Nieklasyczne metody statystyki
Regularyzacja
Krzysztof Kowalski, Maciej Fleks
2024-12-22
To laboratorium na temat Regresji grzbietowej (Ridge Regression - RR)
i Lasso w R pochodzi ze stron 251-255 książki “Introduction to
Statistical Learning with Applications in R” autorstwa Garetha Jamesa,
Danieli Witten, Trevora Hastie i Roberta Tibshirani. Zostało ono
ponownie zaimplementowane jesienią 2016 roku w formacie
tidyverse przez Amelię McNamarę i R. Jordana Crousera w
Smith College.
W tym tygodniu omówimy dwie alternatywne formy regresji liniowej zwane regresją grzbietową i regresją LASSO. Te dwie metody są przykładami metod regularyzacji lub zmniejszania, w których zachęca się do tego, aby parametry modelu były małe.
Regresja Grzbietowa i Lasso
Wykorzystamy pakiet glmnet w celu przeprowadzenia
regresji ridge i lasso. Główną funkcją w tym pakiecie jest
glmnet(), która może być użyta do dopasowania modeli
regresji grzbietowej, modeli lasso i innych.
Funkcja ta ma nieco inną składnię niż inne funkcje dopasowujące modele, z którymi zetknęliśmy się do tej pory. W szczególności, musimy przekazać macierz \(x\) jak również wektor \(y\) i nie używamy składni \(y \sim x\).
Zanim przejdziemy dalej, upewnijmy się najpierw, że brakujące wartości zostały zostały usunięte z danych, jak opisano w poprzednim laboratorium.
Hitters = na.omit(Hitters)W raporcie tym przeprowadzimy regresję grzbietową i lasso, aby
przewidzieć Salary na danych Hitters.
Skonfigurujmy nasze dane:
x = model.matrix(Salary~., Hitters)[,-1] # przycinam pierwszą kolumnę
# zostawiam predyktory
y = Hitters %>%
select(Salary) %>%
unlist() %>%
as.numeric()Funkcja model.matrix() jest szczególnie przydatna do
tworzenia \(x\); nie tylko nie tylko
tworzy macierz odpowiadającą 19 predyktorom, ale również automatycznie
przekształca wszelkie zmienne jakościowe w zmienne dummy.
Ta ostatnia właściwość jest ważna, ponieważ glmnet()
może przyjmować tylko numeryczne, ilościowe dane wejściowe.
Bias vs Variance
Wybór modelu w problemach uczenia nadzorowanego wiąże się z realizacją dwóch sprzecznych celów:
1.) Model powienien być dobrze dopasowany do danych uczących, aby uchwycić zależność pomiędzy danymi.
2.) Model powinien dobrze przybliżać nieznane dane (zapewniać mały błąd generalizacji).
Modele złożone dobdrze dopasowują się do danych wyjściowych, ale charakteryzują się dużą zmiennością wartości wyjściowych. Ryzykiem jest nadmierne dopasowanie = overfitting!
Modele prostsze są obciążone dużym błędem systematyczny (bias) i ich zastosowanie niesie ryzyko niewystarczającego dopasowania (underfitting)!
Składnikiem błędów generalizacji jest nieredukowalny błąd związany ze zmiennością danych.
Regularyzacja
Duża liczna zmiennych objaśniających (predyktorów): Metoda OLS nie daje jednoznacznego rozwiązania, gdy macierz XTX nie jest odwracalna (tzn. gdy zmienne objaśniające są liniowo zależne).
Taka sytuacja może mieć miejsce gdy zmiennych objaśniających jest tyle samo lub więcej niż obserwacji.
Duża wartość θi oznacza dużą wrażliwość funkcji regresji na drobne fluktuacje cechy!
Lepszym rozwiązaniem jest gorsze dopasowanie do danych uczących przy równoczesnym ograniczeniu parametrów świadczących o potencjalnie dużym błędzie generalizacji.
Regresja Grzbietowa
Wprowadzenie
Regresja grzbietowa (ang. Ridge regression) to technika regresji liniowej, która wprowadza regularyzację \(L_2\) do estymacji współczynników modelu. Regularyzacja \(L_2\) polega na dodaniu do funkcji celu kary proporcjonalnej do kwadratu wartości współczynników regresji.
Podstawową ideą regresji grzbietowej jest minimalizacja funkcji celu, która składa się z dwóch składników: błędu dopasowania (sumy kwadratów różnic pomiędzy rzeczywistymi wartościami odpowiedzi a przewidywanymi wartościami modelu) i kary regularyzacyjnej \(L_2\).
Wzór funkcji celu dla regresji grzbietowej można przedstawić jako: Minimize: RSS + \(\lambda \|\beta\|_2^2\), gdzie:
RSS to suma kwadratów różnic pomiędzy rzeczywistymi wartościami odpowiedzi a przewidywanymi wartościami modelu (błąd dopasowania),
\(\lambda\) (lambda) to parametr regularyzacji, który kontroluje siłę regularyzacji,
\(\|\beta\|_2^2\) to norma \(L_2\) współczynników regresji podniesiona do kwadratu.
Dodanie kary regularyzacyjnej \(L_2\) powoduje, że współczynniki regresji są skupione wokół zera, ale nie dokładnie równe zeru (chyba że \(\lambda\)=0).
Regresja grzbietowa zmniejsza wartości współczynników, ale nie powoduje, że stają się one równe zero. Im większa wartość \(\lambda\), tym bardziej są “sciskane” współczynniki regresji.
Regresja grzbietowa jest szczególnie przydatna, gdy mamy do czynienia z modelem, w którym występuje nadmierna wielowymiarowość lub wysokie korelacje między zmiennymi niezależnymi.
Poprzez zmniejszanie wartości współczynników, regresja grzbietowa może pomóc w redukcji wpływu mało istotnych cech, poprawić stabilność modelu i zmniejszyć ryzyko przeuczenia (overfitting).
Jednym ze sposobów kontroli złożoności modelu jest penalizacja jego wielkości. Na przykład, w problemie regresji liniowej:
\[ \min_{\beta \in \mathbb{R}^p} \sum_{i=1}^n (y_i - x_i^\top \beta)^2, \]
możemy kontrolować wielkość współczynników \(\beta\). Oczywiście wielkość \(\beta\) można zdefiniować na różne sposoby, np. norma-2: \(\|\beta\|_2\), norma-1: \(\|\beta\|_1\) czy norma-nieskończoność: \(\|\beta\|_{\infty}\). Regresja grzbietowa wiąże się z karą dwóch norm:
\[ \min_{\beta \in \mathbb{R}^p} \sum_{i=1}^n (y_i - x_i^\top \beta)^2 + \lambda \|\beta\|_2^2 \]
gdzie \(\lambda\) jest parametrem kontrolującym poziom regularyzacji. Zauważ, że \(X\) to macierz \(n\) na \(p\) wymiarów z wierszami: \(x_i^\top\), oraz \(Y\) to \(n\) na 1 wektor \(y_i\). Załóżmy, że \(X^\top X + \lambda I\) jest odwracalna, mamy dokładne rozwiązanie problemu regresji grzbietowej:
\[ \hat \beta_{ridge} = (X^\top X + \lambda I)^{-1}X^\top Y. \]
Przypomnijmy, że rozwiązaniem zwykłej regresji najmniejszych kwadratów jest (zakładając odwracalność macierzy \(X^\top X\)):
\[ \hat \beta_{ols} = (X^\top X)^{-1}X^\top Y. \]
Dwa fakty: kiedy \(\lambda \to 0\), \(\hat \beta_{ridge} \to \hat \beta_{ols}\); kiedy \(\lambda \to \infty\), \(\hat \beta_{ridge} \to 0\).
W szczególnych przypadkach \(X\) jest ortogonalna (tzn. kolumny \(X\) są ortogonalne), mamy:
\[ \hat \beta_{ridge} = \frac{\hat \beta_{ols}}{1 + \lambda}. \]
Widzimy więc, że estymator grzbietowy ma dodatkowo \(1/(1 + \lambda)\) tzw. “shrinkage factor”. W związku z tym na estymatorze grzbietowym występuje obciążliwość (bias).
Przykład
Funkcja glmnet() posiada argument alfa, który określa,
jaki typ modelu jest dopasowywany.
Jeśli alfa = 0 to dopasowywany jest model regresji
grzbietowej, a jeśli alfa = 1 to dopasowywany jest model
lasso.
Najpierw dopasowujemy model regresji grzbietowej:
grid = 10^seq(10, -2, length = 100)
ridge_mod = glmnet(x, y, alpha = 0, lambda = grid)Domyślnie funkcja glmnet() wykonuje regresję grzbietową
dla automatycznie wybranego wybranego zakresu wartości \(\lambda\). Jednakże, tutaj wybraliśmy
implementację funkcję w zakresie wartości od \(\lambda = 10^{10}\) do \(\lambda = 10^{-2}\), zasadniczo pokrywając
pełen zakres scenariuszy od modelu zerowego zawierającego tylko
przechwyt, do dopasowania najmniejszego kwadratu.
Jak widać, możemy również obliczyć dopasowanie modelu dla konkretnej wartości \(\lambda\), która nie jest jedną z oryginalnych wartości siatki.
Zauważ, że domyślnie funkcja glmnet() standaryzuje
zmienne tak, by były w tej samej skali. Aby wyłączyć to domyślne
ustawienie, użyj argumentu standardize = FALSE.
Z każdą wartością \(\lambda\)
związany jest wektor współczynników regresji grzbietowej, przechowywany
w macierzy, do której można uzyskać dostęp przez coef(). W
tym przypadku jest to macierz \(20 \times
100\), z 20 wierszami (po jednym dla każdego predyktora, plus
intercept) i 100 kolumnami (po jednej dla każdej wartości \(\lambda\)).
dim(coef(ridge_mod))## [1] 20 100plot(ridge_mod) # wykres współczynników
Spodziewamy się, że oszacowania współczynników będą znacznie mniejsze, w sensie normy \(l_2\), gdy używana jest duża wartość \(\lambda\), w porównaniu z małą wartością \(\lambda\).
Oto współczynniki, gdy \(\lambda = 11498\), wraz z ich normą \(l_2\):
ridge_mod$lambda[50] # Wyświetl 50-tą wartość lambdy## [1] 11497.57coef(ridge_mod)[,50] # Wyświetl współczynniki związane z 50-tą wartością lambdy## (Intercept) AtBat Hits HmRun Runs
## 407.356050200 0.036957182 0.138180344 0.524629976 0.230701523
## RBI Walks Years CAtBat CHits
## 0.239841459 0.289618741 1.107702929 0.003131815 0.011653637
## CHmRun CRuns CRBI CWalks LeagueN
## 0.087545670 0.023379882 0.024138320 0.025015421 0.085028114
## DivisionW PutOuts Assists Errors NewLeagueN
## -6.215440973 0.016482577 0.002612988 -0.020502690 0.301433531sqrt(sum(coef(ridge_mod)[-1,50]^2)) # Oblicz normę l2## [1] 6.360612Dla kontrastu, oto współczynniki, gdy \(\lambda = 705\), wraz z ich \(l_2\) normą. Zwróć uwagę na znacznie większą normę \(l_2\) współczynników związanych z tą mniejszą wartością \(\lambda\).
ridge_mod$lambda[60] # Wyświetl 60-tą wartość lambdy## [1] 705.4802coef(ridge_mod)[,60] # Wyświetl współczynniki powiązane z 60-tą wartość lambdy## (Intercept) AtBat Hits HmRun Runs RBI
## 54.32519950 0.11211115 0.65622409 1.17980910 0.93769713 0.84718546
## Walks Years CAtBat CHits CHmRun CRuns
## 1.31987948 2.59640425 0.01083413 0.04674557 0.33777318 0.09355528
## CRBI CWalks LeagueN DivisionW PutOuts Assists
## 0.09780402 0.07189612 13.68370191 -54.65877750 0.11852289 0.01606037
## Errors NewLeagueN
## -0.70358655 8.61181213sqrt(sum(coef(ridge_mod)[-1,60]^2)) # Oblicz normę l2## [1] 57.11001Funkcję predict() możemy wykorzystać do wielu celów. Na
przykład, możemy uzyskać współczynniki regresji grzbietowej dla nowej
wartości \(\lambda\), powiedzmy 50:
predict(ridge_mod, s = 50, type = "coefficients")[1:20,]## (Intercept) AtBat Hits HmRun Runs
## 4.876610e+01 -3.580999e-01 1.969359e+00 -1.278248e+00 1.145892e+00
## RBI Walks Years CAtBat CHits
## 8.038292e-01 2.716186e+00 -6.218319e+00 5.447837e-03 1.064895e-01
## CHmRun CRuns CRBI CWalks LeagueN
## 6.244860e-01 2.214985e-01 2.186914e-01 -1.500245e-01 4.592589e+01
## DivisionW PutOuts Assists Errors NewLeagueN
## -1.182011e+02 2.502322e-01 1.215665e-01 -3.278600e+00 -9.496680e+00Podzielimy teraz próbki na zbiór treningowy i testowy w celu oszacować błąd testu regresji grzbietowej i lasso.
set.seed(1)
train = Hitters %>%
sample_frac(0.5)
test = Hitters %>%
setdiff(train)
x_train = model.matrix(Salary~., train)[,-1]
x_test = model.matrix(Salary~., test)[,-1]
y_train = train %>%
select(Salary) %>%
unlist() %>%
as.numeric()
y_test = test %>%
select(Salary) %>%
unlist() %>%
as.numeric()Następnie dopasowujemy model regresji grzbietowej na zbiorze
treningowym i oceniamy jego MSE na zbiorze testowym, używając \(\lambda = 4\). Zwróć uwagę na użycie
funkcji predict(). Ponownie: tym razem otrzymujemy
przewidywania dla zbioru testowego, zastępując
type="coefficients" argumentem newx.
ridge_mod = glmnet(x_train, y_train, alpha=0, lambda = grid, thresh = 1e-12)
ridge_pred = predict(ridge_mod, s = 4, newx = x_test)
mean((ridge_pred - y_test)^2)## [1] 139858.6Testowe MSE wynosi 139858. Zauważ, że gdybyśmy zamiast tego dopasowali po prostu model tylko z wyrazem wolnym, przewidywalibyśmy każdą obserwację testową używając średniej z obserwacji zbioru treningowego. W takim przypadku moglibyśmy obliczyć MSE zestawu testowego w ten sposób:
mean((mean(y_train) - y_test)^2)## [1] 224692.1Moglibyśmy również uzyskać ten sam wynik, dopasowując model regresji
grzbietowej z bardzo dużą wartością \(\lambda\). Zauważ, że 1e10
oznacza \(10^{10}\).
ridge_pred = predict(ridge_mod, s = 1e10, newx = x_test)
mean((ridge_pred - y_test)^2)## [1] 224692.1Tak więc dopasowanie modelu regresji grzbietowej z \(\lambda = 4\) prowadzi do znacznie niższego testu MSE niż dopasowanie modelu z samym przechwytem.
Sprawdzimy teraz, czy jest jakaś korzyść z wykonania regresji grzbietowej z \(\lambda = 4\) zamiast po prostu wykonać regresję najmniejszych kwadratów.
Przypomnijmy, że najmniejsza kwadratura to po prostu regresja grzbietowa z \(\lambda = 0\).
* Uwaga: Aby glmnet() dawał dokładne
(exact) współczynniki najmniejszego kwadratu, gdy \(\lambda = 0\), używamy argumentu
exact=T przy wywołaniu funkcji predict(). W
przeciwnym razie, funkcja predict() będzie interpolować nad
siatką wartości \(\lambda\) użytą w
dopasowaniu modelu glmnet(), dając przybliżone wyniki.
Nawet gdy użyjemy exact = T, pozostaje niewielka
rozbieżność na trzecim miejscu po przecinku między wynikami
glmnet(), gdy \(\lambda =
0\) i wyjściem z lm(); jest to spowodowane
numerycznym przybliżeniem ze strony glmnet().
ridge_pred = predict(ridge_mod, s = 0, newx = x_test)
mean((ridge_pred - y_test)^2)## [1] 174060lm(Salary~., data = train)##
## Call:
## lm(formula = Salary ~ ., data = train)
##
## Coefficients:
## (Intercept) AtBat Hits HmRun Runs RBI
## 2.398e+02 -1.639e-03 -2.179e+00 6.337e+00 7.139e-01 8.735e-01
## Walks Years CAtBat CHits CHmRun CRuns
## 3.594e+00 -1.309e+01 -7.136e-01 3.316e+00 3.407e+00 -5.671e-01
## CRBI CWalks LeagueN DivisionW PutOuts Assists
## -7.525e-01 2.347e-01 1.322e+02 -1.346e+02 2.099e-01 6.229e-01
## Errors NewLeagueN
## -4.616e+00 -8.330e+01predict(ridge_mod, s = 0, type="coefficients")[1:20,]## (Intercept) AtBat Hits HmRun Runs
## 239.89368111 -0.01946204 -2.07305757 6.44254692 0.64610179
## RBI Walks Years CAtBat CHits
## 0.82179888 3.62448842 -13.28142313 -0.70314292 3.26064805
## CHmRun CRuns CRBI CWalks LeagueN
## 3.33170237 -0.54000590 -0.72015101 0.22582579 131.41324242
## DivisionW PutOuts Assists Errors NewLeagueN
## -134.76073238 0.20949301 0.61942855 -4.58545824 -82.35090554Wygląda na to, że rzeczywiście poprawiamy się w stosunku do zwykłego najmniejszego kwadratu!
Uwaga: ogólnie, jeśli chcemy dopasować (niespenalizowany) model
najmniejszych kwadratów, to powinniśmy użyć funkcji lm(),
ponieważ ta funkcja dostarcza bardziej użytecznych wyjścia, takie jak
błędy standardowe i wartości \(p\) dla
współczynników.
Zamiast arbitralnie wybierać \(\lambda =
4\), lepiej byłoby użyć walidacji krzyżowej do wyboru parametru
dostrojenia \(\lambda\). Możemy to
zrobić używając wbudowanej funkcji walidacji krzyżowej,
cv.glmnet(). Domyślnie funkcja ta wykonuje 10-krotną
walidację krzyżową, choć można to zmienić używając argumentu argumentu
folds. Zauważ, że najpierw ustawiamy losowe ziarno, aby
nasze wyniki były powtarzalne, ponieważ wybór krotności walidacji
krzyżowej jest losowy.
set.seed(1)
cv.out = cv.glmnet(x_train, y_train, alpha = 0) # Dopasuj model regresji grzbietowej na danych treningowych
bestlam = cv.out$lambda.min # Wybierz lamdę, która minimalizuje treningowy MSE
bestlam## [1] 326.1406Widzimy zatem, że wartość \(\lambda\), która powoduje najmniejszy błąd walidacji krzyżowej to 326. Możemy również wykreślić MSE jako funkcję \(\lambda\):
plot(cv.out) # Narysuj wykres treningowego MSE jako funkcję lambda
Jaki jest testowy MSE związany z tą wartością \(\lambda\)?
ridge_pred = predict(ridge_mod, s = bestlam, newx = x_test) # Użyj najlepszej lambdy do przewidywania danych testowych
mean((ridge_pred - y_test)^2) # Oblicz testowe MSE## [1] 140056.2Stanowi to dalszą poprawę w stosunku do testowego MSE, które uzyskaliśmy używając \(\lambda = 4\). Ostatecznie, ponownie wyznaczamy nasz model regresji grzbietowej na pełnym zestawie danych, używając wartości \(\lambda\) wybranej w walidacji krzyżowej, i sprawdzamy oszacowania współczynników.
out = glmnet(x, y, alpha = 0) # Dopasuj model regresji grzbietowej do pełnego zbioru danych
predict(out, type = "coefficients", s = bestlam)[1:20,] # Wyświetlanie współczynników przy użyciu lambda wybranego przez CV## (Intercept) AtBat Hits HmRun Runs RBI
## 15.44834992 0.07716945 0.85906253 0.60120338 1.06366687 0.87936073
## Walks Years CAtBat CHits CHmRun CRuns
## 1.62437580 1.35296285 0.01134998 0.05746377 0.40678422 0.11455696
## CRBI CWalks LeagueN DivisionW PutOuts Assists
## 0.12115916 0.05299953 22.08942756 -79.03490992 0.16618830 0.02941513
## Errors NewLeagueN
## -1.36075645 9.12528397Zgodnie z oczekiwaniami, żaden ze współczynników nie jest dokładnie zerowy - regresja grzbietowa nie dokonuje selekcji zmiennych!
Regresja Lasso
Wprowadzenie
Zamiast regularyzacji \(L_2\), LASSO używa penalizacji \(L_1\), to znaczy:
\[ \min_{\beta \in \mathbb{R}^p} \sum_{i=1}^n (y_i - x_i^\top \beta)^2 + \lambda \|\beta\|_1. \]
Ze względu na charakter normy \(L_1\), LASSO ma tendencję do dawania bardziej rzadkich rozwiązań niż regresja grzbietowa. Jest to typowo użyteczne w ustawieniach wielowymiarowych, gdy prawdziwy model jest w rzeczywistości niskowymiarowym osadzeniem.
Model regresji lasso został pierwotnie opracowany w 1989 roku. Jest to alternatywa dla klasycznego oszacowania metodą najmniejszych kwadratów, która unika wielu problemów z nadmiernym dopasowaniem (overfittingiem), gdy mamy dużą liczbę niezależnych zmiennych.
Regresja Lasso (Least Absolute Shrinkage and Selection Operator) to technika regresji liniowej stosowana do oszacowania współczynników modelu, która wprowadza regularyzację \(L_1\). Regularyzacja L1 polega na dodaniu do funkcji celu kary proporcjonalnej do wartości bezwzględnej współczynników regresji.
Regresja Lasso ma zdolność do jednoczesnego wykonania selekcji cech i regularyzacji, co oznacza, że może pomóc w identyfikacji najbardziej istotnych cech modelu, a także zmniejszyć wpływ mniej istotnych cech.
Podstawowym celem regresji Lasso jest minimalizacja funkcji celu, która składa się z dwóch składników: błędu dopasowania (sumy kwadratów różnic pomiędzy rzeczywistymi wartościami odpowiedzi a przewidywanymi wartościami modelu) i kary regularyzacyjnej \(L_1\).
Wzór funkcji celu dla regresji Lasso może być przedstawiony jako: Minimize: RSS + \(\lambda \|\beta\|_1\), gdzie:
RSS to suma kwadratów różnic pomiędzy rzeczywistymi wartościami odpowiedzi a przewidywanymi wartościami modelu (błąd dopasowania),
\(\lambda\) (lambda) to parametr regularyzacji, który kontroluje siłę regularyzacji, a \(\|\beta\|_1\) to norma \(L_1\) współczynników regresji.
Dodanie kary regularyzacyjnej \(L_1\) powoduje, że niektóre współczynniki regresji stają się równe zero, co prowadzi do selekcji cech. Im większa wartość \(\lambda\), tym większa jest tendencja do redukcji współczynników do zera, prowadząc do bardziej rzadkiego modelu z mniejszą liczbą cech.
