Quarterly revenue ($ millions) for Twitter for the first quarter of 2012 through

Question

Quarterly revenue ($ millions) for Twitter for the first quarter of 2012 through the first quarter of 2014 are shown below (adexchange.com, April, 2015):

b.) Using Minitab or Excel, develop a linear trend equation for this time series (to 3 decimals if necessary).
y =   x +  

c. Using Minitab or Excel, develop a quadratic trend equation for this time series (to 4 decimals if necessary).
y =   x 2 +   x +  

d. Compare the MSE for each model (to 3 decimals).

Which model appears better according to MSE?
SelectLinear modelQuadratic modelItem 10

e. Use the models developed in parts (b) and (c) to forecast revenue for the tenth quarter (to 3 decimals).

Explanation / Answer

We Use Minitab to solve this question-

Welcome to Minitab, press F1 for help.

MTB > Trend 'Revenue';
SUBC>   Brief 2;
SUBC>   NoPlot.

Trend Analysis for Revenue

Data      Revenue
Length    9
NMissing 0

Fitted Trend Equation

Yt = 10.9 + 25.17×t

+Accuracy Measures

MAPE   12.628
MAD    15.173
MSD   317.765

Time Revenue    Trend   Detrend
1          54   36.111   17.8889
2          68   61.278    6.7222
3          82   86.444   -4.4444
4         112 111.611    0.3889
5         114 136.778 -22.7778
6         139 161.944 -22.9444
7         169 187.111 -18.1111
8         243 212.278   30.7222
9         250 237.444   12.5556

MTB > Trend 'Revenue';
SUBC>   Quadratic;
SUBC>   Brief 2;
SUBC>   NoPlot.

Trend Analysis for Revenue

Data      Revenue
Length    9
NMissing 0

Fitted Trend Equation

Yt = 53.3 + 2.07×t + 2.310×t^2

Accuracy Measures

MAPE    6.393
MAD     9.302
MSD   135.228

Time Revenue    Trend   Detrend
1          54   57.667   -3.6667
2          68   66.667    1.3333
3          82   80.286    1.7143
4         112   98.524   13.4762
5         114 121.381   -7.3810
6         139 148.857   -9.8571
7         169 180.952 -11.9524
8         243 217.667   25.3333
9         250 259.000   -9.0000

____________________________________________________________________________________

b)

A linear trend equation for this time series is,

Yt = 10.9 + 25.17×t

c)

A quadratic trend equation for this time series is,

Yt = 53.3 + 2.07×t + 2.310×t^2

d)

MSE for each model is,

Linear Model = 317.765

Quadratic Model =135.228

d)

Linear Model,

Yt = 10.9 + 25.17*10 = 262.600

Quadratic Model,

Yt = 53.3 + 2.07*10+ 2.310*10^2 = 305.000

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