all the information is attached below plus a sample project. follow it completely!!!! use this website to collect data : https://www.indexmundi.com/facts/united-states/quick-facts
Top 20 Private Colleges’ 6-Year Graduation Rate
Spring 2015
Note: Your project should have more creative background.
Original Data Table
http://mathforum.org/workshops/sum96/data.collections/datalibrary/data.set6.html
New Data Table
| 6-year Grad. Rate | State | Student/faculty Ratio | Aid From Grants | West | South East | Undergrad. Enrollment | Republican State | Football team | 4-year Grad. Rate | Total Costs | |
| California Institute of Technology | 0.85 | CA | 3 | 0.93 | 1 | 0 | 939 | 0 | 0 | 0.71 | 32682 |
| Rice University | 0.89 | TX | 5 | 0.88 | 1 | 0 | 2787 | 1 | 1 | 0.68 | 28350 |
| Williams College | 0.94 | MA | 8 | 0.89 | 0 | 0 | 1985 | 0 | 1 | 0.89 | 36550 |
| Swarthmore College | 0.92 | PA | 8 | 0.85 | 0 | 0 | 1479 | 1 | 0 | 0.86 | 38676 |
| Amherst College | 0.94 | MA | 9 | 0.92 | 0 | 0 | 1618 | 0 | 1 | 0.84 | 38492 |
| Webb Institute | 0.83 | NY | 7 | 1 | 0 | 0 | 67 | 1 | 1 | 0.79 | 8079 |
| Yale University | 0.95 | CT | 7 | 0.89 | 0 | 0 | 5339 | 0 | 1 | 0.88 | 38432 |
| Washington and Lee University | 0.89 | VA | 11 | 0.87 | 0 | 1 | 1750 | 1 | 1 | 0.86 | 30225 |
| Harvard University | 0.97 | MA | 8 | 0.9 | 0 | 0 | 6637 | 0 | 1 | 0.86 | 38831 |
| Stanford University | 0.93 | CA | 7 | 0.86 | 1 | 0 | 7360 | 0 | 1 | 0.77 | 38875 |
| Princeton University | 0.97 | NJ | 5 | 0.94 | 0 | 0 | 4779 | 0 | 1 | 0.91 | 40169 |
| Massachusetts Institute of Technology | 0.91 | MA | 6 | 0.85 | 0 | 0 | 4178 | 0 | 1 | 0.82 | 39213 |
| Pomona College | 0.88 | CA | 9 | 0.8 | 1 | 0 | 1551 | 0 | 1 | 0.83 | 38130 |
| Emory University | 0.87 | GA | 7 | 0.73 | 0 | 1 | 6302 | 1 | 0 | 0.82 | 37272 |
| Columbia University | 0.93 | NY | 7 | 0.86 | 0 | 0 | 4109 | 1 | 1 | 0.83 | 39493 |
| Duke University | 0.93 | NC | 11 | 0.8 | 0 | 1 | 6206 | 1 | 1 | 0.88 | 40080 |
| Davidson College | 0.91 | NC | 10 | 0.82 | 0 | 1 | 1645 | 1 | 1 | 0.89 | 34706 |
| Wellesley College | 0.88 | MA | 9 | 0.88 | 0 | 0 | 2300 | 0 | 0 | 0.84 | 37419 |
| Vassar College | 0.87 | NY | 9 | 0.78 | 0 | 0 | 2472 | 1 | 0 | 0.81 | 37870 |
| Haverford College | 0.92 | PA | 8 | 0.9 | 0 | 0 | 1105 | 1 | 0 | 0.89 | 38928 |
Dependent variable
Independent variables
Independent
Binary
Independent
Categorical
Categorical Variables
Binary variables included: if the State
was majority Republican and if the school
had a football team. “0” or “1” representing
“no” or ”yes”.
Categorical variables include West, South West and North West. North East will become my reference level.
| West | South East |
| 1 | 0 |
| 1 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 1 |
| 0 | 0 |
| 1 | 0 |
| 0 | 0 |
| 0 | 0 |
| 1 | 0 |
| 0 | 1 |
| 0 | 0 |
| 0 | 1 |
| 0 | 1 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
Reference level
The reference level selected was North East due to the fact the North East region had the highest number of schools out of the top 20.
| West | South East |
| 1 | 0 |
| 1 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
| 0 | 1 |
| 0 | 0 |
| 1 | 0 |
| 0 | 0 |
| 0 | 0 |
| 1 | 0 |
| 0 | 1 |
| 0 | 0 |
| 0 | 1 |
| 0 | 1 |
| 0 | 0 |
| 0 | 0 |
| 0 | 0 |
Depending on how you define regions in
the U.S. calculations on specific school
regions my differ. I kept it simple and only used key
regions relating to my data. Calculating all the regions
may cause the data to produce an error.
