The data in Strategic represent the amount of oil, in billions of barrels, held in the U.S. strategic oil reserve, from 1981 through 2008.

Step 1: Copy the data and paste it into the Excel sheet.

Step 2: To create a scatter plot of the data, go to Insert -> Scatter -> Scatter with only markers. The scatter plot will instantly display on the screen.

Assign a variable t depicting the years. Calculate the values of t squared corresponding to the t series.

Considering oil reserves as y, compute log y. Go to Formulas -> Math and Trigo -> LOG10 In cell E2, enter the number as B2 under the LOG10 dialog box. Auto-fill this formula till cell E29.

Step 1: To calculate the linear trend, go to Data -> Data Analysis.

Select the tool of Regression from the Data Analysis dialog box.

Step 2: In the Regression dialog box, enter the following: Input y range: B1 to B29 Input x range: C1 to C29 Select the tick boxes: label, line fit plots.

Step 3: click on ok. The regression results are displayed:

Step 4: From the regression coefficients given in the summary output, we get the following linear forecasting equation:

Y= 396.19 + 11.03 x

The plot of the trend line is:

Step 1: To calculate the quadratic trend, go to Data -> Data Analysis.

Select the tool of Regression from the Data Analysis dialog box.

Step 2: In the Regression dialog box, enter the following:

Input y range: B1 to B29 Input x range: C1 to C29 Select the tick boxes: label, line fit plots.

Step 3: click on ok. The regression results are displayed:

Step 4: From the regression coefficients given in the summary output, we get the following

linear forecasting equation:

Y= 325.07 + 25.26 x -0.49 x2

The plot of the trend line is:

Step 1: To calculate the exponential trend, go to Data -> Data Analysis.

Select the tool of Regression from the Data Analysis dialog box.

Step 2: In the Regression dialog box, enter the following:

Input y range: E1 to C29

Input x range: C1 to C29

Select the tick boxes: label, line fit plots.

Step 3: click on ok. The regression results are displayed:

Step 4: compute the figure of 10^intercept.

The intercept comes out to be 388.59 Now, we get the following exponential forecasting equation: Y = 388.59*10^^{0.0098*t}Step 5: The plot of the trend line is:

The coefficients of determination for the three time series models we developed are:

Linear model_R^{2}= 68.24% Quadratic model_R^{2}= 75.25% Exponential_R^{2}= 55.7%

Since the coefficient of determination is the highest for the quadratic trend, therefore, the quadratic model seems the most appropriate

- To predict the oil reserves in the year 2009, we take x = 29 and use the equation from the quadratic trend model. Y= -0.4905(29)
^{2}+ 25.258(29) + 325.08 = 645.05 billions - As per the exponential trendline, Y = 388.59*10^
^{0.0098*t}, the prediction for oil reserves in the year 2009 (x = 29) will be 756.68 billions - As per the linear trendline, Y= 396.19 + 11.03 x, the prediction for oil reserves in the year 2009 (x = 29) will be 716.18 Billions
- Actual value of the number of barrels, in billions, in 2009 = 720.22
**Based on this analysis, linear trend model seems to be the model of best fit with predicted values being closest to the observed values.**

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