. (c) In this part we try to find dominant periodic components in the data. Fit the regression model It = a+ >k-1 Bk,1 cos(2kent/12) + BR,2 sin(2kent/12) + wt, where t = 1, ..., 144 . Note that the sin(2kx/12) and cos(2ken/12) waves repeat itself every 12/ unit time. The number f = /12 , called frequency, is the number of times a sin or cosine function repeats itself. . (i) If the model is correct, determine the significant frequencies ( at level .01 ) in the time series. Based on your analysis, how many months it takes for the time series to repeat itself. o (ii) Graph the data, It , and superimpose the fitted values, say It , on the graph. . (iii) Examine the residuals, It - It , and state your conclusions, Does it appear that the model fits the data well (do the residuals look white)? Does it appear that the residuals are a sample from a Normal distribution? Justify your