Removing 2 Variables due to Multicollinearty
I removed “Aid from Grants” because we already have “Total Cost”. The amount of student aid paying for school doesn’t really pertain when the table already gives the total cost of a 6-year graduation rate.
I removed “4-year Grad. Rate” because this model gave us both 4-year and 6-year rates. Since we are looking for a 6-year rate of graduation, they have already passed their 4-year
6
Keeping my variables
I left the States variable because its easier to read the model. Also it helps relate my regions.
Student/faculty ratio was saved because it deals with real numbers relating to how many students are on campus vs. how many faculty members. In my opinion this is interesting and important.
Undergraduate enrollment was left because it represents real data of how many students are in the undergraduate enrollment. Also I'm an undergraduate, so I can relate more to this data.
Total cost was left because I believe this variable is what majority of students look at when choosing a college.
| State |
| CA |
| TX |
| MA |
| PA |
| MA |
| NY |
| CT |
| VA |
| MA |
| CA |
| NJ |
| MA |
| CA |
| GA |
| NY |
| NC |
| NC |
| MA |
| NY |
| PA |
| Student/faculty Ratio |
| 3 |
| 5 |
| 8 |
| 8 |
| 9 |
| 7 |
| 7 |
| 11 |
| 8 |
| 7 |
| 5 |
| 6 |
| 9 |
| 7 |
| 7 |
| 11 |
| 10 |
| 9 |
| 9 |
| 8 |
| Undergrad. Enrollment |
| 939 |
| 2787 |
| 1985 |
| 1479 |
| 1618 |
| 67 |
| 5339 |
| 1750 |
| 6637 |
| 7360 |
| 4779 |
| 4178 |
| 1551 |
| 6302 |
| 4109 |
| 6206 |
| 1645 |
| 2300 |
| 2472 |
| 1105 |
| Total Costs |
| 32682 |
| 28350 |
| 36550 |
| 38676 |
| 38492 |
| 8079 |
| 38432 |
| 30225 |
| 38831 |
| 38875 |
| 40169 |
| 39213 |
| 38130 |
| 37272 |
| 39493 |
| 40080 |
| 34706 |
| 37419 |
| 37870 |
| 38928 |
Lets Run It!
Alpha= 0.05
P-Value of Model=
0.0016
R= .8985
Adjusted R squared=
.6949
Adjusted R squared is used instead of R Square because dealing with multiple regression, multiple variables calculated together will cause inflation in the model.
69% of the variance can be explained by the model.
What is significant?
Alpha = 0.05
West has a p-value of 0.0318
Total Costs has a P-value of 0.0026
Football team
has a p-value of 0.0039
Outliers
The model did not have any outliers ( absence of outliers). All variables had a reasonable p-value
The highest variable p-value was the “Republican State”, at .7026 this is not enough to consider this variable an outlier.
If all the original variables were still included in my model, then the number of outliers would have increased, but since I shorted the list to only specific variables I thought pertained to this model, I must of pulled out all possible outliers.
New model with only significant variables
| 6-year Grad. Rate | State | West | Total Costs | Football team | |
| California Institute of Technology | 0.85 | CA | 1 | 32682 | 0 |
| Rice University | 0.89 | TX | 1 | 28350 | 1 |
| Williams College | 0.94 | MA | 0 | 36550 | 1 |
| Swarthmore College | 0.92 | PA | 0 | 38676 | 0 |
| Amherst College | 0.94 | MA | 0 | 38492 | 1 |
| Webb Institute | 0.83 | NY | 0 | 8079 | 1 |
| Yale University | 0.95 | CT | 0 | 38432 | 1 |
| Washington and Lee University | 0.89 | VA | 0 | 30225 | 1 |
| Harvard University | 0.97 | MA | 0 | 38831 | 1 |
| Stanford University | 0.93 | CA | 1 | 38875 | 1 |
| Princeton University | 0.97 | NJ | 0 | 40169 | 1 |
| Massachusetts Institute of Technology | 0.91 | MA | 0 | 39213 | 1 |
| Pomona College | 0.88 | CA | 1 | 38130 | 1 |
| Emory University | 0.87 | GA | 0 | 37272 | 0 |
| Columbia University | 0.93 | NY | 0 | 39493 | 1 |
| Duke University | 0.93 | NC | 0 | 40080 | 1 |
| Davidson College | 0.91 | NC | 0 | 34706 | 1 |
| Wellesley College | 0.88 | MA | 0 | 37419 | 0 |
| Vassar College | 0.87 | NY | 0 | 37870 | 0 |
| Haverford College | 0.92 | PA | 0 | 38928 | 0 |
| binary varibales | |||||
| categorical with 3 levels | |||||
| independent variables | |||||
| dependent variable | |||||
I left the “States” variable because it
makes it easier to read the model and
there is no numerical value.
