Question

Time series are particularly useful to track variables such as revenues, costs, and profits over time. Time series models help evaluate performance and make predictions. Consider the following and respond in a minimum of 175 words:

• Time series decomposition seeks to separate the time series (Y) into 4 components: trend (T), cycle (C), seasonal (S), and irregular (I). What is the difference between these components?
• The model can be additive or multiplicative.When we do use an additive model? When do we use a multiplicative model?
• The following list gives the gross federal debt(in millions of dollars) for the U.S. every 5 years from 1945 to 2000:

Year    Gross Federal Debt ($millions)

1945    260,123

1950    256,853

1955    274,366

1960    290,525

1965    322,318

1970    380,921

1975    541,925

1980    909,050

1985    1,817,521

1990    3,206,564

1995    4,921,005

2000    5,686,338

• Construct a scatter plot with this data. Do you observe a trend? If so, what type of trend do you observe?
• Use Excel to fit a linear trend and an exponential trend to the data. Display the models and their respective r^2.
• Interpret both models. Which model seems to be more appropriate? Why?

Answer 1

ANSWER::

Scatter plot:

Do you observe a trend?If so, what type of trend do you observe?

Yes there is a positive trend between the variables. It looks like a perfect positive linear relationship

Use Excel to fit a linear trend and an exponential trend to the data. Display the models and their respective r^2.

1. Bring data in to excel sheet

2.Select both x and y variable and insert scatter plot chart. Select any data point in the excel and add trend line. In the format trend line option choose "Linear" and also select "Display an equation on chart" and "Display R-squared value on the chart"

Linear model r^2 = 0.7202

Exponential Trend:

Exponentrial r^2 = 0.8913

Which model seems to be more appropriate? Why?

Exponential trend is more appropriate for the x and y variables ,because the r-squared value is higher than the linear trend

(OR) TRY THIS

scatteplot of data is,

from graph. there is increasing trend i.e. positive trend.

i)linear trend :

ii)exponential trend :

since R-square for exponential is greater than linear model. Exponential model is appropriate.

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