had expected for the firms but the regression results have shown a relationship between the two variables. Relevant comments to the issues being addressed: The issue of whether stock prices and exchange rates are related or not have received considerable attention in the past.

During the crises the countries affected have seen turmoil in both currency and stock markets. If stock prices and exchange rates are related and the causation runs from exchange rates to stock prices then crises in the stock markets can be prevented by controlling the exchange rates. Similarly we see that if the causation runs from stock prices to exchange rates then authorities can focus on domestic economic policies to stabilize the stock market.

If the two markets/prices are related then investors can use this information to predict the behavior of one market using the information on other market. In the past there has been many studies conducted that addressed this issue the results of these studies are, however, inconclusive. Some studies have found a significant positive relationship between stock prices and exchange rates (for instance Smith (1992), Solnik (1987), and Aggarwal (1981)) while others have reported a significant negative relationship between the two (e.

g. , Soenen and Hennigar (1998)). On the other hand, there are some studies that have found very weak or no association between stock prices and exchange rates (for instance, Franck and Young (1972), Eli Bartov and Gordon M. Bodnor (1994)). On the subject of causation in this matter, the evidence is also mixed. Some studies (for instance, Abdalla and Murinde (1997)) have found causation runs from exchange rates to stock prices while other reported a reverse causation (e. g. , Ajayi and Mougoue (1996)).

Bahmani-Oskooee and Sohrabian (1992), however, claim there is a bi-directional causality between stock prices and exchange rates in the Large, Medium and Small companies. As we see there has been no consensus what so ever in this subject we need a study that can deterministically find a solution towards the issue that has been dealt with in this model. Conclusion: This paper examined the association between stock prices and exchange rates in Large, Medium and Small companies in UK for the period Jan 1977 to Dec 1995.

We employed monthly data and applied cointegration, error correction modeling approach and standard Granger causality tests to examine the relationship between stock prices and exchange rates in Large, Medium and Small companies in UK the results however showed high residual sum of squares which means high discrepancy in the estimation and the results the results also showed that there was a lot more relationship between the large company’s stock prices and the exchange rates than there is relation between the small company’s stock prices and the exchange rate this verifies that large companies with high degree of presence in other countries are much more vulnerable to exchange rate fluctuations than the small companies which are present mainly in the country of their inception and are mainly affected by the exchange rates indirectly unlike the large countries which face the exchange rate fluctuations directly. We can also see that the Gulf war of 1991 had an impact on the relationship between stock prices and the exchange rate fluctuations there can be many explanations for this one can be that due to war the trade between the countries was halted resulting in no effect of exchange rate fluctuations other reason could be that due to the war the demand came down in the world which resulted in less exposure towards the exchange rate fluctuations.

If we compare the results of the regression performed on stock prices and exchange rate fluctuations on Large, Medium and Small companies excluding the 1991 Gulf War we would come to a conclusion that exchange rate does play a role in determining the stock prices of firms however large firms with high degree of international operations are much more exposed to the exchange rates resulting in high degree of relationship of their stock prices and the exchange rates. Recommendation: The significance of these results could possibly be improved upon by applying daily or weekly data. The use of more frequent observations may better capture the dynamics of stock and currency market interrelationships. Another possible extension would be to segregate the Multi national corporations which are directly affected by the exchange rate fluctuations with those firms which are not directly affected by the exchange rate fluctuations and then we can compare these two different data to get more interesting results.

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Discussion of coefficients. (2020, Jun 01). Retrieved from

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