Tutorial 12_SOLUTIONS_1 2018_22 May.pdf

# For example for d22 use model 1 the linear equation

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For example, for D22, use Model 1 (the linear equation obtained from your regression output) and calculate the value. Therefore, in cell D22 would be =\$L\$17+\$L\$18*B22 and this could be dragged down to calculate the remaining years using this model. (Note: Squared is ^2.) For E22, you need to use Model 2. For this, you need to substitute the relevant t (B22) and t 2 (B22) 2 into the equation obtained from the scatterplot. Therefore, in cell E22 would be: =3537.6+706.78*B22-0.2981*(B22^2) and this could be dragged down to calculate the remaining years using this model. You now have the forecasted values, for the years 2003 2007 using both Model 1 (linear regression) and Model 2 (quadratic). 4. To save you time, columns F, G, H, I, have been set up with the relevant formulae to calculate the sum of absolute errors and squared forecast errors for Models 1 and 2 respectively. (The numbers in F22:I26 will change accordingly once you enter the relevant values in D22:E26.) Eg: cell F22 gives the difference between C22 and D22 [Excel function = ABS(C22- D22)]; You should study these carefully to ensure you understand what is being done and could replicate it yourself. (Note: Absolute value is the function ABS in Excel and squared is ^2.) 5. Summarise the results of these calculations by completing the table below, and state, with reasons, which model you choose. t Y ˆ t Y ˆ t Y ˆ

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ETF1100 Business Statistics SOLUTIONS Tutorial 12______ 5 Model 1 Model 2 Estimated equation Mean Absolute Deviation (MAD) 16798.312/5= 3,359.6625 16984.656/5= 3,396.9311 Mean Squared Forecast Errors (MSFE) 63,059,962.34/5= 12,611,992.47 64,426,988.15/5= 12,885,397.63 I would choose Model 1 , because the mean of absolute deviation, and the mean of squared forecast errors are both lower for the Model 1 than for Model 2. This means that Model 1 provides the most accurate forecasts. Also worth discussing how to decide on which measure to use. Q12.2 The Presidential election that was held in 2012, put the economic welfare of North Carolina in the spotlight since the preparations involved the Democratic Convention being held there. Below is a time series plot that tells the full story of the unemployment rate in North Carolina each quarter for the 10 years from 2002 to 2012. Note that the time series starts in the second year of the Bush presidency, and t = 29 corresponds to January 2009, the beginning of the Obama presidency. (The quarterly figures are provided in January, April, July and October.)
ETF1100 Business Statistics SOLUTIONS Tutorial 12______ 6 Discuss what components are present in this time series, and what evidence you see in the graph for each of them.

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