Regresja Lasso jest przydatna w przypadkach, gdy mamy do czynienia z wieloma cechami, z których niektóre mogą być nieistotne. Może pomóc w identyfikacji istotnych cech, redukcji nadmiaru danych i zwiększeniu interpretowalności modelu.
Przykład
Zobaczyliśmy, że regresja grzbietowa z mądrym wyborem \(\lambda\) może przewyższać metodę najmniejszych kwadratów, jak również model zerowy na zbiorze danych Hitters.
Teraz zobaczmy, czy lasso może dać albo dokładniejszy, albo bardziej interpretowalny model niż regresja grzbietowa.
W celu dopasowania modelu lasso, po raz kolejny używamy funkcji
glmnet(), jednak tym razem używamy argumentu
alpha=1. Poza tą zmianą postępujemy tak samo jak w
przypadku dopasowywania modelu regresji grzbietowej:
lasso_mod = glmnet(x_train,
y_train,
alpha = 1,
lambda = grid) # Dopasuj model lasso do danych treningowych
plot(lasso_mod) # Wykreśl współczynniki
Zauważmy, że na wykresie współczynników, w zależności od wyboru dostrojenia parametru, niektóre ze współczynników są dokładnie równe zeru. Teraz przeprowadzimy walidację krzyżową i obliczymy związany z nią błąd testu:
set.seed(1)
cv.out = cv.glmnet(x_train, y_train, alpha = 1) # Dopasuj model lasso do danych treningowych
plot(cv.out) # Narysuj wykres MSE dla próby uczącej jako funkcję lambda
bestlam = cv.out$lambda.min # Wybierz lamdę, która minimalizuje MSE w próbie uczącej
lasso_pred = predict(lasso_mod, s = bestlam, newx = x_test) # Użyj najlepszej lambdy do przewidywania danych testowych
mean((lasso_pred - y_test)^2) # Oblicz MSE w próbie testowej## [1] 143273Jest to znacznie niższe MSE zbioru testowego niż modelu zerowego i modelu najmniejszych kwadratów, i bardzo podobny do MSE testu regresji grzbietowej z \(\lambda\) wybranej przez walidację krzyżową.
Jednakże lasso ma istotną przewagę nad regresją grzbietową w tym, że wynikowe oszacowania współczynników są rzadkie. Tutaj widzimy, że 12 z 19 oszacowań współczynników jest dokładnie zerowych:
out = glmnet(x, y, alpha = 1, lambda = grid) # Dopasuj model lasso do pełnego zbioru danych
lasso_coef = predict(out, type = "coefficients", s = bestlam)[1:20,] # Wyświetlanie współczynników przy użyciu lambda wybranego przez CV
lasso_coef## (Intercept) AtBat Hits HmRun Runs
## 1.27429897 -0.05490834 2.18012455 0.00000000 0.00000000
## RBI Walks Years CAtBat CHits
## 0.00000000 2.29189433 -0.33767315 0.00000000 0.00000000
## CHmRun CRuns CRBI CWalks LeagueN
## 0.02822467 0.21627609 0.41713051 0.00000000 20.28190194
## DivisionW PutOuts Assists Errors NewLeagueN
## -116.16524424 0.23751978 0.00000000 -0.85604181 0.00000000Wybierając tylko predyktory o niezerowych współczynnikach widzimy, że model lasso z \(\lambda\) wybranym przez walidację krzyżową zawiera tylko siedem zmiennych:
lasso_coef[lasso_coef != 0] # Wyświetlanie tylko niezerowych współczynników## (Intercept) AtBat Hits Walks Years
## 1.27429897 -0.05490834 2.18012455 2.29189433 -0.33767315
## CHmRun CRuns CRBI LeagueN DivisionW
## 0.02822467 0.21627609 0.41713051 20.28190194 -116.16524424
## PutOuts Errors
## 0.23751978 -0.85604181Twoja kolej!
Teraz nadszedł czas na przetestowanie tych metod (regresja grzbietowa i lasso) oraz metod oceny (zestaw walidacyjny, walidacja krzyżowa) na innych zbiorach danych. Możesz pracować z zespołem nad tą częścią laboratorium.
Możesz użyć dowolnego zbioru danych zawartego w ISLR lub wybrać jeden z pakietów danych na Kaggle/Data World itp. (zmienna zależna musi być ciągła).
Pobierz zbiór danych i spróbuj określić optymalny zestaw parametrów, które należy użyć do jego modelowania!
# Wasz kod tutaj
coll=na.omit(College)
coll## Private Apps Accept Enroll
## Abilene Christian University Yes 1660 1232 721
## Adelphi University Yes 2186 1924 512
## Adrian College Yes 1428 1097 336
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## Samford University Yes 1680 1395 691
## San Diego State University No 9402 7020 2151
## Santa Clara University Yes 4019 2779 888
## Sarah Lawrence College Yes 1380 768 263
## Savannah Coll. of Art and Design Yes 1109 688 386
## Schreiner College Yes 584 413 131
## Scripps College Yes 855 632 139
## Seattle Pacific University Yes 1183 1016 411
## Seattle University Yes 2115 1540 494
## Seton Hall University Yes 4576 3565 1000
## Seton Hill College Yes 936 794 197
## Shippensburg University of Penn. No 5818 3281 1116
## Shorter College Yes 540 445 165
## Siena College Yes 2961 1932 628
## Siena Heights College Yes 464 419 183
## Simmons College Yes 1003 782 295
## Simpson College Yes 1016 872 300
## Sioux Falls College Yes 437 400 211
## Skidmore College Yes 4293 2728 591
## Smith College Yes 2925 1598 632
## South Dakota State University No 2807 2589 1701
## Southeast Missouri State University No 2281 1870 1408
## Southeastern Oklahoma State Univ. No 818 700 447
## Southern California College Yes 385 340 193
## Southern Illinois University at Edwardsville No 2540 2195 994
## Southern Methodist University Yes 4301 3455 1166
## Southwest Baptist University Yes 1093 1093 642
## Southwest Missouri State University No 6118 5254 3204
## Southwest State University No 1047 938 511
## Southwestern Adventist College Yes 321 318 172
## Southwestern College Yes 213 155 75
## Southwestern University Yes 1244 912 352
## Spalding University Yes 283 201 97
## Spelman College Yes 3713 1237 443
## Spring Arbor College Yes 372 362 181
## St. Bonaventure University Yes 1489 1313 375
## St. John's College Yes 323 278 122
## St. John Fisher College Yes 1368 1064 354
## St. Lawrence University Yes 2753 1820 505
## St. Martin's College Yes 191 165 63
## St. Mary's College of California Yes 2643 1611 465
## St. Mary's College of Maryland No 1340 695 285
## St. Mary's University of San Antonio Yes 1243 1020 414
## St. Norbert College Yes 1334 1243 568
## St. Paul's College Yes 651 581 243
## St. Thomas Aquinas College Yes 861 609 215
## Stephens College Yes 450 405 194
## Stetson University Yes 1557 1227 489
## Stevens Institute of Technology Yes 1768 1249 380
## Stockton College of New Jersey No 4019 1579 710
## Stonehill College Yes 3646 2300 585
## SUNY at Albany No 13528 9198 1843
## SUNY at Binghamton No 14463 6166 1757
## SUNY at Buffalo No 15039 9649 3087
## SUNY at Stony Brook No 12512 6969 1724
## SUNY College at Brockport No 7294 3564 904
## SUNY College at Oswego No 8000 4556 1464
## SUNY College at Buffalo No 5318 3515 1025
## SUNY College at Cortland No 7888 3519 1036
## SUNY College at Fredonia No 4877 2798 814
## SUNY College at Geneseo No 8598 4562 1143
## SUNY College at New Paltz No 8399 3609 656
## SUNY College at Plattsburgh No 5549 3583 853
## SUNY College at Potsdam No 3150 2289 650
## SUNY College at Purchase No 2119 1264 390
## Susquehanna University Yes 2096 1512 465
## Sweet Briar College Yes 462 402 146
## Syracuse University Yes 10477 7260 2442
## Tabor College Yes 257 183 109
## Talladega College Yes 4414 1500 335
## Taylor University Yes 1769 1092 437
## Tennessee Wesleyan College Yes 232 182 99
## Texas A&M Univ. at College Station No 14474 10519 6392
## Texas A&M University at Galveston No 529 481 243
## Texas Christian University Yes 4095 3079 1195
## Texas Lutheran College Yes 497 423 215
## Texas Southern University No 4345 3245 2604
## Texas Wesleyan University Yes 592 501 279
## The Citadel No 1500 1242 611
## Thiel College Yes 1154 951 253
## Tiffin University Yes 845 734 254
## Transylvania University Yes 759 729 244
## Trenton State College No 5042 2312 944
## Tri-State University Yes 1262 1102 276
## Trinity College CT Yes 3058 1798 478
## Trinity College DC Yes 247 189 100
## Trinity College VT Yes 222 185 91
## Trinity University Yes 2425 1818 601
## Tulane University Yes 7033 5125 1223
## Tusculum College Yes 626 372 145
## Tuskegee University Yes 2267 1827 611
## Union College KY Yes 484 384 177
## Union College NY Yes 3495 1712 528
## Univ. of Wisconsin at OshKosh No 4800 2900 1515
## University of Alabama at Birmingham No 1797 1260 938
## University of Arkansas at Fayetteville No 3235 3108 2133
## University of California at Berkeley No 19873 8252 3215
## University of California at Irvine No 15698 10775 2478
## University of Central Florida No 6986 2959 1918
## University of Charleston Yes 682 535 204
## University of Chicago Yes 6348 2999 922
## University of Cincinnati No 6855 5553 2408
## University of Connecticut at Storrs No 9735 7187 2064
## University of Dallas Yes 681 588 246
## University of Dayton Yes 6361 5293 1507
## University of Delaware Yes 14446 10516 3252
## University of Denver Yes 2974 2001 580
## University of Detroit Mercy Yes 927 731 415
## University of Dubuque Yes 576 558 137
## University of Evansville Yes 2096 1626 694
## University of Florida No 12445 8836 3623
## University of Georgia No 11220 7871 3320
## University of Hartford Yes 5081 4040 1194
## University of Hawaii at Manoa No 3580 2603 1627
## University of Illinois - Urbana No 14939 11652 5705
## University of Illinois at Chicago No 8384 5727 2710
## University of Indianapolis Yes 1487 1276 388
## University of Kansas No 8579 5561 3681
## University of La Verne Yes 1597 969 226
## University of Louisville No 4777 3057 1823
## University of Maine at Farmington No 1208 803 438
## University of Maine at Machias No 441 369 172
## University of Maine at Presque Isle No 461 381 235
## University of Maryland at Baltimore County No 4269 2594 985
## University of Maryland at College Park No 14292 10315 3409
## University of Massachusetts at Amherst No 14438 12414 3816
## University of Massachusetts at Dartmouth No 3347 2597 1006
## University of Miami Yes 7122 5386 1643
## University of Michigan at Ann Arbor No 19152 12940 4893
## University of Minnesota at Duluth No 4192 3126 1656
## University of Minnesota at Morris No 1458 874 588
## University of Minnesota Twin Cities No 11054 6397 3524
## University of Mississippi No 3844 3383 1669
## University of Missouri at Columbia No 6574 4637 2940
## University of Missouri at Rolla No 1877 1826 823
## University of Missouri at Saint Louis No 1618 1141 479
## University of Mobile Yes 452 331 269
## University of Montevallo No 1351 892 570
## University of Nebraska at Lincoln No 6277 6003 3526
## University of New England Yes 1209 750 265
## University of New Hampshire No 9750 7640 2529
## University of North Carolina at Asheville No 1757 979 394
## University of North Carolina at Chapel Hill No 14596 5985 3331
## University of North Carolina at Charlotte No 5803 4441 1730
## University of North Carolina at Greensboro No 5191 4134 1500
## University of North Carolina at Wilmington No 6071 3856 1449
## University of North Dakota No 2777 2249 1652
## University of North Florida No 1800 1253 560
## University of North Texas No 4418 2737 2049
## University of Northern Colorado No 5530 4007 1697
## University of Northern Iowa No 4144 3379 1853
## University of Notre Dame Yes 7700 3700 1906
## University of Oklahoma No 4743 3970 2233
## University of Oregon No 8631 6732 2546
## University of Pennsylvania Yes 12394 5232 2464
## University of Pittsburgh-Main Campus No 8586 6383 2503
## University of Portland Yes 1758 1485 419
## University of Puget Sound Yes 4044 2826 688
## University of Rhode Island No 9643 7751 1968
## University of Richmond Yes 5892 2718 756
## University of Rochester Yes 8766 5498 1243
## University of San Diego Yes 3934 2735 886
## University of San Francisco Yes 2306 1721 538
## University of Sci. and Arts of Oklahoma No 285 280 208
## University of Scranton Yes 4471 2942 910
## University of South Carolina at Aiken No 848 560 377
## University of South Carolina at Columbia No 7693 5815 2328
## University of South Florida No 7589 4676 1876
## University of Southern California Yes 12229 8498 2477
## University of Southern Colorado No 1401 1239 605
## University of Southern Indiana No 2379 2133 1292
## University of Southern Mississippi No 2850 2044 1046
## University of St. Thomas MN Yes 2057 1807 828
## University of St. Thomas TX Yes 374 280 185
## University of Tennessee at Knoxville No 7473 5372 3013
## University of Texas at Arlington No 3281 2559 1448
## University of Texas at Austin No 14752 9572 5329
## University of Texas at San Antonio No 4217 3100 1686
## University of the Arts Yes 974 704 290
## University of the Pacific Yes 2459 1997 582
## University of the South Yes 1445 966 326
## University of Tulsa Yes 1712 1557 696
## University of Utah No 5095 4491 2400
## University of Vermont No 7663 6008 1735
## University of Virginia No 15849 5384 2678
## University of Washington No 12749 7025 3343
## University of West Florida No 1558 1254 472
## University of Wisconsin-Stout No 2593 1966 1030
## University of Wisconsin-Superior No 910 910 342
## University of Wisconsin-Whitewater No 4400 3719 1472
## University of Wisconsin at Green Bay No 2409 1939 759
## University of Wisconsin at Madison No 14901 10932 4631
## University of Wisconsin at Milwaukee No 5244 3782 1930
## University of Wyoming No 2029 1516 1073
## Upper Iowa University Yes 663 452 192
## Ursinus College Yes 1399 1026 308
## Ursuline College Yes 325 260 86
## Valley City State University No 368 344 212
## Valparaiso University Yes 2075 1727 520
## Vanderbilt University Yes 7791 4690 1499
## Vassar College Yes 3550 1877 653
## Villanova University Yes 7759 5588 1477
## Virginia Commonwealth University No 4963 3497 1567
## Virginia State University No 2996 2440 704
## Virginia Tech No 15712 11719 4277
## Virginia Union University Yes 1847 1610 453
## Virginia Wesleyan College Yes 1470 900 287
## Viterbo College Yes 647 518 271
## Voorhees College Yes 1465 1006 188
## Wabash College Yes 800 623 256
## Wagner College Yes 1416 1015 417
## Wake Forest University Yes 5661 2392 903
## Walsh University Yes 1092 890 477
## Warren Wilson College Yes 440 311 112
## Wartburg College Yes 1231 1074 345
## Washington and Jefferson College Yes 1305 1100 334
## Washington and Lee University Yes 3315 1096 425
## Washington College Yes 1209 942 214
## Washington State University No 6540 5839 2440
## Washington University Yes 7654 5259 1254
## Wayne State College No 1373 1373 724
## Waynesburg College Yes 1190 978 324
## Webber College Yes 280 143 79
## Webster University Yes 665 462 226
## Wellesley College Yes 2895 1249 579
## Wells College Yes 318 240 130
## Wentworth Institute of Technology Yes 1480 1257 452
## Wesley College Yes 980 807 350
## Wesleyan University Yes 4772 1973 712
## West Chester University of Penn. No 6502 3539 1372
## West Liberty State College No 1164 1062 478
## West Virginia Wesleyan College Yes 1566 1400 483
## Western Carolina University No 3224 2519 1057
## Western Maryland College Yes 1205 984 278
## Western Michigan University No 9167 7191 2738
## Western New England College Yes 1650 1471 409
## Western State College of Colorado No 2702 1623 604
## Western Washington University No 5548 3563 1549
## Westfield State College No 3100 2150 825
## Westminster College MO Yes 662 553 184
## Westminster College Yes 996 866 377
## Westminster College of Salt Lake City Yes 917 720 213
## Westmont College No 950 713 351
## Wheaton College IL Yes 1432 920 548
## Westminster College PA Yes 1738 1373 417
## Wheeling Jesuit College Yes 903 755 213
## Whitman College Yes 1861 998 359
## Whittier College Yes 1681 1069 344
## Whitworth College Yes 1121 926 372
## Widener University Yes 2139 1492 502
## Wilkes University Yes 1631 1431 434
## Willamette University Yes 1658 1327 395
## William Jewell College Yes 663 547 315
## William Woods University Yes 469 435 227
## Williams College Yes 4186 1245 526
## Wilson College Yes 167 130 46
## Wingate College Yes 1239 1017 383
## Winona State University No 3325 2047 1301
## Winthrop University No 2320 1805 769
## Wisconsin Lutheran College Yes 152 128 75
## Wittenberg University Yes 1979 1739 575
## Wofford College Yes 1501 935 273
## Worcester Polytechnic Institute Yes 2768 2314 682
## Worcester State College No 2197 1515 543
## Xavier University Yes 1959 1805 695
## Xavier University of Louisiana Yes 2097 1915 695
## Yale University Yes 10705 2453 1317
## York College of Pennsylvania Yes 2989 1855 691
## Top10perc Top25perc F.Undergrad
## Abilene Christian University 23 52 2885
## Adelphi University 16 29 2683
## Adrian College 22 50 1036
## Agnes Scott College 60 89 510
## Alaska Pacific University 16 44 249
## Albertson College 38 62 678
## Albertus Magnus College 17 45 416
## Albion College 37 68 1594
## Albright College 30 63 973
## Alderson-Broaddus College 21 44 799
## Alfred University 37 75 1830
## Allegheny College 44 77 1707
## Allentown Coll. of St. Francis de Sales 38 64 1130
## Alma College 44 73 1306
## Alverno College 23 46 1317
## American International College 9 22 1018
## Amherst College 83 96 1593
## Anderson University 19 40 1819
## Andrews University 14 23 1586
## Angelo State University 24 54 4190
## Antioch University 25 44 712
## Appalachian State University 20 63 9940
## Aquinas College 20 51 1251
## Arizona State University Main campus 24 49 22593
## Arkansas College (Lyon College) 46 74 530
## Arkansas Tech University 12 52 3602
## Assumption College 23 59 1708
## Auburn University-Main Campus 25 57 16262
## Augsburg College 12 30 2074
## Augustana College IL 36 69 1950
## Augustana College 21 58 1337
## Austin College 42 74 1120
## Averett College 16 40 777
## Baker University 21 47 958
## Baldwin-Wallace College 30 61 2718
## Barat College 15 36 453
## Bard College 50 85 1004
## Barnard College 53 95 2121
## Barry University 18 45 1811
## Baylor University 34 66 9919
## Beaver College 23 56 878
## Bellarmine College 39 63 1198
## Belmont Abbey College 17 36 709
## Belmont University 28 67 1964
## Beloit College 26 54 1085
## Bemidji State University 12 36 3796
## Benedictine College 14 24 702
## Bennington College 25 53 457
## Bentley College 20 60 3095
## Berry College 37 68 1620
## Bethany College 16 41 706
## Bethel College KS 19 42 537
## Bethel College 11 28 347
## Bethune Cookman College 12 30 2128
## Birmingham-Southern College 67 88 1376
## Blackburn College 25 55 421
## Bloomsburg Univ. of Pennsylvania 15 55 5847
## Bluefield College 15 30 653
## Bluffton College 20 50 760
## Boston University 45 80 14971
## Bowdoin College 76 100 1490
## Bowling Green State University 14 45 13699
## Bradford College 5 36 453
## Bradley University 30 58 4531
## Brandeis University 48 77 2819
## Brenau University 12 41 917
## Brewton-Parker College 10 26 1320
## Briar Cliff College 16 44 738
## Bridgewater College 22 53 881
## Brigham Young University at Provo 48 82 27378
## Brown University 87 95 5643
## Bryn Mawr College 71 95 1088
## Bucknell University 49 85 3316
## Buena Vista College 32 70 1928
## Butler University 40 68 2607
## Cabrini College 8 28 1035
## Caldwell College 17 42 693
## California Lutheran University 23 52 1427
## California Polytechnic-San Luis 47 73 12911
## California State University at Fresno 5 60 13494
## Calvin College 29 56 3401
## Campbell University 20 54 3191
## Campbellsville College 25 55 935
## Canisius College 16 34 2978
## Capital University 34 66 1662
## Capitol College 10 52 282
## Carleton College 75 93 1870
## Carnegie Mellon University 60 89 4265
## Carroll College 19 55 1357
## Carson-Newman College 27 62 1776
## Carthage College 20 43 1405
## Case Western Reserve University 71 93 3051
## Castleton State College 9 22 1547
## Catawba College 13 34 915
## Catholic University of America 24 49 2159
## Cazenovia College 9 35 1010
## Cedar Crest College 25 58 791
## Cedarville College 25 55 2196
## Centenary College 12 46 396
## Centenary College of Louisiana 35 55 775
## Center for Creative Studies 1 20 525
## Central College 31 65 1355
## Central Connecticut State University 6 24 6394
## Central Missouri State University 10 35 8094
## Central Washington University 8 65 6507
## Central Wesleyan College 8 29 1047
## Centre College 55 82 943
## Chapman University 23 48 1662
## Chatham College 28 56 471
## Chestnut Hill College 25 64 518
## Christendom College 33 71 139
## Christian Brothers University 16 42 1068
## Christopher Newport University 3 37 2910
## Claflin College 21 47 959
## Claremont McKenna College 71 93 887
## Clark University 30 61 1928
## Clarke College 14 45 604
## Clarkson University 35 68 2332
## Clemson University 37 65 11755
## Clinch Valley Coll. of the Univ. of Virginia 15 30 1125
## Coe College 29 60 1127
## Coker College 15 47 690
## Colby College 58 84 1720
## Colgate University 46 75 2649
## College Misericordia 29 58 1121
## College of Charleston 22 55 6851
## College of Mount St. Joseph 14 41 1165
## College of Mount St. Vincent 23 46 707
## College of Notre Dame 11 42 500
## College of Notre Dame of Maryland 35 61 667
## College of Saint Benedict 29 62 1715
## College of Saint Catherine 23 51 1692
## College of Saint Elizabeth 34 53 493
## College of Saint Rose 23 57 1698
## College of Santa Fe 16 42 873
## College of St. Joseph 12 21 201
## College of St. Scholastica 29 60 1350
## College of the Holy Cross 70 95 2675
## College of