Linear Model Project: Analyzing College Education Costs (2004-2014)

This project delves into the analysis of college education costs in non-profit private institutions from 2004 to 2014, focusing on undergraduate tuition, fees, room, and board. The study examines both 4-year and 2-year institutions, utilizing data from the National Centre for Education Statistics (NCES). The project employs a linear model to investigate the relationship between costs in the two types of institutions. The analysis includes calculating the slope, correlation coefficient, and coefficient of determination to assess the strength and accuracy of the linear fit. A strong positive correlation (0.90) is observed, indicating that as costs rise in 4-year institutions, they also rise in 2-year institutions. The coefficient of determination (0.8083) suggests a moderately strong fit, crucial for making predictions. The project concludes by making predictions based on the derived linear equation and discussing the implications of the findings, highlighting the impact of inflation across all institutions. The analysis demonstrates a clear linear relationship between the costs of education, offering insights into trends and potential future costs.

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Curve-fitting Project - Linear Model
Student’s Name
Institutional Affiliation
Date

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LR1, LR2, LR3
This project investigates the trends in the cost of college education in non-profit private
institutions from the year 2004 to 2014. In particular, it investigates the annual prices for
undergraduate tuition, fees, room and board in dollars. Two types of institutions are
investigated in this case. These are 4-year and 2-year non-profit private institutions. The data
used in this analysis was obtained from the National Centre for Education Statistics (NCES).
Part of the data obtained from https://nces.ed.gov/fastfacts/display.asp?id=76 is given in the
table below.
Table 1: Average undergraduate tuition, fees, and room and board rates charged for full-
time students in degree-granting postsecondary institutions, by level and control of
institution for the years 2004-2014
4-year institutions 2-year
institutions
34500.90301 20135.08682
34988.32242 19912.01043
36041.23429 21017.0364
36736.21663 21614.15722
38213.06879 22914.7712
39233.26573 23238.07718
39968.63981 22051.59687
40344.11377 24446.34249
41219.4013 23229.66075
42063.92692 23753.9678

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34000 35000 36000 37000 38000 39000 40000 41000 42000 43000
0
5000
10000
15000
20000
25000
30000
f(x) = 0.521607644457301 x + 2237.57542306747
R² = 0.808327449944841
The cost of education in 2-year and 4-year
institutions
4-year institutions
2-year institutions
Figure 1: Relationship between average undergraduate tuition, fees, and room and board
rates for 4- and 2-year institutions
From figure 1 above, the equation of the line is given as,
y=0.5216 x +2237.6
Where,
slope=0.5216
y−intercept =2237.6
LR-4
The slope of the graph represents the rate of increase of average undergraduate tuition, fees,
and room and board rates. A steeper slope would indicate a higher rate of increase while a
shallower slope would indicate a lower rate.
LR-5
The value of the coefficient of determination ( R2 ¿ from figure 1 is,
R2=0.8 083

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The table below shows the correlation between the two variables,
Figure 2: Correlation coefficient
4-year
institutions
2-year
institutions
4-year
institutions
1 0.899070325
2-year
institutions
0.899070325 1
From the table above, the correlation coefficient is,
r =0. 9 0
The correlation coefficient has a positive value which indicates that as one variable increases,
the other variable increases too. A straight line is a good curve to fit this data as indicated by
the very high correlation coefficient. The value of the coefficient of determination is 0.8083
which also moderately strong.
LR-6
Making a prediction
To make a prediction, we choose a data value on the x-axis and plug it in the straight line
equation obtained in LR-3 to solve for the corresponding value on the y-axis.
y=0.5216 x +2237.6

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let x=43 000
y= ( 0.5216 × 43 000 ) +2237.6
y=24666.4
The coordinates of the new data point become,
43000 , 24666.4
LR-7
Analysis of the education statistics data has revealed that there exists a linear relationship
between the average cost of education between 4-year and 2-year institutions for non-profit
private institutions. The correlation between the two variables is very strong with a
correlation coefficient of 0.90. This can be interpreted to mean that as the cost of education
rises in 4-year institutions, it also rises in 2-year institutions. This is expected since inflation
affects all institutions regardless of the course durations. The coefficient of determination
was moderately strong with a value of about 0.8083. This coefficient is important as it
determines how accurately the model fits the data. It is especially important in prediction of
future values. The higher the value of R2, the higher the accuracy of the model. This means
that predicted values will be very close to the actual values.

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References
Fast Facts: Tuition costs of colleges and universities (76). (n.d.). Retrieved from
https://nces.ed.gov/fastfacts/display.asp?id=76