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(solution) 1 Milestone Three The research for solving the question of which


The attached essay is the third milestone for my final project. I am looking for someone to revise it as my final project.  I need someone who understands R (Rattle) to tweak the decision tree using the attached .csv dataset and then revise the essay according to the instructions doc.


1

 

Milestone Three

 

The research for solving the question of which AP course a college bound student should

 

take math or science, analyzed the national numbers of exam participation for 11th and 12th grade

 

high school students. Because most high schools require four years of math and three years of

 

science with two years of lab, it was expected that AP math would have a higher number of

 

student exam participation. Moreover, it was expected that college bound high school students

 

would take an AP math exam before science because the top U.S. universities offering STEM

 

degrees require a minimum of four years advanced math as a prerequisite of admission.

 

Structure

 

Over the past 20 years, the percentage of high school students completing advanced

 

mathematics and science courses have substantially increased. The number of advanced math

 

courses such as Precalculus completed in high school rose from 13% in 1990 to 35% in 2009, and

 

the number of advanced science courses including Biology, Chemistry, and Physics rose from 19%

 

in 1990 to 30% in 2009 (Digest of Education Statistics, 2015, Table 225.40). NCES Digest of

 

Education Statistics (2015) reported more than 41,000 high schools including private in the

 

United States (Digest of Education Statistics, 2015, Table 214.10).

 

More and more high schools across the U.S. are utilizing the Advanced Placement (AP)

 

Program to advance curriculum with rigorous coursework emphasizing college preparation. For

 

the year 2015, The College Board reported that 21,953 U.S. high schools participate in the AP

 

program (The College Board, 2016). The Associated Press (2012) reported that 18 percent of

 

U.S. high school graduates passed at least one AP exam, up from 11 percent a decade ago.

 

The top-down decision tree depicted below was constructed using the R package Rattle.

 

It is a classification tree model specifically chosen for its algorithm that does the complex work on 2

 

its own requiring limited tweaking by the novice still learning the craft. The paragraphs following

 

Figure 1 Decision Tree AP Program Summary and Figure 2 Summary of the Decision Tree model

 

for Classification explain the structure of the tree presented in detail.

 

Figure 1: Decision Tree AP Program Summary

 

Summary of the Decision Tree model for Classification (built using 'rpart'): n= 72 node), split, n,

 

loss, yval, (yprob) * denotes terminal node

 

1) root 72 63 BIOLOGY (0.12 0.097 0.083 0.11 0.12 0.12 0.097 0.11 0.12)

 

2) X2015.Students.who.took.AP=118,707,152,745,22,789,302,532,52,678 36 28 CHEMISTRY (0

 

0.19 0.17 0.22 0 0 0.19 0.22 0)

 

3) X2015.Students.who.took.AP=171,074,195,526,20,533,223,479 36 27 BIOLOGY (0.25 0 0 0 0.25

 

0.25 0 0 0.25)

 

4) X2015.Students.who.took.AP=118,707,22,789,302,532 20 13 CALCULUS AB (0 0.35 0.3 0 0 0

 

0.35 0 0)

 

5) X2015.Students.who.took.AP=152,745,52,678 16 8 CHEMISTRY (0 0 0 0.5 0 0 0 0.5 0)

 

6) X2015.Students.who.took.AP=20,533,223,479 18 9 BIOLOGY (0.5 0 0 0 0 0.5 0 0 0)

 

7) X2015.Students.who.took.AP=171,074,195,526 18 9 PHYSICS 1 (0 0 0 0 0.5 0 0 0 0.5)

 

8) Mean.Score>=2.935 8 2 CALCULUS BC (0 0.12 0.75 0 0 0 0.12 0 0) *

 

9) Mean.Score< 2.935 12 6 CALCULUS AB (0 0.5 0 0 0 0 0.5 0 0) *

 

10) X2015.Students.who.took.AP=152,745 8 0 CHEMISTRY (0 0 0 1 0 0 0 0 0) *

 

11) X2015.Students.who.took.AP=52,678 8 0 PHYSICS C - MECH (0 0 0 0 0 0 0 1 0) *

 

12) X2015.Students.who.took.AP=223,479 9 0 BIOLOGY (1 0 0 0 0 0 0 0 0) *

 

13) X2015.Students.who.took.AP=20,533 9 0 PHYSICS 2 (0 0 0 0 0 1 0 0 0) *

 

14) X2015.Students.who.took.AP=171,074 9 0 PHYSICS 1 (0 0 0 0 1 0 0 0 0) *

 

15) X2015.Students.who.took.AP=195,526 9 0 STATISTICS (0 0 0 0 0 0 0 0 1) *

 

Classification tree:

 

rpart(formula = AP.Math...Science.Courses ~ ., data = crs$dataset[crs$train, c(crs$input,

 

crs$target)], method = "class", parms = list(split = "information"), control = rpart.control(minsplit

 

= 8, minbucket = 8, usesurrogate = 0, maxsurrogate = 0))

 

Variables actually used in tree construction:

 

[1] Mean.Score X2015.Students.who.took.AP Root node error: 63/72 = 0.875 n= 72 CP nsplit rel error xerror xstd 1 0.138889