William and Mary 68 88 5186
## College of Wooster 29 65 1704
## Colorado College 56 87 1892
## Colorado State University 29 65 15646
## Columbia College MO 10 28 690
## Columbia College 21 67 968
## Columbia University 78 96 3376
## Concordia College at St. Paul 13 29 1049
## Concordia Lutheran College 16 34 534
## Concordia University CA 30 75 641
## Concordia University 22 56 1168
## Connecticut College 42 93 1630
## Converse College 35 70 643
## Cornell College 33 68 1140
## Creighton University 30 60 3450
## Culver-Stockton College 24 55 992
## Cumberland College 26 47 1306
## D'Youville College 18 47 1074
## Dana College 10 36 550
## Daniel Webster College 12 30 460
## Dartmouth College 87 99 3918
## Davidson College 77 96 1601
## Defiance College 10 26 645
## Delta State University 15 48 2806
## Denison University 32 60 1835
## DePauw University 50 80 1983
## Dickinson College 31 68 1889
## Dickinson State University 10 30 1376
## Dillard University 41 88 1539
## Doane College 20 47 1022
## Dominican College of Blauvelt 4 19 756
## Dordt College 25 50 1048
## Dowling College 9 33 1059
## Drake University 34 65 3322
## Drew University 56 84 1192
## Drury College 33 66 1065
## Duke University 90 98 6188
## Earlham College 35 63 1028
## East Carolina University 14 44 13171
## East Tennessee State University 15 36 6706
## East Texas Baptist University 10 36 1050
## Eastern College 16 42 1057
## Eastern Connecticut State University 14 50 2766
## Eastern Illinois University 12 38 9161
## Eastern Mennonite College 19 48 903
## Eastern Nazarene College 17 40 1238
## Eckerd College 33 65 1363
## Elizabethtown College 36 70 1476
## Elmira College 27 50 1109
## Elms College 23 46 544
## Elon College 11 39 2933
## Embry Riddle Aeronautical University 14 40 4772
## Emory & Henry College 30 60 809
## Emory University 76 97 5544
## Emporia State University 43 79 3957
## Erskine College 47 74 532
## Eureka College 36 56 484
## Evergreen State College 14 50 3065
## Fairfield University 30 66 2984
## Fayetteville State University 1 16 2632
## Ferrum College 12 36 1051
## Flagler College 18 52 1345
## Florida Institute of Technology 39 74 1863
## Florida International University 42 89 10208
## Florida Southern College 20 44 1506
## Florida State University 50 90 18906
## Fontbonne College 16 49 981
## Fordham University 30 55 4740
## Fort Lewis College 16 35 3793
## Francis Marion University 13 38 3224
## Franciscan University of Steubenville 22 49 1301
## Franklin College 29 72 840
## Franklin Pierce College 3 14 1818
## Freed-Hardeman University 20 54 1174
## Fresno Pacific College 51 87 704
## Furman University 56 82 2371
## Gannon University 24 57 2693
## Gardner Webb University 18 36 1603
## Geneva College 19 39 1306
## George Fox College 27 52 1271
## George Mason University 17 29 9528
## George Washington University 38 71 5471
## Georgetown College 30 55 1063
## Georgetown University 71 93 5881
## Georgia Institute of Technology 89 99 8528
## Georgia State University 9 24 7732
## Georgian Court College 12 52 1095
## Gettysburg College 42 78 1944
## Goldey Beacom College 10 27 823
## Gonzaga University 31 67 2523
## Gordon College 25 54 1151
## Goshen College 26 51 910
## Goucher College 40 64 850
## Grace College and Seminary 18 46 618
## Graceland College 14 41 996
## Grand Valley State University 20 60 8234
## Green Mountain College 7 20 545
## Greensboro College 10 31 649
## Greenville College 20 46 771
## Grinnell College 56 91 1333
## Grove City College 57 88 2213
## Guilford College 18 44 1410
## Gustavus Adolphus College 36 72 2281
## Gwynedd Mercy College 30 56 716
## Hamilton College 40 82 1646
## Hamline University 34 73 1362
## Hampden - Sydney College 20 40 945
## Hampton University 25 63 4623
## Hanover College 33 65 1024
## Hardin-Simmons University 16 40 1365
## Harding University 35 75 3128
## Hartwick College 22 49 1464
## Harvard University 90 100 6862
## Harvey Mudd College 95 100 654
## Hastings College 22 52 935
## Hendrix College 52 87 954
## Hillsdale College 35 66 1133
## Hiram College 37 66 1000
## Hobart and William Smith Colleges 25 53 1792
## Hofstra University 25 63 6534
## Hollins College 26 58 795
## Hood College 36 64 710
## Hope College 37 69 2505
## Houghton College 30 70 1210
## Huntingdon College 26 47 538
## Huntington College 20 46 488
## Huron University 3 9 392
## Husson College 10 30 951
## Illinois Benedictine College 22 47 1222
## Illinois College 28 63 909
## Illinois Institute of Technology 42 77 1911
## Illinois State University 10 35 15701
## Illinois Wesleyan University 55 86 1818
## Immaculata College 16 44 494
## Incarnate Word College 16 49 1685
## Indiana State University 10 31 8596
## Indiana University at Bloomington 25 72 24763
## Indiana Wesleyan University 20 48 2448
## Iona College 13 33 3906
## Iowa State University 26 59 18676
## Ithaca College 23 52 5612
## James Madison University 32 72 9652
## Jamestown College 14 41 9950
## Jersey City State College 10 30 3817
## John Brown University 24 53 961
## John Carroll University 27 57 3168
## Johns Hopkins University 75 94 3566
## Johnson State College 3 13 1224
## Judson College 10 30 552
## Juniata College 36 55 1075
## Kansas State University 25 55 14914
## Kansas Wesleyan University 16 40 474
## Keene State College 5 19 3480
## Kentucky Wesleyan College 20 49 662
## Kenyon College 44 75 1445
## Keuka College 10 43 738
## King's College 20 45 500
## King College 34 65 509
## Knox College 48 77 967
## La Roche College 10 41 650
## La Salle University 20 56 2738
## Lafayette College 36 59 2018
## LaGrange College 15 35 600
## Lake Forest College 31 70 968
## Lakeland College 24 47 887
## Lamar University 10 27 5438
## Lambuth University 15 35 840
## Lander University 9 33 2074
## Lawrence University 50 77 1129
## Le Moyne College 21 76 1820
## Lebanon Valley College 28 56 965
## Lehigh University 40 84 4298
## Lenoir-Rhyne College 25 46 1188
## Lesley College 12 33 1134
## LeTourneau University 29 54 1532
## Lewis and Clark College 35 64 1763
## Lewis University 12 31 2192
## Lincoln Memorial University 21 55 925
## Lincoln University 15 41 1196
## Lindenwood College 6 33 2155
## Linfield College 48 72 1548
## Livingstone College 22 47 621
## Lock Haven University of Pennsylvania 17 41 3390
## Longwood College 12 47 2874
## Loras College 20 39 1663
## Louisiana College 33 61 912
## Louisiana State University at Baton Rouge 29 57 16269
## Louisiana Tech University 22 45 6720
## Loyola College 25 54 3010
## Loyola Marymount University 42 64 3558
## Loyola University 24 80 2740
## Loyola University Chicago 25 55 5244
## Luther College 38 72 2269
## Lycoming College 16 37 1363
## Lynchburg College 3 21 1524
## Lyndon State College 6 20 959
## Macalester College 56 86 1723
## MacMurray College 12 29 628
## Malone College 21 46 1605
## Manchester College 23 63 909
## Manhattan College 20 63 2578
## Manhattanville College 21 54 830
## Mankato State University 9 29 9649
## Marian College of Fond du Lac 15 41 1160
## Marietta College 27 60 1089
## Marist College 12 31 3557
## Marquette University 36 71 7016
## Marshall University 14 60 7703
## Mary Baldwin College 26 52 846
## Mary Washington College 39 78 2997
## Marymount College Tarrytown 9 34 731
## Marymount Manhattan College 21 30 988
## Marymount University 10 30 1247
## Maryville College 26 52 624
## Maryville University 26 51 1343
## Marywood College 13 51 1452
## Massachusetts Institute of Technology 96 99 4481
## Mayville State University 5 12 658
## McKendree College 16 43 836
## McMurry University 25 50 880
## McPherson College 11 32 336
## Mercer University 37 70 2943
## Mercyhurst College 15 40 1805
## Meredith College 25 58 1721
## Merrimack College 18 36 1927
## Mesa State College 6 18 3471
## Messiah College 30 64 2258
## Miami University at Oxford 35 39 13606
## Michigan State University 23 57 26640
## Michigan Technological University 42 77 5524
## MidAmerica Nazarene College 15 36 1100
## Millersville University of Penn. 22 60 5146
## Milligan College 26 52 685
## Millikin University 29 62 1788
## Millsaps College 32 61 1073
## Milwaukee School of Engineering 36 69 1773
## Mississippi College 36 57 1695
## Mississippi State University 18 57 10094
## Mississippi University for Women 19 46 1673
## Missouri Southern State College 13 50 3689
## Missouri Valley College 5 35 1057
## Monmouth College IL 28 57 671
## Monmouth College 14 34 1893
## Montana College of Mineral Sci. & Tech. 45 72 1470
## Montana State University 15 42 8730
## Montclair State University 19 53 6411
## Montreat-Anderson College 10 24 316
## Moorhead State University 12 37 5983
## Moravian College 23 58 1241
## Morehouse College 41 66 2852
## Morningside College 16 36 950
## Morris College 2 13 926
## Mount Holyoke College 47 79 1891
## Mount Marty College 17 37 600
## Mount Mary College 12 32 931
## Mount Mercy College 20 49 806
## Mount Saint Clare College 16 33 364
## Mount Saint Mary's College 15 36 1243
## Mount Saint Mary College 14 48 1170
## Mount St. Mary's College 37 90 1039
## Mount Union College 26 61 1365
## Mount Vernon Nazarene College 18 36 1114
## Muhlenberg College 30 61 1656
## Murray State University 29 55 5968
## Muskingum College 24 46 1115
## National-Louis University 23 48 2508
## Nazareth College of Rochester 36 68 1274
## New Jersey Institute of Technology 27 62 3311
## New Mexico Institute of Mining and Tech. 40 73 1017
## New York University 70 86 12408
## Newberry College 14 36 601
## Niagara University 65 99 1919
## North Adams State College 1 19 1380
## North Carolina A. & T. State University 12 33 6162
## North Carolina State University at Raleigh 39 78 16505
## North Carolina Wesleyan College 7 24 646
## North Central College 30 64 1310
## North Dakota State University 13 47 7368
## North Park College 19 39 879
## Northeast Missouri State University 36 72 5640
## Northeastern University 16 42 11160
## Northern Arizona University 23 48 11249
## Northern Illinois University 12 37 14826
## Northwest Missouri State University 8 29 4787
## Northwest Nazarene College 29 52 1115
## Northwestern College 22 56 1040
## Northwestern University 85 98 7450
## Norwich University 8 29 1862
## Notre Dame College 15 37 500
## Oakland University 16 56 6441
## Oberlin College 50 89 2587
## Occidental College 52 81 1686
## Oglethorpe University 56 87 769
## Ohio Northern University 35 62 2502
## Ohio University 21 54 14861
## Ohio Wesleyan University 36 65 1780
## Oklahoma Baptist University 35 59 1707
## Oklahoma Christian University 22 44 1419
## Oklahoma State University 29 57 12830
## Otterbein College 26 57 1648
## Ouachita Baptist University 31 73 1310
## Our Lady of the Lake University 22 46 1202
## Pace University 37 70 5809
## Pacific Lutheran University 31 68 2580
## Pacific Union College 20 48 1316
## Pacific University 41 71 1041
## Pembroke State University 14 34 2174
## Pennsylvania State Univ. Main Campus 48 93 28938
## Pepperdine University 86 96 2488
## Peru State College 10 40 959
## Pfeiffer College 11 25 654
## Philadelphia Coll. of Textiles and Sci. 19 42 1664
## Phillips University 19 50 597
## Piedmont College 20 40 641
## Pikeville College 28 48 797
## Pitzer College 37 73 750
## Point Loma Nazarene College 20 43 1889
## Point Park College 7 38 1173
## Polytechnic University 58 89 1379
## Prairie View A. and M. University 10 22 4564
## Presbyterian College 34 63 1133
## Princeton University 90 98 4540
## Providence College 20 55 3717
## Purdue University at West Lafayette 29 60 26213
## Queens College 32 62 630
## Quincy University 22 66 1070
## Quinnipiac College 17 45 2677
## Radford University 15 37 8077
## Ramapo College of New Jersey 6 29 2745
## Randolph-Macon College 21 46 1071
## Randolph-Macon Woman's College 35 66 653
## Reed College 47 80 1199
## Regis College 18 38 581
## Rensselaer Polytechnic Institute 53 82 4291
## Rhodes College 58 82 1345
## Rider University 16 31 2748
## Ripon College 28 52 735
## Rivier College 6 28 590
## Roanoke College 27 54 1460
## Rockhurst College 22 50 1127
## Rocky Mountain College 11 31 743
## Roger Williams University 10 20 2111
## Rollins College 31 55 1668
## Rosary College 28 53 624
## Rowan College of New Jersey 21 70 5303
## Rutgers at New Brunswick 36 79 21401
## Rutgers State University at Camden 27 79 2585
## Rutgers State University at Newark 26 62 4005
## Sacred Heart University 19 51 1707
## Saint Ambrose University 12 48 1345
## Saint Anselm College 15 40 1873
## Saint Cloud State University 10 34 11493
## Saint Francis College IN 13 36 513
## Saint Francis College 21 45 1223
## Saint John's University 18 45 1691
## Saint Joseph's College IN 24 42 815
## Saint Joseph's College 12 33 716
## Saint Joseph's University 39 71 2473
## Saint Joseph College 20 52 543
## Saint Louis University 44 67 4576
## Saint Mary's College 26 60 1433
## Saint Mary's College of Minnesota 14 35 1263
## Saint Mary-of-the-Woods College 23 50 341
## Saint Michael's College 16 64 1715
## Saint Olaf College 38 73 2888
## Saint Peter's College 23 38 1921
## Saint Vincent College 19 35 1035
## Saint Xavier University 15 65 1670
## Salem-Teikyo University 23 52 700
## Salem College 28 69 534
## Salisbury State University 20 52 4296
## Samford University 34 76 2959
## San Diego State University 20 70 16407
## Santa Clara University 40 73 3891
## Sarah Lawrence College 57 82 1000
## Savannah Coll. of Art and Design 20 65 1897
## Schreiner College 19 51 521
## Scripps College 60 83 569
## Seattle Pacific University 42 82 1922
## Seattle University 28 72 2993
## Seton Hall University 16 36 4384
## Seton Hill College 24 56 752
## Shippensburg University of Penn. 14 53 5268
## Shorter College 23 70 1115
## Siena College 24 68 2669
## Siena Heights College 10 31 686
## Simmons College 23 53 1144
## Simpson College 27 57 1116
## Sioux Falls College 13 35 614
## Skidmore College 25 62 2322
## Smith College 51 88 2479
## South Dakota State University 13 37 7000
## Southeast Missouri State University 18 43 6553
## Southeastern Oklahoma State Univ. 20 50 2962
## Southern California College 18 38 784
## Southern Illinois University at Edwardsville 13 40 6063
## Southern Methodist University 41 69 4892
## Southwest Baptist University 12 32 1770
## Southwest Missouri State University 15 37 13131
## Southwest State University 13 33 2091
## Southwestern Adventist College 11 27 620
## Southwestern College 28 66 504
## Southwestern University 44 77 1177
## Spalding University 10 45 589
## Spelman College 47 83 1971
## Spring Arbor College 15 32 1501
## St. Bonaventure University 13 45 1688
## St. John's College 31 51 393
## St. John Fisher College 19 51 1687
## St. Lawrence University 31 56 1801
## St. Martin's College 5 25 494
## St. Mary's College of California 36 80 2615
## St. Mary's College of Maryland 42 73 1315
## St. Mary's University of San Antonio 33 60 2149
## St. Norbert College 30 56 1946
## St. Paul's College 8 17 617
## St. Thomas Aquinas College 10 27 1117
## Stephens College 17 34 614
## Stetson University 37 69 1964
## Stevens Institute of Technology 51 93 1263
## Stockton College of New Jersey 23 65 4365
## Stonehill College 25 69 2022
## SUNY at Albany 16 61 10168
## SUNY at Binghamton 60 94 8544
## SUNY at Buffalo 36 100 13963
## SUNY at Stony Brook 27 66 9744
## SUNY College at Brockport 7 34 5758
## SUNY College at Oswego 17 70 6943
## SUNY College at Buffalo 8 29 7626
## SUNY College at Cortland 6 40 5011
## SUNY College at Fredonia 13 48 4123
## SUNY College at Geneseo 56 93 5060
## SUNY College at New Paltz 19 53 4658
## SUNY College at Plattsburgh 9 40 5004
## SUNY College at Potsdam 16 51 3598
## SUNY College at Purchase 5 33 2478
## Susquehanna University 27 59 1442
## Sweet Briar College 36 68 527
## Syracuse University 28 67 10142
## Tabor College 19 41 396
## Talladega College 30 60 908
## Taylor University 41 80 1757
## Tennessee Wesleyan College 7 29 402
## Texas A&M Univ. at College Station 49 85 31643
## Texas A&M University at Galveston 22 47 1206
## Texas Christian University 33 64 5064
## Texas Lutheran College 27 57 895
## Texas Southern University 15 85 5584
## Texas Wesleyan University 19 44 1204
## The Citadel 12 36 2024
## Thiel College 15 31 791
## Tiffin University 5 21 662
## Transylvania University 57 81 867
## Trenton State College 55 94 5167
## Tri-State University 14 40 978
## Trinity College CT 46 84 1737
## Trinity College DC 19 49 309
## Trinity College VT 16 41 484
## Trinity University 62 93 2110
## Tulane University 47 75 4941
## Tusculum College 12 34 983
## Tuskegee University 20 59 2825
## Union College KY 9 45 634
## Union College NY 49 84 1915
## Univ. of Wisconsin at OshKosh 14 48 7764
## University of Alabama at Birmingham 24 35 6960
## University of Arkansas at Fayetteville 25 65 9978
## University of California at Berkeley 95 100 19532
## University of California at Irvine 85 100 12677
## University of Central Florida 25 60 12330
## University of Charleston 22 43 771
## University of Chicago 68 94 3340
## University of Cincinnati 26 57 11036
## University of Connecticut at Storrs 23 63 12478
## University of Dallas 44 74 1058
## University of Dayton 26 51 5889
## University of Delaware 22 57 14130
## University of Denver 29 60 2666
## University of Detroit Mercy 24 50 2149
## University of Dubuque 11 39 662
## University of Evansville 35 67 2551
## University of Florida 54 85 24470
## University of Georgia 43 79 19553
## University of Hartford 11 26 3768
## University of Hawaii at Manoa 36 69 11028
## University of Illinois - Urbana 52 88 25422
## University of Illinois at Chicago 22 50 13518
## University of Indianapolis 26 51 1417
## University of Kansas 25 50 17880
## University of La Verne 16 38 1431
## University of Louisville 16 33 9844
## University of Maine at Farmington 20 48 1906
## University of Maine at Machias 17 45 633
## University of Maine at Presque Isle 10 40 974
## University of Maryland at Baltimore County 27 57 6476
## University of Maryland at College Park 22 53 19340
## University of Massachusetts at Amherst 12 39 16282
## University of Massachusetts at Dartmouth 10 37 4664
## University of Miami 42 69 7760
## University of Michigan at Ann Arbor 66 92 22045
## University of Minnesota at Duluth 15 45 5887
## University of Minnesota at Morris 56 86 1846
## University of Minnesota Twin Cities 26 55 16502
## University of Mississippi 26 47 7524
## University of Missouri at Columbia 32 62 14782
## University of Missouri at Rolla 49 77 3926
## University of Missouri at Saint Louis 18 54 4793
## University of Mobile 17 54 1417
## University of Montevallo 18 78 2385
## University of Nebraska at Lincoln 33 63 16454
## University of New England 19 54 820
## University of New Hampshire 24 62 10358
## University of North Carolina at Asheville 32 74 2033
## University of North Carolina at Chapel Hill 75 92 14609
## University of North Carolina at Charlotte 19 62 10099
## University of North Carolina at Greensboro 15 44 7532
## University of North Carolina at Wilmington 15 67 6635
## University of North Dakota 20 54 8334
## University of North Florida 44 85 3876
## University of North Texas 23 51 14047
## University of Northern Colorado 12 37 8463
## University of Northern Iowa 18 52 10135
## University of Notre Dame 79 96 7671
## University of Oklahoma 32 63 13436
## University of Oregon 25 61 11669
## University of Pennsylvania 85 100 9205
## University of Pittsburgh-Main Campus 25 59 13138
## University of Portland 27 58 2041
## University of Puget Sound 51 83 2738
## University of Rhode Island 12 40 8894
## University of Richmond 46 72 2854
## University of Rochester 56 75 5071
## University of San Diego 40 70 3698
## University of San Francisco 23 48 4309
## University of Sci. and Arts of Oklahoma 21 43 1140
## University of Scranton 29 60 3674
## University of South Carolina at Aiken 14 24 1855
## University of South Carolina at Columbia 30 66 12594
## University of South Florida 29 63 14770
## University of Southern California 45 71 13259
## University of Southern Colorado 10 34 3716
## University of Southern Indiana 8 25 4283
## University of Southern Mississippi 20 50 9260
## University of St. Thomas MN 26 53 4106
## University of St. Thomas TX 45 77 995
## University of Tennessee at Knoxville 27 53 15749
## University of Texas at Arlington 19 43 10975
## University of Texas at Austin 48 85 30017
## University of Texas at San Antonio 17 46 9375
## University of the Arts 5 22 1145
## University of the Pacific 36 66 2664
## University of the South 46 83 1129
## University of Tulsa 41 68 2936
## University of Utah 27 53 13894
## University of Vermont 18 51 7353
## University of Virginia 74 95 11278
## University of Washington 40 81 20356
## University of West Florida 20 57 3754
## University of Wisconsin-Stout 9 32 6038
## University of Wisconsin-Superior 14 53 1434
## University of Wisconsin-Whitewater 12 38 7804
## University of Wisconsin at Green Bay 17 50 3819