| South East |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 1 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 1 |
| 0 |
| 1 |
| 1 |
| 0 |
| 0 |
| 0 |
| Republican State |
| 0 |
| 1 |
| 0 |
| 1 |
| 0 |
| 1 |
| 0 |
| 1 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 1 |
| 1 |
| 1 |
| 1 |
| 0 |
| 1 |
| 1 |
| Undergrad. Enrollment |
| 939 |
| 2787 |
| 1985 |
| 1479 |
| 1618 |
| 67 |
| 5339 |
| 1750 |
| 6637 |
| 7360 |
| 4779 |
| 4178 |
| 1551 |
| 6302 |
| 4109 |
| 6206 |
| 1645 |
| 2300 |
| 2472 |
| 1105 |
| Student/faculty Ratio |
| 3 |
| 5 |
| 8 |
| 8 |
| 9 |
| 7 |
| 7 |
| 11 |
| 8 |
| 7 |
| 5 |
| 6 |
| 9 |
| 7 |
| 7 |
| 11 |
| 10 |
| 9 |
| 9 |
| 8 |
Non-significant variables that were removed.
New model
Now lets run the model with significant levels only
Alpha= 0.05
R= .8590
Adjusted R squared= .6887
69% of the variance is explained
with this model
P-value= 0 or 6.5118E-05
Looks like “Total Cost” carries the best significant level (0) according to this model.
Having a football team carries a p-value of 0.0008
Results of new model using only significant variables.
Using only significant variables changed how significant each variable was.
At first, “West” had a p-value of 0.03179 and now it carries a p-value of 0.0575. Not that much of a change but still a change.
“Total Cost” started at a p-value of 0.0026 and now it carries a p-value of a value so small we consider it 0. Making “total Cost” the most significant variable
Having a football team originally had a p-value of 0.0039 and now carries a p-value of 0.0008.
Adjusted R squared = .6887 this number actually decreased form original Adjusted R squared which was 0.6949. Not too far off from the original, telling us that 68.8 or 69% of the variance can be explained by this model.
Coefficients of new model
For every change in the X variable (independent variables), the Y variable (independent variable) will change as well.
For total cost, the coefficient is 0.00000364. Since total coast is calculated in $1000s, lets multiply the coefficient by 1000 and you get a coefficient of 0.00364
It does look like having a football team will increase a 6-year graduation rate by 4.3 %.
Total cost will increase the 6-year graduation rate by.36%
3 Predictions
My original data was out of 100 top private schools. For the purpose of this model I only used the top 20. I will be using the next three schools from my original table to make predictions.
Predictions will be based on my final table using only my significant variables
Schools chosen: Northwestern University, Bowdoin College and University of Pennsylvania
3 Predictions
Northwestern University
Has a football team which gives a value of “1” for “yes”
Lets call this region West which gives a value of “1” for “Yes”
Has a total cost of $38,817
Calculating my predictions I took the total cost and multiplied it by the coefficient of the total cost.
38,817 x .000003643 = .141 or 14%
According to the original data the actual % was 92%, indicating something is wrong with my variable units. Or this model is bogus, but I would conclude that using data that carries several different units such as % vs. $ amounts. Some conversions may have to be re converted so all variables could be represented by the same units.
The residual for this prediction was -78%
3 Predictions
Bowdoin College
Has a football team so they get a 1
Region located is North East which is my reference level so they get a 0
Has a total cost of $38,663
Calculations
$38,663 x 0.000003643 = .1408 or 14%
Again my predictions are way off this has a residual of -76%
Original data indicated a 90%
3 Predictions Prof. Decker Note: There are some issues with these predictions. This project was used as an example because the previous slides do such a good job clearly explaining variables and the process of the project.
University of Pennsylvania
Has a football team so they get a 1
Located in the North East region so they get a 0
Total cost is $39,040
Calculating predictions:
39,040 x .000003643 = .142 or 14%
After looking at my predictions and the actual values I would conclude some or all of my variables need to be converted into the same unit of measurement. I would have to say some of the values that were given m