 

2 0.119048 0 1.00000 1.14286 0.000000

 

4 0.44444 0.82540 0.060327 3 0.079365

 

4 0.010000 6 0.20635 0.63492 0.066927

 

7 0.12698 0.42857 0.065205 Time taken: 0.09 secs Rattle timestamp: 2016-09-24 13:43:27 KEPAS Figure 2 Summary of the Decision Tree model for Classification 3

 

The model that has been built is a fairly large decision tree with seven nodes and eight leaf

 

nodes.The first node of the tree is Biology. The information provided tells us that the majority

 

class for the root node (the yval) is No. The 63 tells us how many of the 72 observations will be

 

incorrectly classifed as Yes, this is also known as the loss. 88% of the observations have the target

 

variable AP math and science courses as Yes and 12% of the observations have it as No. The

 

algorithm has chosen 2015 Students who took AP for the next split with a split value of 50/50 for

 

Chemistry and Biology. Node 2 uses the same variable 2015 Students who took AP to branch and

 

split nodes 4 and 5 that shows 28% took Calculus AB and 22% Chemistry.

 

The right side, Node 3 branches and splits to leaf nodes 6 and 7 showing 25% took

 

Biology and 25% took Physics I. The algorithm then chooses the mean score to split on Calculus

 

AB to leaf nodes 8 and 9 showing with 11% on Calculus BC and 17% Calculus AB. Node 5

 

Chemistry splits leaf nodes 10 Chemistry and 11 Physics C Mechanics 11/11. Node 6 Biology

 

splits leaf nodes 12 Biology and 13 Physics II 12%/12%. Finally, Node 7 splits leaf nodes14

 

Physics I and 16 Statistics 12%/12%.

 

What this means is that Biology was taken more than Chemistry, Physics I, Physics II and

 

Physics Mech. Biology was taken more than math. Calculus AB was taken more than Calculus BC

 

and Statistics. Based on the projections of this model, a college bound high school student given

 

the choice between taking an AP math or science course, would take a science course.

 

Process Documentation. The data set for this research, National Report was taken from the

 

College Board?s AP Program Participation and Performance Data 2015. The National Report is an

 

excel document with several worksheets comprising the following raw data (The College Board, 2016).

 

1. Number of AP exams taken by high school students listed by subject 4

 

2. Number of exams by subject for all participating high schools

 

3. Number of exams by subject accepted by colleges

 

4. Number of exam takers broken down with AP scores and mean by high school

 

grade, gender, race/ethnicity

 

The original data presented 36 subjects with all of the above breakdowns. The data chosen

 

by the algorithms on 36 subjects made it impossible to get useful results for making the research

 

decision. The data set was narrowed down to only the math and science subjects and data.

 

Another problem was the gender and race/ethnicity which made analysis difficult when the

 

algorithms chose to split on one of these variables. Those variables were not removed from the

 

dataset. Finally after modifying the partition default from 70/15/15 to 80/10/10 the algorithm

 

chose the ?number of students completing exams? variable to split on the AP subjects. The data

 

set was also saved from an Excel file to a comma-delimited.

 

Figure 3: The College Board?s National

 

Summary 5

 

Evaluation of Results. Although this analysis examined the data that included a wealth of

 

detailed information on the number of students that took AP math and science courses, we did not

 

have information on the number of high school students enrolled in STEM degree college

 

programs. Additionally, while the top 50 U.S. universities who offer STEM degrees were included

 

in the colleges accepting exams they were not identified separately in the data set and specific

 

prerequisite requirements were not obtained. Such information would have allowed more analysis

 

of whether college bound students interested in pursuing STEM degrees should take an AP math

 

or science exam. 6

 

References

 

The Associated Press. (2012, May 5). More students taking Advanced Placement classes, but test

 

pass rate remains about the same. Retrieved from

 

http://www.nj.com/news/index.ssf/2012/05/report_more_students_taking_ad.html

 

The College Board. (2016). AP Program Participation and Performance Data 2015 ? Research ?

 

The College Board. Retrieved from

 

https://research.collegeboard.org/programs/ap/data/archived/ap-2015

 

The College Board. (2016). Number of schools offering AP exams (Rep.). Retrieved

 

https://research.collegeboard.org/programs/ap/data/participation/ap-2016

 

U.S. Department of Education, National Center for Education Statistics. (2012, September).

 

Percentage of public and private high school graduates taking selected mathematics and

 

science courses in high school, by selected student and school characteristics: Selected

 

years, 1990 through 2009. Retrieved from

 

https://nces.ed.gov/programs/digest/d15/tables/dt15_225.40.asp

 

U.S. Department of Education, National Center for Education Statistics. (2015). Advanced

 

mathematics and science courses. Retrieved from https://nces.ed.gov/fastfacts

 

U.S. Department of Education, National Center for Education Statistics. (2016, January).

 

Number of public school districts and public and private elementary and secondary

 

schools: Selected years, 1869-70 through 2013-14. Retrieved from

 

https://nces.ed.gov/programs/digest/index.asp

 

Williams, G. J. (2013). Data mining with Rattle and R: The art of excavating data for knowledge

 

discovery. New York: Springer.

 


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