## University of Wisconsin at Madison 36 80 23945
## University of Wisconsin at Milwaukee 12 37 11561
## University of Wyoming 23 46 7535
## Upper Iowa University 10 35 1481
## Ursinus College 44 77 1131
## Ursuline College 21 47 699
## Valley City State University 5 27 863
## Valparaiso University 49 81 2501
## Vanderbilt University 71 92 5500
## Vassar College 53 87 2164
## Villanova University 30 68 6362
## Virginia Commonwealth University 18 45 10262
## Virginia State University 2 30 3006
## Virginia Tech 29 53 18511
## Virginia Union University 19 59 1298
## Virginia Wesleyan College 20 49 1130
## Viterbo College 17 43 1014
## Voorhees College 10 30 703
## Wabash College 41 76 801
## Wagner College 10 44 1324
## Wake Forest University 75 88 3499
## Walsh University 27 92 847
## Warren Wilson College 25 49 466
## Wartburg College 34 66 1295
## Washington and Jefferson College 42 64 1098
## Washington and Lee University 68 93 1584
## Washington College 31 60 822
## Washington State University 31 70 14445
## Washington University 62 93 4879
## Wayne State College 6 21 2754
## Waynesburg College 12 30 1280
## Webber College 5 27 327
## Webster University 17 44 1739
## Wellesley College 80 96 2195
## Wells College 40 85 416
## Wentworth Institute of Technology 6 25 2961
## Wesley College 10 25 872
## Wesleyan University 60 86 2714
## West Chester University of Penn. 11 51 7484
## West Liberty State College 12 25 2138
## West Virginia Wesleyan College 28 55 1509
## Western Carolina University 11 31 5000
## Western Maryland College 31 50 1071
## Western Michigan University 24 53 15739
## Western New England College 7 21 1803
## Western State College of Colorado 7 24 2315
## Western Washington University 30 71 8909
## Westfield State College 3 20 3234
## Westminster College MO 20 43 665
## Westminster College 29 58 1411
## Westminster College of Salt Lake City 21 60 979
## Westmont College 42 72 1276
## Wheaton College IL 56 84 2200
## Westminster College PA 21 55 1335
## Wheeling Jesuit College 15 49 971
## Whitman College 45 77 1220
## Whittier College 35 63 1235
## Whitworth College 43 70 1270
## Widener University 24 64 2186
## Wilkes University 15 36 1803
## Willamette University 49 80 1595
## William Jewell College 32 67 1279
## William Woods University 17 39 851
## Williams College 81 96 1988
## Wilson College 16 50 199
## Wingate College 10 34 1207
## Winona State University 20 45 5800
## Winthrop University 24 61 3395
## Wisconsin Lutheran College 17 41 282
## Wittenberg University 42 68 1980
## Wofford College 51 83 1059
## Worcester Polytechnic Institute 49 86 2802
## Worcester State College 4 26 3089
## Xavier University 24 47 2849
## Xavier University of Louisiana 34 61 2793
## Yale University 95 99 5217
## York College of Pennsylvania 28 63 2988
## P.Undergrad Outstate Room.Board
## Abilene Christian University 537 7440 3300
## Adelphi University 1227 12280 6450
## Adrian College 99 11250 3750
## Agnes Scott College 63 12960 5450
## Alaska Pacific University 869 7560 4120
## Albertson College 41 13500 3335
## Albertus Magnus College 230 13290 5720
## Albion College 32 13868 4826
## Albright College 306 15595 4400
## Alderson-Broaddus College 78 10468 3380
## Alfred University 110 16548 5406
## Allegheny College 44 17080 4440
## Allentown Coll. of St. Francis de Sales 638 9690 4785
## Alma College 28 12572 4552
## Alverno College 1235 8352 3640
## American International College 287 8700 4780
## Amherst College 5 19760 5300
## Anderson University 281 10100 3520
## Andrews University 326 9996 3090
## Angelo State University 1512 5130 3592
## Antioch University 23 15476 3336
## Appalachian State University 1035 6806 2540
## Aquinas College 767 11208 4124
## Arizona State University Main campus 7585 7434 4850
## Arkansas College (Lyon College) 182 8644 3922
## Arkansas Tech University 939 3460 2650
## Assumption College 689 12000 5920
## Auburn University-Main Campus 1716 6300 3933
## Augsburg College 726 11902 4372
## Augustana College IL 38 13353 4173
## Augustana College 300 10990 3244
## Austin College 15 11280 4342
## Averett College 538 9925 4135
## Baker University 466 8620 4100
## Baldwin-Wallace College 1460 10995 4410
## Barat College 266 9690 4300
## Bard College 15 19264 6206
## Barnard College 69 17926 8124
## Barry University 3144 11290 5360
## Baylor University 484 6450 3920
## Beaver College 519 12850 5400
## Bellarmine College 605 8840 2950
## Belmont Abbey College 131 9000 4850
## Belmont University 623 7800 3664
## Beloit College 81 16304 3616
## Bemidji State University 824 4425 2700
## Benedictine College 501 9550 3850
## Bennington College 2 21700 4100
## Bentley College 1533 13800 5510
## Berry College 49 8050 3940
## Bethany College 62 8740 3363
## Bethel College KS 101 8540 3580
## Bethel College 74 6200 2900
## Bethune Cookman College 82 5188 3396
## Birmingham-Southern College 207 11660 4325
## Blackburn College 27 6500 2700
## Bloomsburg Univ. of Pennsylvania 946 7844 2948
## Bluefield College 129 7150 4350
## Bluffton College 81 9900 3990
## Boston University 3113 18420 6810
## Bowdoin College 8 19030 5885
## Bowling Green State University 1213 7452 3352
## Bradford College 42 14080 6270
## Bradley University 643 10870 4440
## Brandeis University 62 19380 6750
## Brenau University 479 9592 5879
## Brewton-Parker College 822 4371 2370
## Briar Cliff College 430 10260 3597
## Bridgewater College 55 10265 4725
## Brigham Young University at Provo 1253 2340 3580
## Brown University 349 19528 5926
## Bryn Mawr College 16 18165 6750
## Bucknell University 31 18550 4750
## Buena Vista College 442 13306 3797
## Butler University 148 13130 4650
## Cabrini College 446 10518 6250
## Caldwell College 868 8900 4600
## California Lutheran University 432 12950 5300
## California Polytechnic-San Luis 1404 7380 4877
## California State University at Fresno 1254 7706 4368
## Calvin College 136 10230 3710
## Campbell University 1204 7550 2790
## Campbellsville College 184 6060 3070
## Canisius College 434 10750 5340
## Capital University 960 13050 4000
## Capitol College 331 8400 2812
## Carleton College 12 19292 3957
## Carnegie Mellon University 291 17900 5690
## Carroll College 737 12200 3880
## Carson-Newman College 239 8150 3150
## Carthage College 580 13125 3775
## Case Western Reserve University 513 15700 4730
## Castleton State College 294 7656 4690
## Catawba College 80 9270 4100
## Catholic University of America 211 13712 6408
## Cazenovia College 12 9384 4840
## Cedar Crest College 764 14340 5285
## Cedarville College 82 7344 4410
## Centenary College 526 11400 5400
## Centenary College of Louisiana 44 8950 3490
## Center for Creative Studies 323 11230 6643
## Central College 40 10938 3660
## Central Connecticut State University 3881 5962 4444
## Central Missouri State University 1596 4620 3288
## Central Washington University 898 7242 3603
## Central Wesleyan College 33 8300 3080
## Centre College 7 11850 4270
## Chapman University 209 16624 5895
## Chatham College 148 13500 5230
## Chestnut Hill College 232 10335 5015
## Christendom College 3 8730 3600
## Christian Brothers University 364 9300 3260
## Christopher Newport University 1749 7860 4750
## Claflin College 13 4412 2460
## Claremont McKenna College 1 17000 6010
## Clark University 296 17500 4200
## Clarke College 350 10740 3676
## Clarkson University 53 15960 5580
## Clemson University 770 8116 3610
## Clinch Valley Coll. of the Univ. of Virginia 422 7168 3689
## Coe College 205 13925 4390
## Coker College 222 9888 4502
## Colby College 35 18930 5590
## Colgate University 25 19510 5565
## College Misericordia 493 10860 5760
## College of Charleston 1200 6120 3460
## College of Mount St. Joseph 1232 9800 4430
## College of Mount St. Vincent 432 11790 5770
## College of Notre Dame 331 12600 5520
## College of Notre Dame of Maryland 1983 11180 5620
## College of Saint Benedict 103 12247 4221
## College of Saint Catherine 562 12224 4440
## College of Saint Elizabeth 968 10900 5250
## College of Saint Rose 894 9990 5666
## College of Santa Fe 683 11138 4138
## College of St. Joseph 173 8300 4850
## College of St. Scholastica 275 11844 3696
## College of the Holy Cross 22 18000 6300
## College of William and Mary 134 11720 4298
## College of Wooster 1 16240 4690
## Colorado College 7 17142 4190
## Colorado State University 1829 8412 4180
## Columbia College MO 5346 8294 3700
## Columbia College 237 10425 3975
## Columbia University 55 18624 6664
## Concordia College at St. Paul 181 10500 3750
## Concordia Lutheran College 172 6900 3800
## Concordia University CA 101 10800 4440
## Concordia University 145 9216 4191
## Connecticut College 232 18740 6300
## Converse College 80 12050 3700
## Cornell College 10 15248 4323
## Creighton University 644 10628 4372
## Culver-Stockton College 112 8000 3700
## Cumberland College 122 6230 3526
## D'Youville College 336 8920 4310
## Dana College 84 9130 3322
## Daniel Webster College 536 12292 4934
## Dartmouth College 32 19545 6070
## Davidson College 6 17295 5070
## Defiance College 283 10850 3670
## Delta State University 538 4528 1880
## Denison University 14 16900 4720
## DePauw University 36 14300 5020
## Dickinson College 62 18700 5000
## Dickinson State University 237 4486 2146
## Dillard University 45 6700 3650
## Doane College 411 9570 3000
## Dominican College of Blauvelt 863 8310 5500
## Dordt College 56 9800 2650
## Dowling College 2458 9000 3100
## Drake University 726 13420 4770
## Drew University 87 18432 5616
## Drury College 48 8730 3523
## Duke University 53 18590 5950
## Earlham College 13 15036 4056
## East Carolina University 1687 7248 3240
## East Tennessee State University 2640 5800 3000
## East Texas Baptist University 151 4950 2780
## Eastern College 355 11190 4800
## Eastern Connecticut State University 1531 5962 4316
## Eastern Illinois University 845 5710 3066
## Eastern Mennonite College 59 9650 3800
## Eastern Nazarene College 30 8770 3500
## Eckerd College 23 15360 4080
## Elizabethtown College 299 14190 4400
## Elmira College 502 14990 4980
## Elms College 436 11800 4765
## Elon College 334 9100 3883
## Embry Riddle Aeronautical University 856 7800 3750
## Emory & Henry College 32 8578 4408
## Emory University 192 17600 6000
## Emporia State University 588 5401 3144
## Erskine College 35 10485 3840
## Eureka College 16 10955 3450
## Evergreen State College 363 6297 4600
## Fairfield University 1037 15000 6200
## Fayetteville State University 617 6806 2550
## Ferrum College 82 9400 4200
## Flagler College 44 5120 3200
## Florida Institute of Technology 233 13900 4140
## Florida International University 9310 6597 2494
## Florida Southern College 970 8025 4865
## Florida State University 3242 6680 4060
## Fontbonne College 337 8390 4100
## Fordham University 1646 14235 6965
## Fort Lewis College 486 6198 3320
## Francis Marion University 436 5840 3138
## Franciscan University of Steubenville 242 9650 4400
## Franklin College 68 10390 4040
## Franklin Pierce College 1197 13320 4630
## Freed-Hardeman University 50 5500 3340
## Fresno Pacific College 63 9900 3670
## Furman University 175 13440 4048
## Gannon University 691 10970 4280
## Gardner Webb University 374 8180 4270
## Geneva College 258 9476 4820
## George Fox College 43 12500 4130
## George Mason University 3822 10800 4840
## George Washington University 1470 17450 6328
## Georgetown College 48 8100 3950
## Georgetown University 406 18300 7131
## Georgia Institute of Technology 654 6489 4438
## Georgia State University 9054 6744 2655
## Georgian Court College 785 9150 3950
## Gettysburg College 46 19964 4328
## Goldey Beacom College 963 6120 2985
## Gonzaga University 296 13000 4450
## Gordon College 39 12200 4070
## Goshen College 166 9420 3730
## Goucher College 80 15588 6174
## Grace College and Seminary 113 8958 3670
## Graceland College 2281 9100 3100
## Grand Valley State University 2619 6108 3800
## Green Mountain College 42 11750 2700
## Greensboro College 314 8330 3770
## Greenville College 53 10310 4530
## Grinnell College 30 15688 4618
## Grove City College 35 5224 3048
## Guilford College 299 13404 5160
## Gustavus Adolphus College 50 14125 3600
## Gwynedd Mercy College 1108 11000 5550
## Hamilton College 24 19700 5050
## Hamline University 102 13252 4194
## Hampden - Sydney College 1 13218 4773
## Hampton University 740 7161 3518
## Hanover College 15 8200 3485
## Hardin-Simmons University 334 6300 2980
## Harding University 213 5504 3528
## Hartwick College 67 17480 4780
## Harvard University 320 18485 6410
## Harvey Mudd College 5 17230 6690
## Hastings College 37 9376 3272
## Hendrix College 6 8800 3195
## Hillsdale College 42 11090 4700
## Hiram College 275 14067 4560
## Hobart and William Smith Colleges 5 19029 5841
## Hofstra University 1350 11600 5920
## Hollins College 74 13470 5515
## Hood College 399 13960 6040
## Hope College 208 12275 4341
## Houghton College 26 9990 3550
## Huntingdon College 126 8080 3920
## Huntington College 43 9950 3920
## Huron University 69 7260 3090
## Husson College 706 7800 4000
## Illinois Benedictine College 519 10500 4348
## Illinois College 28 8050 3850
## Illinois Institute of Technology 626 14550 4620
## Illinois State University 1823 7799 3403
## Illinois Wesleyan University 23 14360 4090
## Immaculata College 1305 10000 5364
## Incarnate Word College 556 8840 4689
## Indiana State University 1949 6892 3706
## Indiana University at Bloomington 2717 9766 3990
## Indiana Wesleyan University 707 9210 3782
## Iona College 1446 10690 6790
## Iowa State University 1715 7550 3224
## Ithaca College 166 14424 6192
## James Madison University 742 7994 4544
## Jamestown College 71 7620 3050
## Jersey City State College 1394 3946 4800
## John Brown University 99 6398 3672
## John Carroll University 392 11700 5550
## Johns Hopkins University 1569 18800 6740
## Johnson State College 345 7656 4690
## Judson College 67 9414 4554
## Juniata College 43 14850 4460
## Kansas State University 2246 6995 3120
## Kansas Wesleyan University 258 8400 3250
## Keene State College 776 7870 4157
## Kentucky Wesleyan College 121 8000 4150
## Kenyon College 1 19240 3690
## Keuka College 55 9600 4550
## King's College 541 10910 5160
## King College 44 8664 3350
## Knox College 24 15747 4062
## La Roche College 819 8842 4782
## La Salle University 1662 12600 5610
## Lafayette College 226 18730 5740
## LaGrange College 363 6987 3585
## Lake Forest College 20 16880 3970
## Lakeland College 1957 9400 4005
## Lamar University 4058 4752 3040
## Lambuth University 325 5170 3430
## Lander University 341 4938 2987
## Lawrence University 74 17163 3891
## Le Moyne College 558 11040 4840
## Lebanon Valley College 502 13850 4755
## Lehigh University 132 18700 5580
## Lenoir-Rhyne College 166 10100 4000
## Lesley College 336 11700 5300
## LeTourneau University 77 8840 4240
## Lewis and Clark College 59 15800 4790
## Lewis University 1423 10560 4520
## Lincoln Memorial University 605 5950 2890
## Lincoln University 33 4818 3400
## Lindenwood College 191 9200 4800
## Linfield College 840 13380 4210
## Livingstone College 11 4400 3400
## Lock Haven University of Pennsylvania 325 7352 3620
## Longwood College 118 7920 3962
## Loras College 170 11200 4000
## Louisiana College 158 5150 3036
## Louisiana State University at Baton Rouge 3757 5925 2980
## Louisiana Tech University 1822 3957 2325
## Loyola College 184 12990 6300
## Loyola Marymount University 436 13592 5916
## Loyola University 761 11100 5870
## Loyola University Chicago 3417 11500 5330
## Luther College 85 13240 3560
## Lycoming College 74 13900 4300
## Lynchburg College 280 12450 5400
## Lyndon State College 150 7320 4640
## Macalester College 113 15909 4772
## MacMurray College 63 9620 3750
## Malone College 246 9858 3700
## Manchester College 51 10440 3850
## Manhattan College 254 12370 6800
## Manhattanville College 150 14700 6550
## Mankato State University 1792 4300 2643
## Marian College of Fond du Lac 653 9400 3400
## Marietta College 210 13850 3920
## Marist College 658 10700 5925
## Marquette University 804 11610 4760
## Marshall University 2339 5094 4010
## Mary Baldwin College 377 11200 7400
## Mary Washington College 736 6490 4942
## Marymount College Tarrytown 370 11510 6450
## Marymount Manhattan College 785 10200 7000
## Marymount University 776 11390 5280
## Maryville College 128 11200 4208
## Maryville University 1751 9250 4550
## Marywood College 402 11040 4500
## Massachusetts Institute of Technology 28 20100 5975
## Mayville State University 58 4486 2516
## McKendree College 684 7680 3740
## McMurry University 477 6930 3452
## McPherson College 80 7950 3750
## Mercer University 1260 11985 4081
## Mercyhurst College 433 9813 4050
## Meredith College 470 6720 3250
## Merrimack College 1084 12500 6200
## Mesa State College 911 5016 3798
## Messiah College 53 10300 5080
## Miami University at Oxford 807 8856 3960
## Michigan State University 4120 10658 3734
## Michigan Technological University 414 8127 3978
## MidAmerica Nazarene College 166 6840 3720
## Millersville University of Penn. 1532 7844 3830
## Milligan College 49 8200 3300
## Millikin University 95 11910 4378
## Millsaps College 179 11320 4402
## Milwaukee School of Engineering 884 11505 3255
## Mississippi College 721 5580 2830
## Mississippi State University 1621 9866 3084
## Mississippi University for Women 1014 4386 2217
## Missouri Southern State College 2200 3840 2852
## Missouri Valley College 175 8550 5050
## Monmouth College IL 11 13000 4100
## Monmouth College 847 12480 5290
## Montana College of Mineral Sci. & Tech. 416 6073 3400
## Montana State University 993 5552 3710
## Montclair State University 3186 3648 4834
## Montreat-Anderson College 20 8438 3372
## Moorhead State University 1075 4426 2664
## Moravian College 485 14990 4730
## Morehouse College 153 7050 5490
## Morningside College 228 10520 3678
## Morris College 12 4515 2550
## Mount Holyoke College 40 19300 5700
## Mount Marty College 435 6844 2980
## Mount Mary College 487 8950 3119
## Mount Mercy College 542 10500 3555
## Mount Saint Clare College 88 9900 3650
## Mount Saint Mary's College 79 12850 6200
## Mount Saint Mary College 429 7470 4600
## Mount St. Mary's College 466 12474 5678
## Mount Union College 144 12250 3530
## Mount Vernon Nazarene College 94 7400 3346
## Muhlenberg College 352 16975 4565
## Murray State University 955 4738 3110
## Muskingum College 70 13240 3914
## National-Louis University 505 9090 4500
## Nazareth College of Rochester 471 10850 5150
## New Jersey Institute of Technology 1646 8832 5376
## New Mexico Institute of Mining and Tech. 411 5376 3214
## New York University 2814 17748 7262
## Newberry College 36 10194 2600
## Niagara University 334 10320 4762
## North Adams State College 136 5542 4330
## North Carolina A. & T. State University 871 6806 1780
## North Carolina State University at Raleigh 5481 8400 6540
## North Carolina Wesleyan College 84 8242 4230
## North Central College 766 11718 7398
## North Dakota State University 1128 5834 2744
## North Park College 156 12580 4345
## Northeast Missouri State University 266 4856 3416
## Northeastern University 10221 13380 7425
## Northern Arizona University 2682 6746 3728
## Northern Illinois University 1979 7799 3296
## Northwest Missouri State University 472 3735 3136
## Northwest Nazarene College 60 9840 2820
## Northwestern College 52 9900 3075
## Northwestern University 45 16404 5520
## Norwich University 382 14134 5270
## Notre Dame College 311 9990 4900
## Oakland University 3982 9114 4030
## Oberlin College 120 19670 5820
## Occidental College 35 16560 5140
## Oglethorpe University 377 12900 4340
## Ohio Northern University 66 15990 4080
## Ohio University 1310 7629 4095
## Ohio Wesleyan University 48 16732 5650
## Oklahoma Baptist University 705 5390 3140
## Oklahoma Christian University 228 6400 3150
## Oklahoma State University 1658 5336 3344
## Otterbein College 936 12888 4440
## Ouachita Baptist University 61 6530 2800
## Our Lady of the Lake University 942 8530 3644
## Pace University 4379 11000 5160
## Pacific Lutheran University 302 13312 4488
## Pacific Union College 139 11925 3825
## Pacific University 35 14210 3994
## Pembroke State University 529 6360 2760
## Pennsylvania State Univ. Main Campus 2025 10645 4060
## Pepperdine University 625 18200 6770
## Peru State College 457 2580 2624
## Pfeiffer College 162 8640 3700
## Philadelphia Coll. of Textiles and Sci. 1042 11690 5062
## Phillips University 83 10500 3860
## Piedmont College 63 5640 3620
## Pikeville College 100 6000 3000
## Pitzer College 30 17688 5900
## Point Loma Nazarene College 217 10178 4190
## Point Park College 1402 9700 4830
## Polytechnic University 214 16200 4200
## Prairie View A. and M. University 448 4290 3500
## Presbyterian College 30 11859 3635
## Princeton University 146 19900 5910
## Providence College 1358 14400 6200
## Purdue University at West Lafayette 4065 9556 3990
## Queens College 549 11020 4970
## Quincy