Question

2. The following table gives the average monthly exchange rate between the Omani rial (OMR) and the Indian rupee (INR) for 2019. It shows that 1 OMR was equivalent to 181.39 INR in January 2019. Month January February March April May June Monthly Exchange Rate (y) 181.39 184.94 184.82 179.91 182.17 18276 180.32 1 88.08 188 88 18703 187.87 18739 July August September October November December a. Develop a trendline that could be used to predict the exchange rate (y) for the year 2019. b. Use the model you developed in 'a' above to forecast the exchange rate (y) for next June 2020

Answer 1

(a) The trend line can be considered to be as a linear trend line, in which case applying OLS to the data would be sufficient. We have the independent variable as t=1,2,...,12. The regression model would be as $\widehat{y} = \hat \beta_0 + \hat \beta_1 t$ .

The slope coefficeint would be as $\hat \beta_1 = \frac{\sum (y - \overline{y})(t - \overline t)}{\sum (t - \overline t)^2}$ or $\hat \beta_1 = \frac{83.99}{143}$ or $\hat \beta_1 = 0.5873$ , and $\hat \beta_0 = \overline{y} - \hat \beta_1 * \overline t$ or $\hat \beta_0 = 184.63 - 0.5873 * 6.5$ or $\hat \beta_0 = 180.8125$ .

Hence, the trend line would be as $\widehat{y} = 180.8125 + 0.5873 t$ .

(b) We have t=18 for the June, 2020. We have the expected exchange rate as $\widehat{y} = 180.8125 + 0.5873 *18$ or $\widehat{y} = 191.3839 \approx 191.38$ .