Consider the quarterly data for corporate profits (in billions of dollars) in th

Question

Consider the quarterly data for corporate profits (in billions of dollars) in the United States that is given above...

(a) Estimate a linear trend model and submit a copy of your results

(b) Write the equation of the linear trend model.

(c) Estimate a growth trend model and submit a copy of your results. Please use natural logs (ln) in obtaining your results.

(d) Write the equation of the growth trend model.

(e) Forecast the value of corporate profits for quarter 1 and quarter 3 of 2018 using the linear trend model. Please show your calculations.

(f) Forecast the value of corporate profits for quarter 1 and quarter 3 of 2018 using the growth trend model. Please show your calculations.

Corporate Profits (in billions of dollars 2007 Quarter 1 1270.8 Quarter 2 1341.7 Quarter 3 1285.3 Quarter 4 1313.7 2008 Quarter 1 1203.5 Quarter 2 1229.6 Quarter 3 1188.8 Quarter 4 671.4 2009 Quarter 1 1044.3 Quarter 2 1120.6 Quarter 3 1273.2 Quarter 4 1374.4 2010 Quarter 1 1450.2 Quarter 2 1436.8 Quarter 3 1499.1 Quarter 4 1494.5 2011 Quarter 1 1350.2 Quarter 2 1423.1 Quarter 3 1430.4 Quarter 4 1507.1 2012 Quarter 1 1727.4 Quarter 2 1654.8 Quarter 3 1686.6 Quarter 4 1663.9 2013 Quarter 1 1679.5 Quarter 2 1658.1 Quarter 3 1685.6 Quarter 4 1730.3 2014 Quarter 1 1657.8 Quarter 2 1733.3 Quarter 3 1758.0 Quarter 4 1771.5 2015 Quarter 1 1636.7 Quarter 2 1664.3 Quarter 3 1610.8 Quarter 4 1423.4 2016 Quarter 1 1550.5 Quarter 2 1636.7 Quarter 3 1679.4 Quarter 4 1741.2 2017 Quarter 1 1729.2

Explanation / Answer

(a)

    The linear trend model for the given data is given by,

From the Excel first enter the data in excel worksheet and select the data then go to insert -> graph->scatter graph->layout->select trend line then the linear trend of corporate profits is given by

(b)

    Then we find the equation of linear trend is given by

     From the excel by using Regression we can find out the equation of linear trend,that is given by

    First enter the data in excel worksheet then goto -> data->data analysis->select regression->select the input Y(Corporate profits) and Select input X(t values) form the above table->and click on line plot-> click on ok then we get the results are given by

Hence from the above results the Equation of linear trend is given by

     Y = 1158.626341 + 15.54865854X

    The plot of the trend line is given by

(C)

    Now we estimate Growth trend Model is given by

   First we know that formula of Annual growth rate in Excel is given by

     =(End value/Start value)^(1/periods-1)-1

     So by using this formula calculate the Predicted values of Corporate profits when we applying the formula to every cell in the Predicited value column is given by

Hence the Annual Growth rate is = (End value/Start value)^(1/periods-1)-1

                                                    = (1729.2/1270.8)^(1/41-1)-1    (since from the given table of profit values)

                                                     = 0.00773

Then by using the above growth rate we find out Predicited values table is given by

in predicted column we write like this = (preceding value*(1+0.00773)) then we can get the value after that we drag it then we can get the all values of Predicited column that is given by

Hence the graph for the Growth rate is given by from the excel

(d)

      Hence we findout the Euation of Growth trend model by using Regression on Excel is given by

    Hence the Equation of Growth trend model is Y = 287.2746809 + 0.191533054 X

-------------------------------------------- x ------------------------------------------------------------

  

   

Corporate Profits (in billions of dollars t 2007 Quarter 1 1270.8 1 Quarter 2 1341.7 2 Quarter 3 1285.3 3 Quarter 4 1313.7 4 2008 Quarter 1 1203.5 5 Quarter 2 1229.6 6 Quarter 3 1188.8 7 Quarter 4 671.4 8 2009 Quarter 1 1044.3 9 Quarter 2 1120.6 10 Quarter 3 1273.2 11 Quarter 4 1374.4 12 2010 Quarter 1 1450.2 13 Quarter 2 1436.8 14 Quarter 3 1499.1 15 Quarter 4 1494.5 16 2011 Quarter 1 1350.2 17 Quarter 2 1423.1 18 Quarter 3 1430.4 19 Quarter 4 1507.1 20 2012 Quarter 1 1727.4 21 Quarter 2 1654.8 22 Quarter 3 1686.6 23 Quarter 4 1663.9 24 2013 Quarter 1 1679.5 25 Quarter 2 1658.1 26 Quarter 3 1685.6 27 Quarter 4 1730.3 28 2014 Quarter 1 1657.8 29 Quarter 2 1733.3 30 Quarter 3 1758 31 Quarter 4 1771.5 32 2015 Quarter 1 1636.7 33 Quarter 2 1664.3 34 Quarter 3 1610.8 35 Quarter 4 1423.4 36 2016 Quarter 1 1550.5 37 Quarter 2 1636.7 38 Quarter 3 1679.4 39 Quarter 4 1741.2 40 2017 Quarter 1 1729.2 41

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