University 72 10100 4140
## Quinnipiac College 714 12030 6140
## Radford University 472 6684 4110
## Ramapo College of New Jersey 1938 4449 4860
## Randolph-Macon College 27 13840 3735
## Randolph-Macon Woman's College 56 13970 6110
## Reed College 61 19960 5490
## Regis College 533 12700 5800
## Rensselaer Polytechnic Institute 16 17475 5976
## Rhodes College 59 15200 4768
## Rider University 1309 13250 5420
## Ripon College 28 15200 4100
## Rivier College 1196 9870 4860
## Roanoke College 239 13425 4425
## Rockhurst College 754 9490 4100
## Rocky Mountain College 118 8734 3362
## Roger Williams University 1489 12520 6050
## Rollins College 1052 16425 5220
## Rosary College 269 10950 4600
## Rowan College of New Jersey 3942 4356 4830
## Rutgers at New Brunswick 3712 7410 4748
## Rutgers State University at Camden 1300 7411 4748
## Rutgers State University at Newark 1886 7410 4748
## Sacred Heart University 1889 11070 5780
## Saint Ambrose University 390 10450 4020
## Saint Anselm College 94 12950 5400
## Saint Cloud State University 2206 4259 2625
## Saint Francis College IN 247 8670 3820
## Saint Francis College 451 10880 5050
## Saint John's University 72 12247 4081
## Saint Joseph's College IN 222 11200 4250
## Saint Joseph's College 2196 9985 5180
## Saint Joseph's University 1314 12750 6350
## Saint Joseph College 712 12200 4600
## Saint Louis University 1140 11690 4730
## Saint Mary's College 27 12730 4514
## Saint Mary's College of Minnesota 118 10800 3600
## Saint Mary-of-the-Woods College 768 10300 4130
## Saint Michael's College 106 13030 5860
## Saint Olaf College 105 14350 3750
## Saint Peter's College 1154 9408 5520
## Saint Vincent College 182 10850 3936
## Saint Xavier University 726 10860 4624
## Salem-Teikyo University 45 10575 3952
## Salem College 216 10475 6300
## Salisbury State University 1027 5130 4690
## Samford University 402 8236 3700
## San Diego State University 5550 8384 5110
## Santa Clara University 128 13584 5928
## Sarah Lawrence College 105 19300 6694
## Savannah Coll. of Art and Design 208 8325 5000
## Schreiner College 99 8955 5900
## Scripps College 7 17238 7350
## Seattle Pacific University 704 12669 4875
## Seattle University 347 12825 4375
## Seton Hall University 1530 12000 6484
## Seton Hill College 210 11240 4180
## Shippensburg University of Penn. 300 7844 3504
## Shorter College 111 7210 3600
## Siena College 616 10800 5100
## Siena Heights College 287 9240 3880
## Simmons College 160 16160 6950
## Simpson College 602 11250 4980
## Sioux Falls College 271 8990 3064
## Skidmore College 263 18710 5970
## Smith College 95 18820 6390
## South Dakota State University 1103 3811 2190
## Southeast Missouri State University 1246 4680 3540
## Southeastern Oklahoma State Univ. 651 3738 2619
## Southern California College 127 9520 4124
## Southern Illinois University at Edwardsville 2550 5472 3598
## Southern Methodist University 387 12772 5078
## Southwest Baptist University 967 7070 2500
## Southwest Missouri State University 3374 4740 2590
## Southwest State University 546 4285 2750
## Southwestern Adventist College 280 7536 3736
## Southwestern College 147 7200 3532
## Southwestern University 43 11850 4675
## Spalding University 263 8400 2800
## Spelman College 107 7000 5565
## Spring Arbor College 353 8600 3550
## St. Bonaventure University 131 10456 4927
## St. John's College 4 16150 5450
## St. John Fisher College 677 10570 5600
## St. Lawrence University 45 18720 5730
## St. Martin's College 574 11550 4270
## St. Mary's College of California 248 13332 6354
## St. Mary's College of Maryland 209 6800 4730
## St. Mary's University of San Antonio 418 8678 3858
## St. Norbert College 95 12140 4450
## St. Paul's College 34 5000 3650
## St. Thomas Aquinas College 815 8650 5700
## Stephens College 388 13900 5200
## Stetson University 81 12315 4565
## Stevens Institute of Technology 11 16900 5680
## Stockton College of New Jersey 765 3040 4351
## Stonehill College 926 12170 6172
## SUNY at Albany 1231 6550 4355
## SUNY at Binghamton 671 6550 4598
## SUNY at Buffalo 3124 6550 4731
## SUNY at Stony Brook 1351 6550 4712
## SUNY College at Brockport 1363 6550 4460
## SUNY College at Oswego 869 6550 4810
## SUNY College at Buffalo 2091 6550 4040
## SUNY College at Cortland 346 6550 4680
## SUNY College at Fredonia 298 6550 4420
## SUNY College at Geneseo 146 6550 4170
## SUNY College at New Paltz 1478 6550 4240
## SUNY College at Plattsburgh 475 6550 4176
## SUNY College at Potsdam 234 6840 4660
## SUNY College at Purchase 1441 6550 4760
## Susquehanna University 166 16130 4710
## Sweet Briar College 41 14500 6000
## Syracuse University 117 15150 6870
## Tabor College 38 7850 3410
## Talladega College 119 5666 2964
## Taylor University 81 10965 4000
## Tennessee Wesleyan College 237 7070 3640
## Texas A&M Univ. at College Station 2798 5130 3412
## Texas A&M University at Galveston 134 4860 3122
## Texas Christian University 660 8490 3320
## Texas Lutheran College 429 7850 3410
## Texas Southern University 3101 7860 3360
## Texas Wesleyan University 392 6400 3484
## The Citadel 292 7070 2439
## Thiel College 140 11172 4958
## Tiffin University 351 7600 3800
## Transylvania University 51 10900 4450
## Trenton State College 902 5391 5411
## Tri-State University 98 9456 4350
## Trinity College CT 244 18810 5690
## Trinity College DC 639 11412 6430
## Trinity College VT 541 11010 5208
## Trinity University 95 12240 5150
## Tulane University 1534 19040 5950
## Tusculum College 40 7700 3400
## Tuskegee University 144 6735 3395
## Union College KY 78 7800 2950
## Union College NY 123 18732 6204
## Univ. of Wisconsin at OshKosh 1472 6874 2394
## University of Alabama at Birmingham 4698 4440 5175
## University of Arkansas at Fayetteville 1530 5028 3300
## University of California at Berkeley 2061 11648 6246
## University of California at Irvine 864 12024 5302
## University of Central Florida 7152 6618 4234
## University of Charleston 611 9500 3540
## University of Chicago 39 18930 6380
## University of Cincinnati 2011 8907 4697
## University of Connecticut at Storrs 1660 11656 5072
## University of Dallas 73 10760 6230
## University of Dayton 665 11380 4220
## University of Delaware 4522 10220 4230
## University of Denver 554 15192 4695
## University of Detroit Mercy 2217 11130 3996
## University of Dubuque 131 10430 3620
## University of Evansville 407 11800 4340
## University of Florida 3286 7090 4180
## University of Georgia 2748 5697 3600
## University of Hartford 1415 14220 6000
## University of Hawaii at Manoa 2411 4460 3038
## University of Illinois - Urbana 911 7560 4574
## University of Illinois at Chicago 2916 7230 5088
## University of Indianapolis 1646 11120 4080
## University of Kansas 1673 6994 3384
## University of La Verne 1522 13540 5050
## University of Louisville 6198 6540 3600
## University of Maine at Farmington 344 6810 3970
## University of Maine at Machias 317 6600 3680
## University of Maine at Presque Isle 503 6600 3630
## University of Maryland at Baltimore County 2592 8594 4408
## University of Maryland at College Park 3991 8723 5146
## University of Massachusetts at Amherst 1940 8566 3897
## University of Massachusetts at Dartmouth 1630 6919 4500
## University of Miami 876 16500 6526
## University of Michigan at Ann Arbor 1339 15732 4659
## University of Minnesota at Duluth 1254 8828 3474
## University of Minnesota at Morris 154 9843 3180
## University of Minnesota Twin Cities 21836 8949 3744
## University of Mississippi 804 4916 3810
## University of Missouri at Columbia 1583 9057 3485
## University of Missouri at Rolla 561 9057 3600
## University of Missouri at Saint Louis 4552 7246 3964
## University of Mobile 301 6150 3680
## University of Montevallo 331 4440 3030
## University of Nebraska at Lincoln 3171 5595 3145
## University of New England 159 11450 5045
## University of New Hampshire 1338 11180 3862
## University of North Carolina at Asheville 1078 5972 3420
## University of North Carolina at Chapel Hill 1100 8400 4200
## University of North Carolina at Charlotte 3255 7248 3109
## University of North Carolina at Greensboro 1847 8677 3505
## University of North Carolina at Wilmington 1145 7558 3680
## University of North Dakota 1435 5634 2703
## University of North Florida 3588 6634 4360
## University of North Texas 5134 4104 3579
## University of Northern Colorado 1498 7731 4128
## University of Northern Iowa 1448 6197 2930
## University of Notre Dame 30 16850 4400
## University of Oklahoma 2582 5173 3526
## University of Oregon 1605 10602 3660
## University of Pennsylvania 531 17020 7270
## University of Pittsburgh-Main Campus 4289 10786 4560
## University of Portland 174 12040 4100
## University of Puget Sound 138 16230 4500
## University of Rhode Island 2456 10330 5558
## University of Richmond 594 14500 3285
## University of Rochester 438 17840 6582
## University of San Diego 217 13600 5940
## University of San Francisco 549 13226 6452
## University of Sci. and Arts of Oklahoma 473 3687 1920
## University of Scranton 493 11584 5986
## University of South Carolina at Aiken 1412 5800 3066
## University of South Carolina at Columbia 3661 8074 3522
## University of South Florida 10962 6760 3776
## University of Southern California 1429 17230 6482
## University of Southern Colorado 675 7100 4380
## University of Southern Indiana 2973 4973 3192
## University of Southern Mississippi 1387 4652 2470
## University of St. Thomas MN 982 11712 4037
## University of St. Thomas TX 408 8550 4050
## University of Tennessee at Knoxville 3237 5764 3262
## University of Texas at Arlington 8431 4422 2780
## University of Texas at Austin 5189 5130 3309
## University of Texas at San Antonio 5457 4104 5376
## University of the Arts 39 12520 3860
## University of the Pacific 299 16320 5326
## University of the South 24 15350 4080
## University of Tulsa 433 11750 4160
## University of Utah 8374 6857 3975
## University of Vermont 1674 15516 4928
## University of Virginia 114 12212 3792
## University of Washington 4582 8199 4218
## University of West Florida 2477 6172 3994
## University of Wisconsin-Stout 579 6704 2592
## University of Wisconsin-Superior 417 7032 2780
## University of Wisconsin-Whitewater 1552 6950 2500
## University of Wisconsin at Green Bay 1347 6900 2800
## University of Wisconsin at Madison 2200 9096 4290
## University of Wisconsin at Milwaukee 7443 8786 2964
## University of Wyoming 1488 5988 3422
## Upper Iowa University 1160 8840 3060
## Ursinus College 17 14900 5160
## Ursuline College 717 9600 4202
## Valley City State University 189 4286 2570
## Valparaiso University 198 11800 3260
## Vanderbilt University 90 17865 6525
## Vassar College 77 18920 5950
## Villanova University 1292 15925 6507
## Virginia Commonwealth University 5065 10217 4182
## Virginia State University 338 5587 4845
## Virginia Tech 604 10260 3176
## Virginia Union University 67 7384 3494
## Virginia Wesleyan College 417 10900 5100
## Viterbo College 387 9140 3365
## Voorhees College 20 4450 2522
## Wabash College 5 12925 4195
## Wagner College 117 13500 5800
## Wake Forest University 172 13850 4360
## Walsh University 497 8670 4180
## Warren Wilson College 7 10000 3052
## Wartburg College 105 11600 3610
## Washington and Jefferson College 151 16260 4005
## Washington and Lee University 3 13750 4619
## Washington College 46 15276 5318
## Washington State University 1344 8200 4210
## Washington University 1274 18350 5775
## Wayne State College 474 2700 2660
## Waynesburg College 61 8840 3620
## Webber College 110 5590 2900
## Webster University 1550 9160 4340
## Wellesley College 156 18345 5995
## Wells College 19 14900 5550
## Wentworth Institute of Technology 572 9850 6050
## Wesley College 448 9890 4674
## Wesleyan University 27 19130 5600
## West Chester University of Penn. 1904 7844 4108
## West Liberty State College 227 4470 2890
## West Virginia Wesleyan College 170 14200 3775
## Western Carolina University 706 6390 2380
## Western Maryland College 98 14510 5340
## Western Michigan University 4278 6940 4100
## Western New England College 1116 8994 5500
## Western State College of Colorado 146 5918 3755
## Western Washington University 506 8124 4144
## Westfield State College 941 5542 3788
## Westminster College MO 37 10720 4050
## Westminster College 72 12065 3615
## Westminster College of Salt Lake City 743 8820 4050
## Westmont College 9 14320 5304
## Wheaton College IL 56 11480 4200
## Westminster College PA 30 18460 5970
## Wheeling Jesuit College 305 10500 4545
## Whitman College 46 16670 4900
## Whittier College 30 16249 5699
## Whitworth College 160 12660 4500
## Widener University 2171 12350 5370
## Wilkes University 603 11150 5130
## Willamette University 159 14800 4620
## William Jewell College 75 10060 2970
## William Woods University 120 10535 4365
## Williams College 29 19629 5790
## Wilson College 676 11428 5084
## Wingate College 157 7820 3400
## Winona State University 872 4200 2700
## Winthrop University 670 6400 3392
## Wisconsin Lutheran College 22 9100 3700
## Wittenberg University 144 15948 4404
## Wofford College 34 12680 4150
## Worcester Polytechnic Institute 86 15884 5370
## Worcester State College 2029 6797 3900
## Xavier University 1107 11520 4960
## Xavier University of Louisiana 166 6900 4200
## Yale University 83 19840 6510
## York College of Pennsylvania 1726 4990 3560
## Books Personal PhD Terminal
## Abilene Christian University 450 2200 70 78
## Adelphi University 750 1500 29 30
## Adrian College 400 1165 53 66
## Agnes Scott College 450 875 92 97
## Alaska Pacific University 800 1500 76 72
## Albertson College 500 675 67 73
## Albertus Magnus College 500 1500 90 93
## Albion College 450 850 89 100
## Albright College 300 500 79 84
## Alderson-Broaddus College 660 1800 40 41
## Alfred University 500 600 82 88
## Allegheny College 400 600 73 91
## Allentown Coll. of St. Francis de Sales 600 1000 60 84
## Alma College 400 400 79 87
## Alverno College 650 2449 36 69
## American International College 450 1400 78 84
## Amherst College 660 1598 93 98
## Anderson University 550 1100 48 61
## Andrews University 900 1320 62 66
## Angelo State University 500 2000 60 62
## Antioch University 400 1100 69 82
## Appalachian State University 96 2000 83 96
## Aquinas College 350 1615 55 65
## Arizona State University Main campus 700 2100 88 93
## Arkansas College (Lyon College) 500 800 79 88
## Arkansas Tech University 450 1000 57 60
## Assumption College 500 500 93 93
## Auburn University-Main Campus 600 1908 85 91
## Augsburg College 540 950 65 65
## Augustana College IL 540 821 78 83
## Augustana College 600 1021 66 70
## Austin College 400 1150 81 95
## Averett College 750 1350 59 67
## Baker University 400 2250 58 68
## Baldwin-Wallace College 1000 1000 68 74
## Barat College 500 500 57 77
## Bard College 750 750 98 98
## Barnard College 600 850 83 93
## Barry University 600 1800 76 78
## Baylor University 600 1346 71 76
## Beaver College 400 800 78 89
## Bellarmine College 750 1290 74 82
## Belmont Abbey College 300 2480 78 85
## Belmont University 650 900 61 61
## Beloit College 355 715 87 95
## Bemidji State University 660 1800 57 62
## Benedictine College 350 250 64 84
## Bennington College 600 500 35 59
## Bentley College 630 850 87 87
## Berry College 350 2375 80 80
## Bethany College 550 1700 62 68
## Bethel College KS 500 1400 61 80
## Bethel College 600 800 63 63
## Bethune Cookman College 650 2500 48 48
## Birmingham-Southern College 400 900 74 79
## Blackburn College 500 1000 76 76
## Bloomsburg Univ. of Pennsylvania 500 1680 66 68
## Bluefield College 450 1500 61 67
## Bluffton College 400 900 76 71
## Boston University 475 1025 80 81
## Bowdoin College 1495 875 93 96
## Bowling Green State University 600 1700 81 89
## Bradford College 500 900 57 80
## Bradley University 2000 1522 75 81
## Brandeis University 410 1000 90 97
## Brenau University 500 700 71 80
## Brewton-Parker College 500 2000 62 62
## Briar Cliff College 600 1500 39 66
## Bridgewater College 560 875 68 73
## Brigham Young University at Provo 860 1220 76 76
## Brown University 720 1100 99 100
## Bryn Mawr College 500 1200 100 100
## Bucknell University 800 1200 95 97
## Buena Vista College 450 950 62 69
## Butler University 500 1600 77 81
## Cabrini College 300 300 59 76
## Caldwell College 425 1000 87 96
## California Lutheran University 612 576 72 74
## California Polytechnic-San Luis 612 2091 72 81
## California State University at Fresno 600 1926 90 90
## Calvin College 400 1210 75 81
## Campbell University 600 500 77 77
## Campbellsville College 600 1300 62 66
## Canisius College 400 1130 90 92
## Capital University 500 800 64 69
## Capitol College 300 2134 10 50
## Carleton College 550 550 81 93
## Carnegie Mellon University 450 1250 86 93
## Carroll College 480 930 74 81
## Carson-Newman College 400 500 61 62
## Carthage College 500 1300 74 89
## Case Western Reserve University 525 1460 95 95
## Castleton State College 400 700 89 91
## Catawba College 600 1860 75 82
## Catholic University of America 526 1100 90 96
## Cazenovia College 600 500 22 47
## Cedar Crest College 500 1000 58 83
## Cedarville College 570 1000 50 52
## Centenary College 500 760 41 85
## Centenary College of Louisiana 600 1900 86 92
## Center for Creative Studies 2340 620 8 58
## Central College 650 600 76 90
## Central Connecticut State University 500 985 69 73
## Central Missouri State University 300 2250 69 80
## Central Washington University 654 1416 67 89
## Central Wesleyan College 600 600 62 62
## Centre College 600 900 95 99
## Chapman University 600 1100 72 80
## Chatham College 400 850 95 98
## Chestnut Hill College 700 850 71 71
## Christendom College 400 800 92 92
## Christian Brothers University 600 900 81 81
## Christopher Newport University 525 1889 80 82
## Claflin College 500 1000 69 69
## Claremont McKenna College 500 850 99 99
## Clark University 500 950 94 95
## Clarke College 350 900 67 71
## Clarkson University 700 1300 95 95
## Clemson University 800 1618 82 88
## Clinch Valley Coll. of the Univ. of Virginia 600 1900 67 67
## Coe College 500 2200 73 86
## Coker College 400 1000 64 77
## Colby College 500 1000 83 94
## Colgate University 500 750 95 98
## College Misericordia 550 900 56 62
## College of Charleston 666 2316 73 78
## College of Mount St. Joseph 400 1150 46 46
## College of Mount St. Vincent 500 1000 75 77
## College of Notre Dame 630 2250 77 80
## College of Notre Dame of Maryland 600 700 64 64
## College of Saint Benedict 500 600 70 88
## College of Saint Catherine 450 1000 63 87
## College of Saint Elizabeth 380 1000 68 70
## College of Saint Rose 800 1500 66 71
## College of Santa Fe 600 1200 40 74
## College of St. Joseph 450 1300 53 53
## College of St. Scholastica 450 1146 54 76
## College of the Holy Cross 400 900 92 96
## College of William and Mary 600 800 89 92
## College of Wooster 500 500 84 96
## Colorado College 450 1200 85 97
## Colorado State University 470 1800 87 89
## Columbia College MO 400 900 87 87
## Columbia College 500 1500 61 77
## Columbia University 550 300 97 98
## Concordia College at St. Paul 450 950 69 75
## Concordia Lutheran College 450 1825 67 76
## Concordia University CA 570 1515 55 60
## Concordia University 400 1000 56 64
## Connecticut College 600 500 86 95
## Converse College 500 900 63 76
## Cornell College 550 800 71 76
## Creighton University 650 2055 85 90
## Culver-Stockton College 400 500 51 52
## Cumberland College 400 600 42 44
## D'Youville College 680 1320 68 68
## Dana College 450 1450 46 51
## Daniel Webster College 500 500 61 61
## Dartmouth College 550 1100 95 99
## Davidson College 600 1011 95 97
## Defiance College 400 1159 58 60
## Delta State University 500 1200 49 63
## Denison University 500 600 88 97
## DePauw University 550 950 78 94
## Dickinson College 595 1250 87 94
## Dickinson State University 600 2000 50 64
## Dillard University 500 2307 52 52
## Doane College 400 1000 67 72
## Dominican College of Blauvelt 600 1800 43 43
## Dordt College 450 2800 61 60
## Dowling College 450 1413 77 78
## Drake University 560 1675 88 93
## Drew University 520 660 93 97
## Drury College 500 750 82 92
## Duke University 625 1162 95 96
## Earlham College 600 600 90 94
## East Carolina University 500 1700 74 78
## East Tennessee State University 600 2200 73 75
## East Texas Baptist University 530 1500 62 62
## Eastern College 450 1230 60 60
## Eastern Connecticut State University 650 500 71 76
## Eastern Illinois University 120 1730 62 71
## Eastern Mennonite College 600 1300 46 65
## Eastern Nazarene College 450 700 58 58
## Eckerd College 600 1000 82 89
## Elizabethtown College 500 750 65 68
## Elmira College 450 550 77 98
## Elms College 450 1700 71 71
## Elon College 490 1777 70 74
## Embry Riddle Aeronautical University 570 3020 37 43
## Emory & Henry College 700 1600 79 88
## Emory University 600 870 97 98
## Emporia State University 450 1888 72 75
## Erskine College 475 1246 76 80
## Eureka College 330 670 62 87
