W3_Rotimi_Estimation of American University Fees Estimation in 13 Years Time.

 

1.    Problem Definition

 Determine the real cost of University Education in the U.S, 13 years from now (2025)

 

2.    Development of feasible alternatives

The alternatives that may be adopted to arrive at a realistic estimate of arriving at the cost of university education in 13 years’ time  are;

i)      Top-down approach

ii)     Bottom-up approach

iii)    Regression Analysis

 

3.    Development of the outcomes and cash flows for each alternative

a)      Top-down approach

In this approach, we use the historical cost  of a project and adjust for inflation, deflation, It assumed that University cost in the U.S increases by 6% per annum.

Using the top-down approach, the current cost of university education for our preferred university is $14,500 / Annum. Other associated cost is about $5,000.

Totalling $19,500.00

 

i.e  Yr 1: Future Cost⁽²⁰²⁵⁾  = 19,500 ( 1.06)¹³

                                          = 19,500 * 2.1329    = $41,592.10

                                      

Year 2                               = $41,592.10 * 1.06 =$ 44,087.63

Year 3                               = $44,087.63 *1.06 = $46,732.88

 

Year 4                               = $46,732.88*1.06    =$49,536.85

 

b)    Bottom-Up Approach

       The bottom-up requires that we breakdown anticipated expenses into typical categories. this approach is well suited for situations where details concrning the desired output are well defined and clear. this is not the case here. c  

c)     Regression Analysis

Dependent Variable: Year and control of institution

Independent Variable 1: All institutions total tuition, room and board rates charged for full-time undergraduate students in degree-granting institutions.

Independent Variable 2: Public institutions total tuition, room and board rates charged for full-time undergraduate students in degree-granting institutions

Independent Variable 3: Private not-for-profit and for-profit institutions total tuition, room and board rates charged for full-time undergraduate students in degree-granting institutions.

																																																													0.01*Indep1 + 0.00*Indep2 + 0.00*Indep3 +
Equation Parameters
R Squared	0.9941	99.41% of the change in Dependent can be explained by the change in the 3 Independent Variables
Adjusted R Squared	0.9918	Adjusted for Sample Size bias						1.27574	Durbin-Watson Statistic				Critical D-W Values: Lower (Dl)=0.82; Upper (Du)=1.75
Standard Error	0.4639	to +/- on result of Regression Equation							Therefore Positive Autocorrelation maybe present at 95% Confidence
F - Statistic	445.9801	Therefore analysis IS Significant						3.58743	Critical F-Statistic at 95% Confidence						(Significance holds to 99.9% Confidence)
Multiple Regression Equation					Independent Analysis			Auto Correlation	Tests for Multicollinearity between Independent Variables
	Coefficients	Standard Error	t Stat	p Value	R Squared	Gradient	Intercept	Dl=1.08 Du=1.36	Adjusted R-Squared against other Indep	Independent R-Square Matrix
Intercept	1,965.452	1.250	1,572.168	0.00%				DW-Stat
Indep1	0.006	0.001	6.457	0.02%	98.32%	0.00	1966.87	3.76	99.34%	100%	99%	83%																						1.08
Indep2	-0.004	0.001	-3.821	0.51%	96.12%	0.00	1968.87	3.22	99.26%	99%	100%	82%																						1.36
Indep3	0.000	0.000	-0.964	36.32%	81.80%	0.00	1964.95	2.99	80.75%	83%	82%	100%
Number of Periods to Forecast					10
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 Equation Parameters

This section display the R-squared for the multiple regression equation, show the equation’s standard error margin, and tests the analysis for statistical significance at a 95% confidence interval.

The adjusted R-squared is adjusted for by the sample size and is useful when either increasing or decreasing the number of independent variable in the analysis.

For example, when several redundant independent variables are added, the standard R-squared may increase marginally, however the adjusted R-squared reduces, indicating the weaker overall relationship.

99.41% of the change in Dependent can be explained by the change in the 3 Independent Variables.

Adjusted for Sample Size bias to +/- on result of Regression Equation                                  

Therefore analysis IS Significant                                                                                                                                      

The Durbin-Watson statistic

The Durbin-Watson statistic is employed to determine if sequential (adjacent) residuals are correlated. One of the assumptions of regression analysis is that the residuals (errors) are independent of each other. Sometimes, however, the data set may unknowingly contain an “order effect”, meaning that a previous measurement could influence the outcome of the successive observations.

