Education Expenditure The following chart shows the percentage of the U.S. discretionary budget allocated to education from 2003 to 2009 (t = 3 represents the start of 2003).Percentage of U.S. budget on education7.07.06.96.86.56.36.245678Year since 2000The following table shows the percentage of the U.S. discretionary budget allocated to education in 2003, 2005, and 2009 (t = 3 represents the start of 2003).†Year t39.Percentage6.876.2Find a quadratic model for these three years. (Round your coefficients to two decimal places.)p(t) =Use your model to estimate the percentage of the U.S. discretionary budget allocated to education in 2007. (Round your answer to two decimal places.)%Compare your answer with the actual figure shown in the chart.The actual percentage was%, which [---Select--- V] in close agreement with the predicted figure.Need Help?Watch ItRead ItPercentage

Answered: Education Expenditure The following…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Education Expenditure The following chart shows the percentage of the U.S. discretionary budget allocated to education from 2003 to 2009 (t = 3 represents the start of 2003).
Percentage of U.S. budget on education
7.0
7.0
6.9
6.8
6.5
6.3
6.2
4
5
6
7
8
Year since 2000
The following table shows the percentage of the U.S. discretionary budget allocated to education in 2003, 2005, and 2009 (t = 3 represents the start of 2003).†
Year t
3
9.
Percentage
6.8
7
6.2
Find a quadratic model for these three years. (Round your coefficients to two decimal places.)
p(t) =
Use your model to estimate the percentage of the U.S. discretionary budget allocated to education in 2007. (Round your answer to two decimal places.)
%
Compare your answer with the actual figure shown in the chart.
The actual percentage was
%, which [---Select--- V] in close agreement with the predicted figure.
Need Help?
Watch It
Read It
Percentage

Expert Solution

Step 1

The quadratic regression is given by $p (t) = A t^{2} + B t + C$

The coefficients A, B, and C are given by

$A = \frac{S_{t^{2} p} S_{t t} - S_{t p} S_{t t^{2}}}{S_{t t} S_{t^{2} t^{2}} - {(S_{t t^{2}})}^{2}}$

$B = \frac{S_{t p} S_{t^{2} t^{2}} - S_{t^{2} p} S_{t t^{2}}}{S_{t t} S_{t^{2} t^{2}} - {(S_{t t^{2}})}^{2}}$

$C = p - B t - A t^{2}$

where

$S_{t t} = \sum {(t_{i} - t)}^{2} = \sum {t_{i}}^{2} - n . t^{2} S_{t p} = \sum (t_{i} - t) (p_{i} - p) = \sum t_{i} p_{i} - n . t p S_{t t^{2}} = \sum (t_{i} - t) ({t_{i}}^{2} - t^{2}) = \sum {t_{i}}^{3} - n . t t^{2} S_{t^{2} t^{2}} = \sum {({t_{i}}^{2} - t^{2})}^{2} = \sum {t_{i}}^{4} - n . t^{2} t^{2} S_{t^{2} p} = \sum ({t_{i}}^{2} - t^{2}) (p_{i} - p) = \sum {t_{i}}^{2} p_{i} - n . t^{2} p$

The correlation coefficient is

$r = \sqrt{1 - \frac{\sum {(p_{i} - (A + B t_{i} + C {t_{i}}^{2}))}^{2}}{\sum {(p_{i} - p)}^{2}}}$

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