## Evergreen State College 600 1323 75 78
## Fairfield University 700 1100 86 90
## Fayetteville State University 350 766 75 75
## Ferrum College 500 1600 53 58
## Flagler College 500 2140 52 60
## Florida Institute of Technology 750 1500 90 90
## Florida International University 800 3028 81 96
## Florida Southern College 400 650 65 74
## Florida State University 600 1020 80 89
## Fontbonne College 350 1500 45 55
## Fordham University 600 1735 86 97
## Fort Lewis College 500 2500 89 97
## Francis Marion University 400 2430 76 76
## Franciscan University of Steubenville 600 1000 57 69
## Franklin College 525 1345 54 78
## Franklin Pierce College 500 800 50 56
## Freed-Hardeman University 600 1600 68 76
## Fresno Pacific College 630 1818 59 59
## Furman University 600 1250 92 95
## Gannon University 500 1380 47 51
## Gardner Webb University 500 500 65 58
## Geneva College 500 1100 67 67
## George Fox College 400 1050 53 53
## George Mason University 580 1050 93 96
## George Washington University 700 950 92 93
## Georgetown College 550 550 73 76
## Georgetown University 670 1700 91 92
## Georgia Institute of Technology 795 1164 92 92
## Georgia State University 720 3450 87 89
## Georgian Court College 500 800 56 59
## Gettysburg College 500 500 94 95
## Goldey Beacom College 531 1830 25 25
## Gonzaga University 600 2400 78 90
## Gordon College 400 1200 73 82
## Goshen College 600 1230 51 56
## Goucher College 500 1200 78 90
## Grace College and Seminary 300 1000 53 59
## Graceland College 550 880 51 61
## Grand Valley State University 500 1000 64 66
## Green Mountain College 400 850 77 83
## Greensboro College 550 1300 64 80
## Greenville College 400 800 57 61
## Grinnell College 400 400 88 92
## Grove City College 525 350 65 65
## Guilford College 450 1050 78 86
## Gustavus Adolphus College 400 700 79 89
## Gwynedd Mercy College 500 500 36 41
## Hamilton College 300 800 91 96
## Hamline University 450 550 89 93
## Hampden - Sydney College 660 600 95 97
## Hampton University 600 2000 60 64
## Hanover College 500 1200 84 84
## Hardin-Simmons University 700 2140 75 79
## Harding University 700 910 71 77
## Hartwick College 500 700 75 87
## Harvard University 500 1920 97 97
## Harvey Mudd College 700 900 100 100
## Hastings College 500 1902 57 63
## Hendrix College 500 1200 82 99
## Hillsdale College 400 750 80 80
## Hiram College 400 1000 75 95
## Hobart and William Smith Colleges 600 600 99 99
## Hofstra University 1000 1000 81 90
## Hollins College 500 850 78 91
## Hood College 450 690 82 88
## Hope College 465 1100 72 81
## Houghton College 500 1500 85 90
## Huntingdon College 500 1100 63 72
## Huntington College 300 1300 76 76
## Huron University 600 1840 31 35
## Husson College 350 1500 36 44
## Illinois Benedictine College 650 1500 81 91
## Illinois College 600 1000 75 75
## Illinois Institute of Technology 500 700 80 88
## Illinois State University 537 2605 77 84
## Illinois Wesleyan University 400 650 77 92
## Immaculata College 500 1000 56 64
## Incarnate Word College 750 2775 67 69
## Indiana State University 600 2500 72 76
## Indiana University at Bloomington 600 2000 77 88
## Indiana Wesleyan University 700 1000 49 51
## Iona College 570 1150 66 83
## Iowa State University 640 2055 81 88
## Ithaca College 634 1000 58 79
## James Madison University 500 732 77 81
## Jamestown College 400 400 51 53
## Jersey City State College 400 1500 63 67
## John Brown University 400 1350 68 68
## John Carroll University 600 450 89 90
## Johns Hopkins University 500 1040 96 97
## Johnson State College 500 624 80 91
## Judson College 500 1700 34 55
## Juniata College 450 420 97 97
## Kansas State University 600 2000 76 86
## Kansas Wesleyan University 500 1400 63 55
## Keene State College 500 1150 73 73
## Kentucky Wesleyan College 500 1300 57 65
## Kenyon College 750 480 95 95
## Keuka College 600 750 55 94
## King's College 400 1795 66 72
## King College 600 3000 65 68
## Knox College 400 800 88 95
## La Roche College 600 1100 57 73
## La Salle University 450 3160 90 90
## Lafayette College 600 1000 93 96
## LaGrange College 750 1500 77 83
## Lake Forest College 920 1320 91 94
## Lakeland College 500 1000 49 65
## Lamar University 508 1463 48 82
## Lambuth University 600 1590 61 61
## Lander University 528 1702 67 77
## Lawrence University 525 975 76 92
## Le Moyne College 400 900 89 92
## Lebanon Valley College 400 1125 84 84
## Lehigh University 750 1130 96 99
## Lenoir-Rhyne College 400 1000 88 92
## Lesley College 550 805 71 88
## LeTourneau University 600 1400 58 70
## Lewis and Clark College 450 950 97 98
## Lewis University 500 1200 36 48
## Lincoln Memorial University 600 1300 67 72
## Lincoln University 350 1400 71 72
## Lindenwood College 1000 4200 65 85
## Linfield College 500 900 89 91
## Livingstone College 800 900 53 93
## Lock Haven University of Pennsylvania 225 500 47 55
## Longwood College 550 2200 74 80
## Loras College 500 1200 61 62
## Louisiana College 500 1655 64 74
## Louisiana State University at Baton Rouge 600 2242 83 87
## Louisiana Tech University 618 1656 66 77
## Loyola College 600 900 86 88
## Loyola Marymount University 545 1328 84 88
## Loyola University 600 750 77 88
## Loyola University Chicago 700 2000 94 95
## Luther College 600 400 73 85
## Lycoming College 500 900 75 81
## Lynchburg College 450 870 62 66
## Lyndon State College 500 600 48 65
## Macalester College 500 700 85 91
## MacMurray College 550 950 49 55
## Malone College 450 1200 42 45
## Manchester College 525 1450 63 72
## Manhattan College 500 1800 92 92
## Manhattanville College 450 400 97 97
## Mankato State University 450 1660 57 68
## Marian College of Fond du Lac 500 1100 37 37
## Marietta College 470 810 80 97
## Marist College 550 1200 74 81
## Marquette University 600 1950 86 94
## Marshall University 700 1560 77 86
## Mary Baldwin College 600 1300 66 79
## Mary Washington College 650 2102 75 80
## Marymount College Tarrytown 575 1075 71 93
## Marymount Manhattan College 350 1100 63 76
## Marymount University 500 750 77 82
## Maryville College 500 1642 80 90
## Maryville University 425 1350 52 58
## Marywood College 600 700 65 76
## Massachusetts Institute of Technology 725 1600 99 99
## Mayville State University 600 1900 68 68
## McKendree College 500 800 70 74
## McMurry University 400 1525 57 64
## McPherson College 600 2740 54 54
## Mercer University 400 1500 93 95
## Mercyhurst College 425 1000 45 63
## Meredith College 450 1520 77 82
## Merrimack College 375 1000 73 75
## Mesa State College 540 2256 48 48
## Messiah College 475 1200 68 75
## Miami University at Oxford 500 1382 81 89
## Michigan State University 504 600 93 95
## Michigan Technological University 900 1200 82 82
## MidAmerica Nazarene College 1100 4913 33 33
## Millersville University of Penn. 450 1258 72 74
## Milligan College 550 1000 63 69
## Millikin University 450 965 60 77
## Millsaps College 550 1350 82 89
## Milwaukee School of Engineering 1000 2075 35 46
## Mississippi College 600 700 77 79
## Mississippi State University 480 1479 77 77
## Mississippi University for Women 600 1500 49 54
## Missouri Southern State College 200 400 52 54
## Missouri Valley College 400 900 35 67
## Monmouth College IL 400 460 91 91
## Monmouth College 530 1740 70 85
## Montana College of Mineral Sci. & Tech. 550 1400 71 71
## Montana State University 550 2300 75 83
## Montclair State University 700 950 82 87
## Montreat-Anderson College 500 2958 42 50
## Moorhead State University 600 1000 76 81
## Moravian College 550 1250 86 92
## Morehouse College 250 600 71 74
## Morningside College 500 1000 48 68
## Morris College 850 2100 53 60
## Mount Holyoke College 750 750 79 91
## Mount Marty College 500 500 45 55
## Mount Mary College 550 1125 51 51
## Mount Mercy College 500 2285 44 50
## Mount Saint Clare College 500 1200 32 37
## Mount Saint Mary's College 550 900 77 82
## Mount Saint Mary College 250 1400 74 75
## Mount St. Mary's College 630 1278 53 71
## Mount Union College 400 1150 85 87
## Mount Vernon Nazarene College 600 600 57 57
## Muhlenberg College 600 850 76 86
## Murray State University 700 940 72 76
## Muskingum College 600 800 73 85
## National-Louis University 650 500 62 65
## Nazareth College of Rochester 550 800 77 93
## New Jersey Institute of Technology 700 1850 92 98
## New Mexico Institute of Mining and Tech. 600 1100 99 100
## New York University 450 1000 87 98
## Newberry College 500 1500 57 63
## Niagara University 450 650 68 100
## North Adams State College 500 1000 65 71
## North Carolina A. & T. State University 600 1651 72 72
## North Carolina State University at Raleigh 600 1300 92 98
## North Carolina Wesleyan College 600 1295 77 77
## North Central College 450 1800 73 87
## North Dakota State University 600 2000 79 83
## North Park College 400 970 76 79
## Northeast Missouri State University 400 1100 69 72
## Northeastern University 600 1750 73 82
## Northern Arizona University 620 2342 78 83
## Northern Illinois University 470 1750 73 78
## Northwest Missouri State University 250 1630 62 65
## Northwest Nazarene College 450 822 59 59
## Northwestern College 300 1800 68 68
## Northwestern University 759 1585 96 100
## Norwich University 500 800 71 74
## Notre Dame College 400 600 44 47
## Oakland University 400 650 88 90
## Oberlin College 575 1119 77 96
## Occidental College 558 1152 91 93
## Oglethorpe University 600 4110 91 95
## Ohio Northern University 600 825 73 78
## Ohio University 550 2300 79 87
## Ohio Wesleyan University 550 550 93 93
## Oklahoma Baptist University 515 1290 63 71
## Oklahoma Christian University 500 1900 58 64
## Oklahoma State University 800 3100 84 92
## Otterbein College 420 840 62 68
## Ouachita Baptist University 500 1500 63 67
## Our Lady of the Lake University 616 1576 56 64
## Pace University 660 1115 90 95
## Pacific Lutheran University 600 1516 78 78
## Pacific Union College 630 1926 48 87
## Pacific University 450 1100 76 76
## Pembroke State University 550 1498 77 77
## Pennsylvania State Univ. Main Campus 512 2394 77 96
## Pepperdine University 500 700 95 98
## Peru State College 500 900 48 100
## Pfeiffer College 400 1915 62 62
## Philadelphia Coll. of Textiles and Sci. 600 1664 48 80
## Phillips University 600 940 58 64
## Piedmont College 600 750 89 89
## Pikeville College 500 500 48 57
## Pitzer College 650 850 100 100
## Point Loma Nazarene College 800 750 71 71
## Point Park College 400 1200 45 90
## Polytechnic University 436 2486 90 90
## Prairie View A. and M. University 598 1582 55 93
## Presbyterian College 554 1429 80 85
## Princeton University 675 1575 91 96
## Providence College 450 1100 66 74
## Purdue University at West Lafayette 570 1060 86 86
## Queens College 610 1900 73 75
## Quincy University 450 1080 69 71
## Quinnipiac College 1000 500 63 73
## Radford University 500 900 73 83
## Ramapo College of New Jersey 600 1655 74 95
## Randolph-Macon College 400 900 77 80
## Randolph-Macon Woman's College 370 920 88 97
## Reed College 500 450 90 90
## Regis College 450 700 81 85
## Rensselaer Polytechnic Institute 1230 1100 94 98
## Rhodes College 550 1500 90 96
## Rider University 700 3100 84 92
## Ripon College 350 650 87 90
## Rivier College 600 1100 59 59
## Roanoke College 450 1200 85 89
## Rockhurst College 500 1500 60 79
## Rocky Mountain College 600 625 56 78
## Roger Williams University 500 730 44 54
## Rollins College 955 750 81 85
## Rosary College 550 950 79 82
## Rowan College of New Jersey 800 800 76 81
## Rutgers at New Brunswick 690 2009 90 95
## Rutgers State University at Camden 690 2009 90 95
## Rutgers State University at Newark 690 2009 90 95
## Sacred Heart University 400 600 71 73
## Saint Ambrose University 500 1500 56 56
## Saint Anselm College 450 1120 70 82
## Saint Cloud State University 350 1884 70 75
## Saint Francis College IN 450 1000 43 78
## Saint Francis College 400 1235 64 64
## Saint John's University 500 600 76 85
## Saint Joseph's College IN 600 950 55 60
## Saint Joseph's College 500 800 53 89
## Saint Joseph's University 350 1690 84 90
## Saint Joseph College 650 950 87 90
## Saint Louis University 800 6800 84 94
## Saint Mary's College 500 1525 74 95
## Saint Mary's College of Minnesota 400 820 68 74
## Saint Mary-of-the-Woods College 500 1700 44 58
## Saint Michael's College 500 750 79 88
## Saint Olaf College 550 550 82 88
## Saint Peter's College 500 450 78 78
## Saint Vincent College 500 900 62 64
## Saint Xavier University 600 794 87 100
## Salem-Teikyo University 400 620 46 24
## Salem College 500 2000 68 68
## Salisbury State University 600 1450 73 75
## Samford University 569 1650 74 75
## San Diego State University 612 2400 87 93
## Santa Clara University 630 1278 88 92
## Sarah Lawrence College 600 700 89 93
## Savannah Coll. of Art and Design 1200 1600 14 98
## Schreiner College 500 1488 51 56
## Scripps College 600 800 95 100
## Seattle Pacific University 600 1250 83 85
## Seattle University 500 1500 85 85
## Seton Hall University 650 1000 81 84
## Seton Hill College 350 2000 71 71
## Shippensburg University of Penn. 450 1700 80 83
## Shorter College 500 2000 62 65
## Siena College 575 1090 71 82
## Siena Heights College 475 1090 29 49
## Simmons College 500 1200 74 81
## Simpson College 550 1400 66 73
## Sioux Falls College 500 1700 73 73
## Skidmore College 500 700 87 92
## Smith College 500 1050 85 97
## South Dakota State University 500 1970 62 65
## Southeast Missouri State University 200 2150 75 76
## Southeastern Oklahoma State Univ. 450 1022 55 59
## Southern California College 630 1818 63 65
## Southern Illinois University at Edwardsville 221 2216 76 81
## Southern Methodist University 576 1802 74 88
## Southwest Baptist University 400 1000 52 54
## Southwest Missouri State University 500 1360 70 75
## Southwest State University 600 1800 58 75
## Southwestern Adventist College 430 1651 44 77
## Southwestern College 550 1500 56 56
## Southwestern University 600 1050 83 89
## Spalding University 600 900 50 56
## Spelman College 660 2400 73 80
## Spring Arbor College 385 665 48 48
## St. Bonaventure University 500 1050 91 91
## St. John's College 275 800 63 72
## St. John Fisher College 400 800 86 81
## St. Lawrence University 650 825 90 94
## St. Martin's College 300 500 43 77
## St. Mary's College of California 630 1584 88 89
## St. Mary's College of Maryland 675 1250 84 89
## St. Mary's University of San Antonio 700 1736 82 83
## St. Norbert College 425 1100 74 78
## St. Paul's College 600 600 45 45
## St. Thomas Aquinas College 500 1750 69 73
## Stephens College 450 2150 46 63
## Stetson University 600 1365 85 90
## Stevens Institute of Technology 450 750 89 89
## Stockton College of New Jersey 711 1125 78 92
## Stonehill College 480 800 79 79
## SUNY at Albany 700 1560 93 96
## SUNY at Binghamton 700 1000 83 100
## SUNY at Buffalo 708 957 90 97
## SUNY at Stony Brook 600 1200 91 96
## SUNY College at Brockport 500 705 79 83
## SUNY College at Oswego 500 1500 69 85
## SUNY College at Buffalo 550 1230 71 78
## SUNY College at Cortland 630 1274 82 85
## SUNY College at Fredonia 620 1481 82 90
## SUNY College at Geneseo 600 650 79 84
## SUNY College at New Paltz 550 1500 85 93
## SUNY College at Plattsburgh 600 1380 80 90
## SUNY College at Potsdam 500 1000 71 75
## SUNY College at Purchase 1125 1362 80 100
## Susquehanna University 400 800 83 86
## Sweet Briar College 500 600 91 99
## Syracuse University 635 960 73 84
## Tabor College 400 1500 55 70
## Talladega College 1000 1400 56 58
## Taylor University 450 1250 60 61
## Tennessee Wesleyan College 400 3158 59 65
## Texas A&M Univ. at College Station 600 2144 89 91
## Texas A&M University at Galveston 600 650 103 88
## Texas Christian University 650 2400 81 93
## Texas Lutheran College 490 1700 54 58
## Texas Southern University 600 1700 65 75
## Texas Wesleyan University 600 1800 80 83
## The Citadel 400 779 95 94
## Thiel College 700 1350 68 76
## Tiffin University 600 1200 59 74
## Transylvania University 500 1000 81 91
## Trenton State College 700 1000 81 87
## Tri-State University 468 1323 53 53
## Trinity College CT 500 680 91 96
## Trinity College DC 500 900 89 93
## Trinity College VT 550 500 58 78
## Trinity University 500 490 94 96
## Tulane University 350 800 98 98
## Tusculum College 450 800 70 70
## Tuskegee University 600 1425 70 74
## Union College KY 500 600 60 88
## Union College NY 450 1024 94 96
## Univ. of Wisconsin at OshKosh 518 1890 73 78
## University of Alabama at Birmingham 750 2200 96 96
## University of Arkansas at Fayetteville 500 2000 73 89
## University of California at Berkeley 636 1933 93 97
## University of California at Irvine 790 1818 96 96
## University of Central Florida 700 1600 80 98
## University of Charleston 400 750 26 58
## University of Chicago 500 1254 99 99
## University of Cincinnati 556 1851 89 95
## University of Connecticut at Storrs 700 2300 89 95
## University of Dallas 500 1200 85 93
## University of Dayton 500 900 81 85
## University of Delaware 530 1300 82 87
## University of Denver 400 1350 84 91
## University of Detroit Mercy 600 2166 72 79
## University of Dubuque 400 1500 85 98
## University of Evansville 700 960 60 81
## University of Florida 630 1530 88 97
## University of Georgia 525 1755 88 95
## University of Hartford 500 1440 61 76
## University of Hawaii at Manoa 687 1281 85 87
## University of Illinois - Urbana 500 1982 87 90
## University of Illinois at Chicago 630 3228 82 84
## University of Indianapolis 525 1405 55 56
## University of Kansas 700 2681 88 94
## University of La Verne 630 2298 66 68
## University of Louisville 530 2440 84 92
## University of Maine at Farmington 450 1647 67 75
## University of Maine at Machias 600 400 46 46
## University of Maine at Presque Isle 400 1675 67 67
## University of Maryland at Baltimore County 494 2768 82 88
## University of Maryland at College Park 550 1550 89 92
## University of Massachusetts at Amherst 500 1400 88 92
## University of Massachusetts at Dartmouth 500 1250 74 90
## University of Miami 630 1985 82 94
## University of Michigan at Ann Arbor 476 1600 90 98
## University of Minnesota at Duluth 753 2610 79 91
## University of Minnesota at Morris 600 1500 74 78
## University of Minnesota Twin Cities 714 2910 88 90
## University of Mississippi 600 550 81 86
## University of Missouri at Columbia 600 1983 87 87
## University of Missouri at Rolla 700 1435 88 88
## University of Missouri at Saint Louis 500 4288 71 73
## University of Mobile 550 1200 59 63
## University of Montevallo 300 600 72 72
## University of Nebraska at Lincoln 500 2070 86 92
## University of New England 900 2500 72 75
## University of New Hampshire 650 2450 89 87
## University of North Carolina at Asheville 600 750 77 83
## University of North Carolina at Chapel Hill 550 1200 88 93
## University of North Carolina at Charlotte 600 1900 79 91
## University of North Carolina at Greensboro 600 1300 75 94
## University of North Carolina at Wilmington 500 1500 82 85
## University of North Dakota 450 1200 97 97
## University of North Florida 600 2604 82 85
## University of North Texas 450 1700 86 94
## University of Northern Colorado 540 2286 75 75
## University of Northern Iowa 595 2380 78 82
## University of Notre Dame 600 1350 96 92
## University of Oklahoma 765 3176 86 90
## University of Oregon 570 1530 79 87
## University of Pennsylvania 500 1544 95 96
## University of Pittsburgh-Main Campus 400 900 93 93
## University of Portland 600 1100 92 96
## University of Puget Sound 630 1800 79 86
## University of Rhode Island 500 1250 84 89
## University of Richmond 700 1125 75 89
## University of Rochester 500 882 93 99
## University of San Diego 630 1820 93 96
## University of San Francisco 750 2450 86 86
## University of Sci. and Arts of Oklahoma 600 1800 67 77
## University of Scranton 650 800 83 83
## University of South Carolina at Aiken 500 1500 62 62
## University of South Carolina at Columbia 495 2941 84 88
## University of South Florida 500 2180 84 89
## University of Southern California 600 2210 90 94
## University of Southern Colorado 540 2948 63 88
## University of Southern Indiana 500 1425 56 65
## University of Southern Mississippi 500 500 78 99
## University of St. Thomas MN 500 800 80 80
## University of St. Thomas TX 500 1344 75 75
## University of Tennessee at Knoxville 750 3300 86 92
## University of Texas at Arlington 500 2850 73 73
## University of Texas at Austin 650 3140 91 99
## University of Texas at San Antonio 452 1200 94 100
## University of the Arts 1300 700 16 59
## University of the Pacific 646 1171 87 94
## University of the South 450 810 89 93
## University of Tulsa 1200 2350 94 96
## University of Utah 858 3093 89 93
## University of Vermont 500 990 87 90
## University of Virginia 500 1000 90 92
## University of Washington 708 2172 96 94
## University of West Florida 541 1387 83 87
## University of Wisconsin-Stout 376 1750 78 78
## University of Wisconsin-Superior 550 1960 75 81
## University of Wisconsin-Whitewater 300 1200 90 95
## University of Wisconsin