If the residuals are not correlated, the Durbin-Watson statistic should be close to 2

Critical values displayed to the right of the statistic are based on the sample and number of independent variables. Based on the position of the Durbin-Watson statistic relative to these values, the following assumptions can be made.

0 to D1 – Positive Autocorrelation is detected

D1 to Du – Positive Autocorrelation is maybe present

Du to (4-Du) – There is No Autocorrelation

(4-Du) to (4-D1) - Negative Autocorrelation is maybe present

(4-D1) to 4 - Negative Autocorrelation is detected

 

Critical D-W Values: Lower (Dl) = 0.82; Upper (Du) = 1.75                                             

Therefore Positive Autocorrelation maybe present at 95% Confidence                                                                                                                                  

Multiple Regression Equation

This section summarises the individual equation coefficient components with corresponding error margins.

The sun of these error margins will differ to overall standard error of the equation due to the offsetting between the components.

The t stat represents a ratio of the estimated coefficient to its standard error. The t stat can be interpreted as a measure of predictability of variable with higher being better.

The p value represents the probability that the t stat can be outside of the extremities of the standard error. The p value can be interpreted as the probability that the error margin is due to chance rather than a real difference with lower being better.

Independent Analysis

This section displays a simple linear regression analysis of each of the independent variables against the dependent variable.

The independent R-squared results display her are useful for determining which independent variable should be included in the analysis. Low R-squared results should be excluded. (as a rule of thumb, below 50% indicates a weak relationship).

Dependent = 0.01*Indep1 + 0.00*Indep2 + 0.00Indep3 + 1965.45(+/-0.46)

Y = 0.9941x / 11.912

R² = 0.9941

 

Forecast Output

 

Sn	Indep1 ($)	Indep2 ($)	Indep3 ($)	Dependent
1	10620.00	7699.00	20894.00	1991-2000
2	13393.00	9390.00	26456.00	2000-2001
3	13842.00	9757.00	27261.00	2001-2002
4	14298.00	10118.00	22778.00	2002-2003
5	15086.00	10769.00	28679.00	2003-2004
6	15595.00	11153.00	29189.00	2004-2005
7	15939.00	11386.00	29307.00	2005-2006
8	16438.00	11731.00	30194.00	2006-2007
9	16617.00	11848.00	30475.00	2007-2008
10	17257.00	12375.00	31102.00	2008-2009
11	17649.00	12804.00	31023.00	2009-2010
12	18133.00	13297.00	31395.00	2010-2011
13	19061.20	13809.05	33380.53	2011-2012
14	19623.60	14237.01	34173.01	2012-2013
15	20186.00	14664.98	34965.49	2013-2014
16	20748.40	15092.95	35757.97	2014-2015
17	21310.81	15520.92	36550.45	2015-2016
18	21873.21	15948.89	37342.93	2016-2017
19	22435.61	16376.86	38135.40	2017-2018
20	22998.01	16804.83	38927.88	2018-2019
21	23560.41	17232.79	39720.36	2019-2020
22	24122.82	17660.76	40512.84	2020-2021
23	24685.22	18088.73	41305.32	2021-2022

 

 

 

 

 

 

 

 

 

 Number of Periods of Forecast = 10

 

4.         Selection of a Criteria

           The estimating criteria to be used to select the preferred method of estimating is based on the level of detail we can come up with, predicting the events that may occur regarding university education in the U.S 13 years from now.

5.         Analysis and comparison of alternatives

            The Top-down approach uses historical data from Universities on their tuition charges by modifying these data for changes in inflation. As we have used an inflation rate of 6% yearly, the acyual rates may be higher or lower than the 6% inflation rate figure.

            Regression on the other hand allows  us use

6.         Selection of preferred alternative

            The estimate produced from the regression analysis will be selected and used since it has established a relationship between the past and the future.

 

7.         Performance Monitoring and Post Evaluation Results

To monitor how well results from the regression analysis is accurate in estimating the cost of university education in the U.S in 13 years time, I will compare results from my yearly predictions against the actual cost of university education on a yearly basis.

 

References

Sullivan, W., Wicks, E., Koelling, P., Kumar, p., & Kumar, N. (2012). Engineering economy (15^th edition). England: Pearson Education Limited

U.S. Department of Education, National Center for Education Statistics. (2012). Digest of Education Statistics, 2011 (NCES 2012-001), Retrieved from http://nces.ed.gov/fastfacts/display.asp?id=76