   Chapter 2.3, Problem 20TE

Chapter
Section
Textbook Problem

Social Security Trust Fund Assets The projected assets of the Social Security trust fund (in trillions of dollars) from 2010 through 2033 are given in the following table: Year 2010 2015 2020 2025 2030 2033 Assets 2.61 2.68 2.44 1.87 0.78 0 Use QuartReg to find a fourth-degree polynomial regression model for the data. Let t = 0 correspond to 2010.Source: Social Security Administration

To determine

To find: The fourth degree polynomial regression model with the use of Quart Reg.

Explanation

Given Information:

The projected assets of the social security trust fund (in trillions of dollars) from 2010 to 2033 is given as,

 Year 2010 2015 2020 2025 2030 2033 Assets 2.61 2.68 2.44 1.87 0.78 0

Calculation:

Let (t=0) for the beginning of the year 2010, use (t=5) for the beginning of the year 2015, (t=10) for the beginning of the year 2020, (t=15) for the beginning of the year 2025 and so on.

Form a new table of assets and time (t) for the corresponding year.

 time 0 1 2 3 4 5 6 debt 8.17 8.68 9.229 10.7 12.311 14.02 15.223

To find the fourth degree regression, follow the steps below.

First press “ON” button on graphical calculator and press STAT key to enter the data and then press 1 to edit the data.

Input all the data from the first row of the above table in line 1 followed by ENTER keystrokes and press key to enter the data of the second row in the line 2.

Figure 1

The screen of the calculator after the above steps looks like Figure 1.

Now, press 2nd + 0 key to enter the CATALOG Menu and scroll down to select the diagnostic ON command stored in the CATALOG menu and press ENTER the display look like the figure below,

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