at Green Bay 475 1200 81 89
## University of Wisconsin at Madison 535 1545 93 96
## University of Wisconsin at Milwaukee 570 1980 79 87
## University of Wyoming 600 1500 91 94
## Upper Iowa University 500 1000 69 75
## Ursinus College 500 800 82 85
## Ursuline College 450 750 39 69
## Valley City State University 600 2000 39 41
## Valparaiso University 500 800 87 89
## Vanderbilt University 630 952 93 98
## Vassar College 600 800 90 98
## Villanova University 400 300 89 90
## Virginia Commonwealth University 500 3630 81 87
## Virginia State University 500 600 61 63
## Virginia Tech 740 2200 85 89
## Virginia Union University 500 1763 51 67
## Virginia Wesleyan College 500 550 70 81
## Viterbo College 500 2245 51 65
## Voorhees College 500 1200 43 43
## Wabash College 500 635 78 85
## Wagner College 585 1700 67 78
## Wake Forest University 500 1250 95 97
## Walsh University 500 1450 42 58
## Warren Wilson College 400 1100 65 75
## Wartburg College 400 850 66 91
## Washington and Jefferson College 300 500 91 91
## Washington and Lee University 680 1115 81 96
## Washington College 500 300 79 86
## Washington State University 800 2719 84 87
## Washington University 768 1512 91 98
## Wayne State College 540 1660 60 68
## Waynesburg College 500 1200 57 58
## Webber College 650 1952 53 63
## Webster University 500 500 68 68
## Wellesley College 500 700 94 98
## Wells College 600 500 93 98
## Wentworth Institute of Technology 850 920 10 68
## Wesley College 500 1350 52 57
## Wesleyan University 1400 1400 90 94
## West Chester University of Penn. 400 2000 76 79
## West Liberty State College 600 1210 33 33
## West Virginia Wesleyan College 450 1100 58 81
## Western Carolina University 110 1622 67 78
## Western Maryland College 500 1400 84 91
## Western Michigan University 500 1700 80 84
## Western New England College 498 2065 74 97
## Western State College of Colorado 500 2050 76 79
## Western Washington University 639 2385 83 89
## Westfield State College 500 1300 75 79
## Westminster College MO 600 1650 66 70
## Westminster College 430 685 62 78
## Westminster College of Salt Lake City 600 2025 68 83
## Westmont College 490 1410 77 77
## Wheaton College IL 530 1400 81 83
## Westminster College PA 700 850 92 96
## Wheeling Jesuit College 600 600 66 71
## Whitman College 750 800 80 83
## Whittier College 500 1998 84 92
## Whitworth College 678 2424 80 80
## Widener University 500 1350 88 86
## Wilkes University 550 1260 78 92
## Willamette University 400 790 91 94
## William Jewell College 500 2600 74 80
## William Woods University 550 3700 39 66
## Williams College 500 1200 94 99
## Wilson College 450 475 67 76
## Wingate College 550 1550 69 81
## Winona State University 300 1200 53 60
## Winthrop University 580 2150 71 80
## Wisconsin Lutheran College 500 1400 48 48
## Wittenberg University 400 800 82 95
## Wofford College 605 1440 91 92
## Worcester Polytechnic Institute 530 730 92 94
## Worcester State College 500 1200 60 60
## Xavier University 600 1250 73 75
## Xavier University of Louisiana 617 781 67 75
## Yale University 630 2115 96 96
## York College of Pennsylvania 500 1250 75 75
## S.F.Ratio perc.alumni Expend
## Abilene Christian University 18.1 12 7041
## Adelphi University 12.2 16 10527
## Adrian College 12.9 30 8735
## Agnes Scott College 7.7 37 19016
## Alaska Pacific University 11.9 2 10922
## Albertson College 9.4 11 9727
## Albertus Magnus College 11.5 26 8861
## Albion College 13.7 37 11487
## Albright College 11.3 23 11644
## Alderson-Broaddus College 11.5 15 8991
## Alfred University 11.3 31 10932
## Allegheny College 9.9 41 11711
## Allentown Coll. of St. Francis de Sales 13.3 21 7940
## Alma College 15.3 32 9305
## Alverno College 11.1 26 8127
## American International College 14.7 19 7355
## Amherst College 8.4 63 21424
## Anderson University 12.1 14 7994
## Andrews University 11.5 18 10908
## Angelo State University 23.1 5 4010
## Antioch University 11.3 35 42926
## Appalachian State University 18.3 14 5854
## Aquinas College 12.7 25 6584
## Arizona State University Main campus 18.9 5 4602
## Arkansas College (Lyon College) 12.6 24 14579
## Arkansas Tech University 19.6 5 4739
## Assumption College 13.8 30 7100
## Auburn University-Main Campus 16.7 18 6642
## Augsburg College 12.8 31 7836
## Augustana College IL 12.7 40 9220
## Augustana College 10.4 30 6871
## Austin College 13.0 33 11361
## Averett College 22.4 11 6523
## Baker University 11.0 21 6136
## Baldwin-Wallace College 17.6 20 8086
## Barat College 9.7 35 9337
## Bard College 10.4 30 13894
## Barnard College 10.3 33 12580
## Barry University 12.6 11 9084
## Baylor University 18.5 38 7503
## Beaver College 12.2 30 8954
## Bellarmine College 13.1 31 6668
## Belmont Abbey College 13.2 10 7550
## Belmont University 11.1 19 7614
## Beloit College 11.1 26 12957
## Bemidji State University 19.6 16 3752
## Benedictine College 14.1 18 5922
## Bennington College 10.1 33 16364
## Bentley College 17.5 20 10941
## Berry College 16.3 17 10511
## Bethany College 11.6 29 7718
## Bethel College KS 8.8 32 8324
## Bethel College 11.7 13 7623
## Bethune Cookman College 13.8 9 6817
## Birmingham-Southern College 14.0 34 8649
## Blackburn College 14.3 53 8377
## Bloomsburg Univ. of Pennsylvania 18.0 19 7041
## Bluefield College 17.8 3 6259
## Bluffton College 13.3 19 9073
## Boston University 11.9 16 16836
## Bowdoin College 11.2 52 20447
## Bowling Green State University 21.1 14 6918
## Bradford College 10.2 21 15387
## Bradley University 14.4 21 7671
## Brandeis University 9.8 24 17150
## Brenau University 13.7 12 5935
## Brewton-Parker College 12.6 10 4900
## Briar Cliff College 13.1 26 8355
## Bridgewater College 13.2 24 8655
## Brigham Young University at Provo 20.5 40 7916
## Brown University 7.6 39 20440
## Bryn Mawr College 12.3 49 17449
## Bucknell University 14.2 36 13675
## Buena Vista College 8.8 10 6333
## Butler University 10.9 29 9511
## Cabrini College 16.5 36 7117
## Caldwell College 13.9 25 7922
## California Lutheran University 12.4 17 8985
## California Polytechnic-San Luis 19.8 13 8453
## California State University at Fresno 21.2 8 7268
## Calvin College 14.8 41 7786
## Campbell University 21.8 34 3739
## Campbellsville College 17.7 13 5391
## Canisius College 14.6 26 7972
## Capital University 12.1 27 9557
## Capitol College 12.1 24 7976
## Carleton College 10.4 60 17960
## Carnegie Mellon University 9.2 31 24386
## Carroll College 17.8 25 7666
## Carson-Newman College 13.6 16 6716
## Carthage College 15.9 22 7364
## Case Western Reserve University 2.9 29 19733
## Castleton State College 14.7 8 6318
## Catawba College 13.5 27 8425
## Catholic University of America 9.3 18 12751
## Cazenovia College 14.3 20 7697
## Cedar Crest College 11.7 39 10961
## Cedarville College 15.3 34 6897
## Centenary College 9.5 20 9583
## Centenary College of Louisiana 11.3 25 9685
## Center for Creative Studies 6.8 4 13025
## Central College 13.5 29 8444
## Central Connecticut State University 16.7 4 4900
## Central Missouri State University 19.7 4 5501
## Central Washington University 18.1 0 6413
## Central Wesleyan College 15.2 18 3365
## Centre College 11.4 60 13118
## Chapman University 12.8 6 12692
## Chatham College 9.3 37 16095
## Chestnut Hill College 8.3 29 7729
## Christendom College 9.3 17 10922
## Christian Brothers University 11.1 24 8129
## Christopher Newport University 21.2 16 4639
## Claflin College 16.9 31 7083
## Claremont McKenna College 9.6 52 18443
## Clark University 10.5 35 11951
## Clarke College 11.0 27 7963
## Clarkson University 15.8 32 11659
## Clemson University 18.0 17 7597
## Clinch Valley Coll. of the Univ. of Virginia 18.1 9 4417
## Coe College 12.7 32 10141
## Coker College 12.1 39 8741
## Colby College 10.2 41 15954
## Colgate University 10.5 45 15494
## College Misericordia 12.9 23 8604
## College of Charleston 17.2 18 4776
## College of Mount St. Joseph 11.1 35 6889
## College of Mount St. Vincent 11.9 35 10015
## College of Notre Dame 10.4 7 9773
## College of Notre Dame of Maryland 11.5 32 7477
## College of Saint Benedict 13.1 26 8847
## College of Saint Catherine 11.5 32 7315
## College of Saint Elizabeth 11.4 23 9447
## College of Saint Rose 14.3 28 6084
## College of Santa Fe 14.0 7 8820
## College of St. Joseph 9.5 19 6936
## College of St. Scholastica 11.6 33 8996
## College of the Holy Cross 11.3 55 12138
## College of William and Mary 12.1 31 9534
## College of Wooster 11.1 43 14140
## Colorado College 11.3 51 14664
## Colorado State University 19.2 10 7850
## Columbia College MO 15.3 2 5015
## Columbia College 14.7 34 8693
## Columbia University 5.9 21 30639
## Concordia College at St. Paul 12.8 18 6955
## Concordia Lutheran College 12.1 9 6875
## Concordia University CA 13.1 13 8415
## Concordia University 12.1 13 7309
## Connecticut College 10.7 40 14773
## Converse College 10.2 31 10965
## Cornell College 12.2 31 10340
## Creighton University 6.5 32 22906
## Culver-Stockton College 14.1 28 5807
## Cumberland College 13.0 4 8189
## D'Youville College 14.6 42 6898
## Dana College 12.6 25 8686
## Daniel Webster College 22.2 10 8643
## Dartmouth College 4.7 49 29619
## Davidson College 12.0 46 17581
## Defiance College 12.8 19 7505
## Delta State University 17.1 16 5113
## Denison University 11.6 45 12423
## DePauw University 11.1 31 11525
## Dickinson College 11.2 39 13861
## Dickinson State University 16.5 28 4525
## Dillard University 14.1 12 7566
## Doane College 15.1 42 6852
## Dominican College of Blauvelt 12.7 5 5480
## Dordt College 12.5 17 7325
## Dowling College 12.4 7 11178
## Drake University 15.0 24 9473
## Drew University 10.2 28 14907
## Drury College 13.2 35 9303
## Duke University 5.0 44 27206
## Earlham College 10.6 46 14634
## East Carolina University 13.2 18 9002
## East Tennessee State University 14.0 9 9825
## East Texas Baptist University 15.7 7 5619
## Eastern College 13.6 22 8135
## Eastern Connecticut State University 16.9 14 5719
## Eastern Illinois University 16.2 5 5682
## Eastern Mennonite College 11.4 29 10188
## Eastern Nazarene College 17.3 17 6430
## Eckerd College 12.8 26 15003
## Elizabethtown College 12.8 25 9815
## Elmira College 21.5 21 7502
## Elms College 11.3 21 8952
## Elon College 18.9 34 6329
## Embry Riddle Aeronautical University 16.5 4 12878
## Emory & Henry College 13.9 51 8061
## Emory University 5.0 28 28457
## Emporia State University 19.3 4 5527
## Erskine College 13.5 47 7527
## Eureka College 10.6 31 9552
## Evergreen State College 18.1 14 8355
## Fairfield University 15.1 30 11220
## Fayetteville State University 15.1 10 6972
## Ferrum College 12.5 9 7967
## Flagler College 18.1 9 3930
## Florida Institute of Technology 10.6 7 8923
## Florida International University 13.9 20 6722
## Florida Southern College 17.4 10 6339
## Florida State University 23.1 15 7250
## Fontbonne College 21.5 24 4607
## Fordham University 14.4 14 10864
## Fort Lewis College 19.1 6 4362
## Francis Marion University 19.1 8 5039
## Franciscan University of Steubenville 14.9 8 6336
## Franklin College 12.5 37 11751
## Franklin Pierce College 17.6 16 6418
## Freed-Hardeman University 16.1 13 6078
## Fresno Pacific College 10.5 14 8095
## Furman University 13.5 28 12940
## Gannon University 13.3 18 7711
## Gardner Webb University 15.2 12 5664
## Geneva College 20.1 26 6786
## George Fox College 13.5 22 7136
## George Mason University 19.3 7 6751
## George Washington University 7.6 15 14745
## Georgetown College 13.3 28 7508
## Georgetown University 7.2 27 19635
## Georgia Institute of Technology 19.3 33 11271
## Georgia State University 19.0 10 7762
## Georgian Court College 12.2 27 7348
## Gettysburg College 12.1 32 14720
## Goldey Beacom College 27.6 4 6081
## Gonzaga University 14.7 32 9553
## Gordon College 14.2 32 9226
## Goshen College 9.9 46 10270
## Goucher College 9.2 34 16623
## Grace College and Seminary 15.3 26 9798
## Graceland College 23.6 24 5609
## Grand Valley State University 20.6 9 5063
## Green Mountain College 14.0 24 6475
## Greensboro College 13.0 31 7949
## Greenville College 14.3 16 8222
## Grinnell College 9.5 54 18979
## Grove City College 18.4 18 4957
## Guilford College 15.6 30 9114
## Gustavus Adolphus College 12.5 58 9907
## Gwynedd Mercy College 7.8 22 7483
## Hamilton College 9.6 60 17761
## Hamline University 13.0 33 10296
## Hampden - Sydney College 13.3 53 12263
## Hampton University 14.0 9 6791
## Hanover College 10.6 26 9248
## Hardin-Simmons University 13.7 10 7054
## Harding University 17.7 37 6466
## Hartwick College 12.3 32 11625
## Harvard University 9.9 52 37219
## Harvey Mudd College 8.2 46 21569
## Hastings College 13.0 17 7335
## Hendrix College 13.1 26 8588
## Hillsdale College 12.0 31 12639
## Hiram College 10.6 34 12165
## Hobart and William Smith Colleges 12.1 37 13040
## Hofstra University 13.9 10 10093
## Hollins College 11.1 48 13957
## Hood College 14.4 34 12434
## Hope College 12.5 40 9284
## Houghton College 15.0 24 8187
## Huntingdon College 11.4 9 7703
## Huntington College 11.8 25 9466
## Huron University 12.9 4 9249
## Husson College 22.0 4 4923
## Illinois Benedictine College 11.6 29 8324
## Illinois College 15.6 30 7348
## Illinois Institute of Technology 12.3 26 12851
## Illinois State University 21.0 16 5569
## Illinois Wesleyan University 12.9 34 9605
## Immaculata College 11.2 33 7305
## Incarnate Word College 11.4 21 6095
## Indiana State University 16.6 8 6996
## Indiana University at Bloomington 21.3 24 8686
## Indiana Wesleyan University 39.8 15 6562
## Iona College 16.0 14 8107
## Iowa State University 19.2 22 8420
## Ithaca College 11.5 25 9812
## James Madison University 17.9 29 5212
## Jamestown College 17.0 21 3186
## Jersey City State College 14.9 10 8367
## John Brown University 13.3 19 8118
## John Carroll University 14.5 28 7738
## Johns Hopkins University 3.3 38 56233
## Johnson State College 14.4 15 6564
## Judson College 10.6 30 7840
## Juniata College 12.7 37 12067
## Kansas State University 18.5 22 6122
## Kansas Wesleyan University 12.4 14 6535
## Keene State College 16.1 13 6195
## Kentucky Wesleyan College 11.3 32 7058
## Kenyon College 11.1 46 14067
## Keuka College 13.3 43 7863
## King's College 15.6 37 7649
## King College 10.7 25 8954
## Knox College 12.7 33 13224
## La Roche College 14.2 14 7022
## La Salle University 15.1 9 9084
## Lafayette College 10.5 38 15365
## LaGrange College 12.5 12 9067
## Lake Forest College 10.7 19 15687
## Lakeland College 17.2 25 4054
## Lamar University 18.4 12 5879
## Lambuth University 16.1 10 5531
## Lander University 17.0 11 6119
## Lawrence University 10.1 57 13965
## Le Moyne College 13.3 28 8118
## Lebanon Valley College 12.3 30 8196
## Lehigh University 12.5 43 14665
## Lenoir-Rhyne College 12.0 20 8539
## Lesley College 27.8 18 8694
## LeTourneau University 20.8 23 6863
## Lewis and Clark College 12.3 21 12999
## Lewis University 14.3 10 7701
## Lincoln Memorial University 14.6 35 5177
## Lincoln University 12.6 8 10912
## Lindenwood College 24.1 9 3480
## Linfield College 17.8 34 8747
## Livingstone College 10.4 16 9268
## Lock Haven University of Pennsylvania 16.1 14 6374
## Longwood College 18.4 23 5553
## Loras College 14.2 24 7578
## Louisiana College 10.5 11 7547
## Louisiana State University at Baton Rouge 15.9 11 6741
## Louisiana Tech University 20.0 13 4546
## Loyola College 14.7 27 9448
## Loyola Marymount University 14.2 10 11677
## Loyola University 11.7 14 9456
## Loyola University Chicago 6.2 15 13009
## Luther College 13.8 38 8949
## Lycoming College 14.0 32 8024
## Lynchburg College 12.4 24 8832
## Lyndon State College 12.6 15 7114
## Macalester College 11.9 37 14213
## MacMurray College 10.8 33 10642
## Malone College 17.6 16 4796
## Manchester College 11.8 20 7940
## Manhattan College 13.6 25 10062
## Manhattanville College 11.3 24 11291
## Mankato State University 19.0 11 5801
## Marian College of Fond du Lac 8.4 21 5352
## Marietta College 13.2 30 10223
## Marist College 17.6 34 8408
## Marquette University 13.5 25 9982
## Marshall University 16.6 10 6203
## Mary Baldwin College 6.8 50 10819
## Mary Washington College 17.6 30 5358
## Marymount College Tarrytown 10.3 30 10502
## Marymount Manhattan College 11.7 20 10622
## Marymount University 10.6 17 8575
## Maryville College 11.1 43 8317
## Maryville University 13.1 13 5925
## Marywood College 11.8 30 9034
## Massachusetts Institute of Technology 10.1 35 33541
## Mayville State University 15.7 11 6971
## McKendree College 17.7 21 6652
## McMurry University 11.0 11 6383
## McPherson College 9.8 45 9754
## Mercer University 9.2 15 8995
## Mercyhurst College 16.7 29 7307
## Meredith College 13.9 33 6881
## Merrimack College 16.8 22 8707
## Mesa State College 28.8 12 3871
## Messiah College 14.1 30 7762
## Miami University at Oxford 17.6 20 7846
## Michigan State University 14.0 9 10520
## Michigan Technological University 17.0 25 7473
## MidAmerica Nazarene College 15.4 20 5524
## Millersville University of Penn. 16.8 20 7832
## Milligan College 12.0 16 8128
## Millikin University 11.4 25 8149
## Millsaps College 12.7 38 11218
## Milwaukee School of Engineering 16.7 23 7140
## Mississippi College 16.5 18 6170
## Mississippi State University 15.9 20 6223
## Mississippi University for Women 15.8 8 5704
## Missouri Southern State College 20.3 9 4172
## Missouri Valley College 17.4 16 4333
## Monmouth College IL 11.6 43 11087
## Monmouth College 14.2 15 9492
## Montana College of Mineral Sci. & Tech. 16.4 31 6112
## Montana State University 17.6 8 6324
## Montclair State University 21.5 9 6717
## Montreat-Anderson College 11.1 4 11989
## Moorhead State University 18.1 19 4795
## Moravian College 15.2 28 9566
## Morehouse College 17.8 10 8122
## Morningside College 13.0 32 8111
## Morris College 18.6 34 6990
## Mount Holyoke College 9.0 51 18359
## Mount Marty College 11.7 38 5073
## Mount Mary College 10.7 26 7016
## Mount Mercy College 11.3 30 6695
## Mount Saint Clare College 13.6 43 6525
## Mount Saint Mary's College 12.8 36 8536
## Mount Saint Mary College 15.3 23 6898
## Mount St. Mary's College 11.9 19 10613
## Mount Union College 16.7 35 7215
## Mount Vernon Nazarene College 19.8 7 6869
## Muhlenberg College 12.8 39 10888
## Murray State University 20.2 27 5972
## Muskingum College 13.4 27 9333
## National-Louis University 18.3 2 7905
## Nazareth College of Rochester 13.6 24 8797
## New Jersey Institute of Technology 13.5 19 12529
## New Mexico Institute of Mining and Tech. 13.7 11 9241
## New York University 7.8 16 21227
## Newberry College 11.4 32 5788
## Niagara University 14.2 20 7788
## North Adams State College 14.2 17 6562
## North Carolina A. & T. State University 16.7 9 7090
## North Carolina State University at Raleigh 17.5 21 9670
## North Carolina Wesleyan College 12.7 11 10090
## North Central College 16.4 33 8871
## North Dakota State University 17.0 24 6310
## North Park College 13.1 24 10889
## Northeast Missouri State University 15.7 13 6601
## Northeastern University 12.9 17 9563
## Northern Arizona University 21.7 7 6157
## Northern Illinois University 17.3 11 6086
## Northwest Missouri State University 21.7 23 5284
## Northwest Nazarene College 14.8 20 6261
## Northwestern College 14.9 34 6357
## Northwestern University 6.8 25 26385
## Norwich University 13.1 22 9209
## Notre Dame College 12.1 26 4948
## Oakland University 19.7 13 6637
## Oberlin College 10.1 47 16593
## Occidental College 10.5 30 16196
## Oglethorpe University 13.1 27 8568
## Ohio Northern University 14.5 31 9979
## Ohio University 20.4 13 8811
## Ohio Wesleyan University 12.1 32 12011
## Oklahoma Baptist University 15.1 18 5511
## Oklahoma Christian University 16.2 8 6578
## Oklahoma State University 15.3 14 6433
## Otterbein College 13.9 30 8802
## Ouachita Baptist University 13.3 10 6413
## Our Lady of the Lake University 14.9 25 7114
## Pace University 13.8 10 10059
## Pacific Lutheran University 11.0 23 9431
## Pacific Union College 12.3 12 9157
## Pacific University 10.9 22 11216
## Pembroke State University 15.0 5 6443
## Pennsylvania State Univ. Main Campus 18.1 19 8992
## Pepperdine University 11.6 13 16185
## Peru State College 20.1 24 4870
## Pfeiffer College 12.2 13 7634
## Philadelphia Coll. of Textiles and Sci. 12.9 15 8028
## Phillips University 11.6 19 8990
## Piedmont College 13.2 17 7309
## Pikeville College 13.4 14 5557
## Pitzer College 10.4 11 14820
## Point Loma Nazarene College 16.1 19 7895
## Point Park College 14.5 10 7652
## Polytechnic University 10.4 14 14329
## Prairie View A. and M. University 19.4 1 5967
## Presbyterian College 13.4 42 8354
## Princeton University 8.4 54 28320
## Providence College 18.4 35 8135
## Purdue University at West Lafayette 18.2 15 8604
## Queens College 14.0 36 9315
## Quincy University 16.3 32 6880
## Quinnipiac College 12.0 33 8847
## Radford University 19.6 9 4519
## Ramapo College of New Jersey 17.8 8 7333
## Randolph-Macon College 10.7 38 11080
## Randolph-Macon Woman's College 9.2 24 16358
## Reed College 11.8 37 15886
## Regis College 10.3 37 11758
## Rensselaer Polytechnic Institute 15.4 21 15605
## Rhodes College 10.8 47 13388
## Rider University 12.3 23 11299
## Ripon College 9.4 49 12472
## Rivier College 12.2 19 6744
## Roanoke College 13.0 26 9405
## Rockhurst College 10.7 21 7519
## Rocky Mountain College 11.3 27 6422
## Roger Williams University 16.4 8 7957
## Rollins College 13.3 23 11561
## Rosary College 12.9 30 9264
## Rowan College of New Jersey 22.1 6 7252
## Rutgers at New Brunswick 19.5 19 10474
## Rutgers State University at Camden 18.6 12 10134
## Rutgers State University at Newark 17.4 16 11878
## Sacred Heart University 14.8 16 7120
## Saint Ambrose University 14.1 16 7444
## Saint Anselm College 14.5 29 6719
## Saint Cloud State University 18.9 10 4629
## Saint Francis College IN 12.5 4 7440
## Saint Francis College 19.3 24 7344
## Saint John's University 12.0 38 9853
## Saint Joseph's College IN 14.8 19 7360
## Saint Joseph's College 27.2 8 4322
## Saint Joseph's University 17.4 13 8243
## Saint Joseph College 11.2 32 8680
## Saint Louis University 4.6 19 18367
## Saint Mary's College 9.9 31 11165
## Saint Mary's College of Minnesota 18.8 19 5081
## Saint Mary-of-the-Woods College 10.2 37 9678
## Saint Michael's College 14.5 34 10190
## Saint Olaf College 10.0 31 12502
## Saint Peter's College 12.1 22 7669
## Saint Vincent College 12.3 31 8534
## Saint Xavier University 13.7 15 8953
## Salem-Teikyo University 13.0 9 8946
## Salem College 11.2 46 9599
## Salisbury State University 17.9 18 5125
## Samford University 14.7 17 9533
## San Diego State University 19.5 7 7930
## Santa Clara University 13.9 19 10872
## Sarah Lawrence College 6.1 18 14779
## Savannah Coll. of Art and Design 16.1 26 6874
## Schreiner College 11.8 23 8545
## Scripps College 8.2 41 18372
## Seattle Pacific University 16.8 20 10368
## Seattle University 12.2 16 10175
## Seton Hall University 14.4 15 10080
## Seton Hill College 11.2 37 10065
## Shippensburg University of Penn. 18.8 13 6719
## Shorter College 13.2 18 7356
## Siena College 14.1 42 8189
## Siena Heights College 7.2 17 9431
## Simmons College 8.9 33 14086
## Simpson College 15.8 36 7411
## Sioux Falls College 14.8 7 7881
## Skidmore College 12.7 29 14837
## Smith College 10.3 44 21199
## South Dakota State University 15.0 29 5084
## Southeast Missouri State University 17.1 8 5916
## Southeastern Oklahoma State Univ. 19.6 9 4444
## Southern California College 18.6 11 8219
## Southern Illinois University at Edwardsville 16.5 8 7498
## Southern Methodist University 13.5 17 12726
## Southwest Baptist University 15.9 13 4718
## Southwest Missouri State University 19.9 11 4632
## Southwest State University 16.5 31 6591
## Southwestern Adventist College 13.0 12 5309
## Southwestern College 11.8 12 7818
## Southwestern University 11.3 35 12995
## Spalding University 10.6 40 6860
## Spelman College 12.5 18 9988
## Spring Arbor College 15.4 9 10938
## St. Bonaventure University 17.7 32 9828
## St. John's College 7.2 26 15622
## St. John Fisher College 14.5 29 7908
## St. Lawrence University 11.5 38 14980
## St. Martin's College 14.5 8 9209
## St. Mary's College of California 16.1 17 9619
## St. Mary's College of Maryland 11.6 23 10357
## St. Mary's University of San Antonio 16.2 7 7651
## St. Norbert College 15.1 36 8595
## St. Paul's College 14.0 8 8426
## St. Thomas Aquinas College 16.1 13 6534
## Stephens College 10.9 17 9995
## Stetson University 12.5 24 10307
## Stevens Institute of Technology 19.0 33 12837
## Stockton College of New Jersey 19.5 7 5599
## Stonehill College 13.0 30 7495
## SUNY at Albany 17.4 16 9075
## SUNY at Binghamton 18.0 15 8055
## SUNY at Buffalo 13.6 15 11177
## SUNY at Stony Brook 10.5 7 13705
## SUNY College at Brockport 19.0 14 6632
## SUNY College at Oswego 22.0 21 5280
## SUNY College at Buffalo 18.7 12 7511
## SUNY College at Cortland 17.8 17 5563
## SUNY College at Fredonia 16.3 10 6442
## SUNY College at Geneseo 19.1 25 5716
## SUNY College at New Paltz 15.3 8 6608
## SUNY College at Plattsburgh 17.9 16 6174
## SUNY College at Potsdam 15.1 17 6436
## SUNY College at Purchase 14.9 8 8170
## Susquehanna University 13.9 37 10554
## Sweet Briar College 6.5 48 18953
## Syracuse University 11.3 13 14231
## Tabor College 10.0 15 7233
## Talladega College 15.5 7 5970
## Taylor University 14.2 32 8294
## Tennessee Wesleyan College 8.9 16 6286
## Texas A&M Univ. at College Station 23.1 29 8471
## Texas A&M University at Galveston 17.4 16 6415
## Texas Christian University 14.8 23 9158
## Texas Lutheran College 13.8 24 7002
## Texas Southern University 18.2 21 3605
## Texas Wesleyan University 14.5 10 7936
## The Citadel 17.1 17 7744
## Thiel College 11.6 16 9186
## Tiffin University 19.0 40 5096
## Transylvania University 12.1 41 10219
## Trenton State College 14.4 6 8504
## Tri-State University 12.8 24 7603
## Trinity College CT 10.4 48 18034
## Trinity College DC 8.3 37 11806
## Trinity College VT 10.4 26 9586
## Trinity University 9.6 20 14703
## Tulane University 9.1 21 16920
## Tusculum College 21.9 28 4933
## Tuskegee University 12.2 7 10872
## Union College KY 14.1 9 6864
## Union College NY 11.5 49 15411
## Univ. of Wisconsin at OshKosh 19.2 14 5901
## University of Alabama at Birmingham 6.7 16 16352
## University of Arkansas at Fayetteville 14.8 10 6820
## University of California at Berkeley 15.8 10 13919
## University of California at Irvine 16.1 11 15934
## University of Central Florida 22.2 9 6742
## University of Charleston 2.5 10 7683
## University of Chicago 5.3 36 36854
## University of Cincinnati 10.8 6 13889
## University of Connecticut at Storrs 16.0 16 10178
## University of Dallas 13.4 26 8731
## University of Dayton 14.8 25 8894
## University of Delaware 18.3 15 10650
## University of Denver 15.9 21 11762
## University of Detroit Mercy 13.5 14 10891
## University of Dubuque 16.5 18 8767
## University of Evansville 15.8 26 7780
## University of Florida 13.4 20 14737
## University of Georgia 14.7 22 7881
## University of Hartford 10.7 9 10625
## University of Hawaii at Manoa 11.8 6 12833
## University of Illinois - Urbana 17.4 13 8559
## University of Illinois at Chicago 10.0 6 13883
## University of Indianapolis 11.1 23 6735
## University of Kansas 13.7 17 9657
## University of La Verne 14.1 23 10139
## University of Louisville 11.1 24 10207
## University of Maine at Farmington 15.9 26 5712
## University of Maine at Machias 15.1 4 5935
## University of Maine at Presque Isle 15.2 11 6408
## University of Maryland at Baltimore County 18.4 6 7618
## University of Maryland at College Park 18.1 12 9021
## University of Massachusetts at Amherst 16.7 15 10276
## University of Massachusetts at Dartmouth 15.0 20 7462
## University of Miami 5.9 17 17500
## University of Michigan at Ann Arbor 11.5 26 14847
## University of Minnesota at Duluth 19.0 11 6393
## University of Minnesota at Morris 14.6 16 6716
## University of Minnesota Twin Cities 12.2 37 16122
## University of Mississippi 20.3 14 6971
## University of Missouri at Columbia 12.7 15 10145
## University of Missouri at Rolla 14.4 23 9699
## University of Missouri at Saint Louis 13.4 15 6433
## University of Mobile 16.6 4 5412
## University of Montevallo 18.9 8 5883
## University of Nebraska at Lincoln 15.1 48 6813
## University of New England 11.4 13 9718
## University of New Hampshire 17.5 16 7855
## University of North Carolina at Asheville 13.0 11 7011
## University of North Carolina at Chapel Hill 8.9 23 15893
## University of North Carolina at Charlotte 16.8 7 6227
## University of North Carolina at Greensboro 15.5 17 7392
## University of North Carolina at Wilmington 19.1 15 6005
## University of North Dakota 15.9 16 9424
## University of North Florida 17.8 14 6104
## University of North Texas 22.6 6 5657
## University of Northern Colorado 21.5 8 6309
## University of Northern Iowa 16.3 26 6333
## University of Notre Dame 13.1 46 13936
## University of Oklahoma 11.5 11 10244
## University of Oregon 19.7 13 8020
## University of Pennsylvania 6.3 38 25765
## University of Pittsburgh-Main Campus 7.8 10 13789
## University of Portland 13.2 17 9060
## University of Puget Sound 15.0 17 11217
## University of Rhode Island 16.6 7 9158
## University of Richmond 11.7 32 11984
## University of Rochester 5.9 23 26037
## University of San Diego 15.6 13 10813
## University of San Francisco 13.6 8 10074
## University of Sci. and Arts of Oklahoma 23.6 3 3864
## University of Scranton 14.1 41 9131
## University of South Carolina at Aiken 14.8 3 5035
## University of South Carolina at Columbia 16.9 18 8246
## University of South Florida 17.0 7 11020
## University of Southern California 11.4 10 17007
## University of Southern Colorado 19.4 0 5389
## University of Southern Indiana 22.0 21 4078
## University of Southern Mississippi 18.7 23 5917
## University of St. Thomas MN 13.8 13 8546
## University of St. Thomas TX 12.6 17 7237
## University of Tennessee at Knoxville 16.5 22 8612
## University of Texas at Arlington 21.0 4 4696
## University of Texas at Austin 19.7 11 7837
## University of Texas at San Antonio 25.3 3 4329
## University of the Arts 7.5 9 11641
## University of the Pacific 11.2 14 13706
## University of the South 10.3 52 18784
## University of Tulsa 11.5 10 11743
## University of Utah 12.8 9 9275
## University of Vermont 9.9 10 12646
## University of Virginia 9.5 22 13597
## University of Washington 9.0 10 16527
## University of West Florida 23.4 12 8488
## University of Wisconsin-Stout 21.0 17 6254
## University of Wisconsin-Superior 15.2 15 6490
## University of Wisconsin-Whitewater 23.1 16 5559
## University of Wisconsin at Green Bay 22.2 1 5968
## University of Wisconsin at Madison 11.5 20 11006
## University of Wisconsin at Milwaukee 15.9 8 8094
## University of Wyoming 15.1 13 8745
## Upper Iowa University 17.4 19 3733
## Ursinus College 11.6 40 12082
## Ursuline College 10.5 15 7164
## Valley City State University 14.9 25 4958
## Valparaiso University 14.2 23 9681
## Vanderbilt University 5.8 26 23850
## Vassar College 9.7 39 17089
## Villanova University 13.4 24 10458
## Virginia Commonwealth University 8.7 11 11183
## Virginia State University 16.0 11 5733
## Virginia Tech 13.8 20 8944
## Virginia Union University 13.7 8 6757
## Virginia Wesleyan College 15.7 14 7804
## Viterbo College 10.7 31 8050
## Voorhees College 22.9 3 5861
## Wabash College 9.9 55 14904
## Wagner College 13.2 23 9006
## Wake Forest University 4.3 37 41766
## Walsh University 11.3 33 5738
## Warren Wilson College 11.4 20 9430
## Wartburg College 12.4 37 7735
## Washington and Jefferson College 12.1 40 10162
## Washington and Lee University 9.6 45 15736
## Washington College 11.2 37 10830
## Washington State University 16.9 30 10912
## Washington University 3.9 31 45702
## Wayne State College 20.3 29 4550
## Waynesburg College 16.2 26 6563
## Webber College 15.1 4 4839
## Webster University 20.6 14 6951
## Wellesley College 10.6 51 21409
## Wells College 8.3 42 13935
## Wentworth Institute of Technology 15.4 8 17858
## Wesley College 14.4 15 6243
## Wesleyan University 12.1 39 16262
## West Chester University of Penn. 15.3 16 6773
## West Liberty State College 16.3 10 4249
## West Virginia Wesleyan College 16.4 42 8080
## Western Carolina University 14.6 9 6554
## Western Maryland College 12.5 39 10026
## Western Michigan University 24.7 11 5983
## Western New England College 15.4 15 8409
## Western State College of Colorado 19.4 4 4599
## Western Washington University 22.7 10 7203
## Westfield State College 15.7 20 4222
## Westminster College MO 12.5 20 7925
## Westminster College 12.5 41 8596
## Westminster College of Salt Lake City 10.5 34 7170
## Westmont College 14.9 17 8837
## Wheaton College IL 12.7 40 11916
## Westminster College PA 13.2 41 22704
## Wheeling Jesuit College 14.1 27 7494
## Whitman College 10.5 51 13198
## Whittier College 13.6 29 11778
## Whitworth College 16.9 20 8328
## Widener University 12.6 19 9603
## Wilkes University 13.3 24 8543
## Willamette University 13.3 37 10779
## William Jewell College 11.2 19 7885
## William Woods University 12.9 16 7438
## Williams College 9.0 64 22014
## Wilson College 8.3 43 10291
## Wingate College 13.9 8 7264
## Winona State University 20.2 18 5318
## Winthrop University 12.8 26 6729
## Wisconsin Lutheran College 8.5 26 8960
## Wittenberg University 12.8 29 10414
## Wofford College 15.3 42 7875
## Worcester Polytechnic Institute 15.2 34 10774
## Worcester State College 21.0 14 4469
## Xavier University 13.3 31 9189
## Xavier University of Louisiana 14.4 20 8323
## Yale University 5.8 49 40386
## York College of Pennsylvania 18.1 28 4509
## Grad.Rate
## Abilene Christian University 60
## Adelphi University 56
## Adrian College 54
## Agnes Scott College 59
## Alaska Pacific University 15
## Albertson College 55
## Albertus Magnus College 63
## Albion College 73
## Albright College 80
## Alderson-Broaddus College 52
## Alfred University 73
## Allegheny College 76
## Allentown Coll. of St. Francis de Sales 74
## Alma College 68
## Alverno College 55
## American International College 69
## Amherst College 100
## Anderson University 59
## Andrews University 46
## Angelo State University 34
## Antioch University 48
## Appalachian State University 70
## Aquinas College 65
## Arizona State University Main campus 48
## Arkansas College (Lyon College) 54
## Arkansas Tech University 48
## Assumption College 88
## Auburn University-Main Campus 69
## Augsburg College 58
## Augustana College IL 71
## Augustana College 69
## Austin College 71
## Averett College 48
## Baker University 65
## Baldwin-Wallace College 85
## Barat College 71
## Bard College 79
## Barnard College 91
## Barry University 72
## Baylor University 72
## Beaver College 73
## Bellarmine College 84
## Belmont Abbey College 52
## Belmont University 49
## Beloit College 69
## Bemidji State University 46
## Benedictine College 58
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## York College of Pennsylvania 99Aby zaliczyć to laboratorium, zamieść odpowiedzi na następujące pytania:
- Który zbiór danych wybrałeś?
- Jaka była Twoja zmienna zależna (tzn. co próbowałeś modelować)?
- Czy oczekiwałeś, że regresja grzbietowa będzie lepsza od lasso, czy odwrotnie? Jak wypada w stosunku do OLS? Pokaż odpowiednie raporty, miary dopasowania i krótko je omów (porównaj).
- Które predyktory okazały się ważne w ostatecznym modelu (modelach)?
Przeprowadziliśmy regresję grzbietową i lasso, aby przewidzieć Grand.Rate na danych College.
- Regresja grzbietowa ze zmienną Grad.Rate jako objaśnianą
x1 = model.matrix(Grad.Rate~., coll)[,-1] # przycinam pierwszą kolumnę
# zostawiam predyktory
y1 = coll %>%
select(Grad.Rate) %>%
unlist() %>%
as.numeric()Dopasowanie modelu regresji grzbietowej:
grid = 10^seq(10, -2, length = 100)
ridge_mod2 = glmnet(x1, y1, alpha = 0, lambda = grid)dim(coef(ridge_mod2))## [1] 18 100plot(ridge_mod2)
Współczynniki, gdy λ=11498, wraz z ich normą l2:
ridge_mod2$lambda[50] ## [1] 11497.57coef(ridge_mod2)[,50] ## (Intercept) PrivateYes Apps Accept Enroll
## 6.524147e+01 1.924300e-02 9.686567e-07 7.024066e-07 -6.112685e-07
## Top10perc Top25perc F.Undergrad P.Undergrad Outstate
## 7.153334e-04 6.143038e-04 -4.144832e-07 -4.310351e-06 3.619870e-06
## Room.Board Books Personal PhD Terminal
## 9.873884e-06 1.194325e-07 -1.014868e-05 4.754458e-04 5.000512e-04
## S.F.Ratio perc.alumni Expend
## -1.970232e-03 1.009748e-03 1.899832e-06sqrt(sum(coef(ridge_mod2)[-1,50]^2)) ## [1] 0.01940515Następnie wykorzystaliśmy funkcję predict() do uzyskania współczynników regresji grzbietowej dla λ=50:
predict(ridge_mod2, s = 50, type = "coefficients")[1:18,]## (Intercept) PrivateYes Apps Accept Enroll
## 4.671830e+01 1.903498e+00 1.234870e-04 1.146584e-04 3.405181e-06
## Top10perc Top25perc F.Undergrad P.Undergrad Outstate
## 6.176559e-02 5.629912e-02 -3.664026e-05 -5.169350e-04 3.385363e-04
## Room.Board Books Personal PhD Terminal
## 9.118980e-04 -5.822815e-04 -1.095459e-03 3.462916e-02 3.067362e-02
## S.F.Ratio perc.alumni Expend
## -1.141984e-01 1.039575e-01 1.091441e-04Następnym krokiem było podzielenie próbek na zbiór treningowy i testowy w celu oszacowania błędu testu regresji grzbietowej i lasso.
set.seed(125)
train2 = College %>%
sample_frac(0.5)
test2 = College %>%
setdiff(train2)
x_train2 = model.matrix(Grad.Rate~., train2)[,-1]
x_test2 = model.matrix(Grad.Rate~., test2)[,-1]
y_train2 = train2 %>%
select(Grad.Rate) %>%
unlist() %>%
as.numeric()
y_test2 = test2 %>%
select(Grad.Rate) %>%
unlist() %>%
as.numeric()Następnie dopasowaliśmy model regresji grzbietowej na zbiorze treningowym i oceniliśmy jego MSE na zbiorze testowym, używając λ różnej wartości:
ridge_mod2 = glmnet(x_train2, y_train2, alpha=0, lambda = grid, thresh = 1e-12)
ridge_pred2 = predict(ridge_mod2, s =3, newx = x_test2)
mean((ridge_pred2 - y_test2)^2)## [1] 166.8088wartości przy różnych wartościach s (lambda):
lambda=4
166.8997lambda=0 (klasyczna metoda najmniejszych kwadratów)
170.5452lambda=10
168.8885lambda=2
166.892lambda=3
166.8088Najniższą wartość błędu MSE odnotowano przy lambda=3.
Regresja grzbietowa (lambda=3) kontra klasyczna metoda najmniejszych kwadratów
gvk=166.8088/170.5452
gvk## [1] 0.9780914Błąd MSE dla regresji grzbietowej przy optymalnej wartości parametru lambda stanowi około 97.81% błędu dla klasycznej metody najmniejszych kwadratów.
Wyniki KMNK:
lm(Grad.Rate~., data = coll)##
## Call:
## lm(formula = Grad.Rate ~ ., data = coll)
##
## Coefficients:
## (Intercept) PrivateYes Apps Accept Enroll Top10perc
## 33.8736716 3.3813758 0.0012984 -0.0006961 0.0021593 0.0548964
## Top25perc F.Undergrad P.Undergrad Outstate Room.Board Books
## 0.1351288 -0.0004712 -0.0014836 0.0010174 0.0019143 -0.0022205
## Personal PhD Terminal S.F.Ratio perc.alumni Expend
## -0.0016635 0.0872827 -0.0747023 0.0758222 0.2793343 -0.0004565predict(ridge_mod2, s = 0, type="coefficients")[1:18,]## (Intercept) PrivateYes Apps Accept Enroll
## 32.5502115068 3.3266548219 0.0012868611 -0.0015901921 0.0065704676
## Top10perc Top25perc F.Undergrad P.Undergrad Outstate
## -0.0465187428 0.2838538202 -0.0009039100 -0.0009724489 0.0011791806
## Room.Board Books Personal PhD Terminal
## 0.0012868239 -0.0014187403 -0.0022780022 0.0381458614 -0.0785007755
## S.F.Ratio perc.alumni Expend
## 0.0973357900 0.2687857117 -0.0004219473Poszukiwanie najlepszej lambdy- wynik jest bliższy do 3 niż do 4, więc dokonano optymalnego wyboru wartości liczby całkowitej
set.seed(125)
cv.out = cv.glmnet(x_train2, y_train2, alpha = 0) # Dopasuj model regresji grzbietowej na danych treningowych
bestlam2 = cv.out$lambda.min # Wybierz lamdę, która minimalizuje treningowy MSE
bestlam2## [1] 3.455662plot(cv.out)
ridge_pred2 = predict(ridge_mod2, s = bestlam2, newx = x_test2)
mean((ridge_pred2 - y_test2)^2) ## [1] 166.8356Dla porównania, dla lambda=3 (bez miejsc po przecinku) wartość MSE wynosi 166.8088.
Regresja Lasso:
lasso_mod2 = glmnet(x_train2,
y_train2,
alpha = 1,
lambda = grid) # Dopasuj model lasso do danych treningowych
plot(lasso_mod2) # Wykreśl współczynniki## Warning in regularize.values(x, y, ties, missing(ties), na.rm = na.rm):
## zwijanie do unikalnych wartości 'x'
Walidacja krzyżowa i związany z nią błąd testu, dopasowanie modelu lasso do danych treningowych i wykres MSE dla próby uczącej się:
set.seed(1)
cv.out2 = cv.glmnet(x_train2, y_train2, alpha = 1)
plot(cv.out2)
Wybranie lambdy, która minimalizuje MSE w próbie uczącej, użycie najlepszej lambdy do przewidywania danych testowych i obliczenie MSE w próbie testowej:
bestlam2 = cv.out2$lambda.min
lasso_pred2 = predict(lasso_mod2, s = bestlam2, newx = x_test2)
mean((lasso_pred2 - y_test2)^2)## [1] 170.3991Wartość MSE zbioru testowego wynosi jest większa niż MSE modelu regresji grzbietowej i podobny do MSE modelu najmniejszych kwadratów. Jednak model lasso ma istotną przewagę nad regresją grzbietową ze względu na zerowe wartości większości współczynników:
out2 = glmnet(x1, y1, alpha = 1, lambda = grid) # Dopasowanie modelu lasso do pełnego zbioru danych
lasso_coef2 = predict(out2, type = "coefficients", s = bestlam2)[1:18,] # Wyświetlanie współczynników przy użyciu lambda wybranego przez CV
lasso_coef2## (Intercept) PrivateYes Apps Accept Enroll
## 35.3131641240 2.4947532956 0.0006593252 0.0000000000 0.0000000000
## Top10perc Top25perc F.Undergrad P.Undergrad Outstate
## 0.0390761840 0.1355530607 0.0000000000 -0.0014093328 0.0009131234
## Room.Board Books Personal PhD Terminal
## 0.0016180262 -0.0008145847 -0.0016503700 0.0077086877 0.0000000000
## S.F.Ratio perc.alumni Expend
## 0.0000000000 0.2633928922 -0.0001607316Wyświetlenie tylko niezerowych współczynników:
lasso_coef2[lasso_coef2 != 0]## (Intercept) PrivateYes Apps Top10perc Top25perc
## 35.3131641240 2.4947532956 0.0006593252 0.0390761840 0.1355530607
## P.Undergrad Outstate Room.Board Books Personal
## -0.0014093328 0.0009131234 0.0016180262 -0.0008145847 -0.0016503700
## PhD perc.alumni Expend
## 0.0077086877 0.2633928922 -0.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