ALL INFORMATION IS PROVIDED! USE R- CODE. ANYTHING IN BOLD IS R-CODE THAT IS PROVIDED.

##### Problem 1

Consider the business school admission data available in `admission.csv`. The admission officer of a business school has used an "index" of undergraduate grade point average ($X_1$=`GPA`) and graduate management aptitude test ($X_2$=`GMAT`) scores to help decide which applicants should be admitted to the school's graduate programs. This index is used to categorize each applicant into one of three groups - `admit` (group 1), `do not admit` (group 2), and `borderline` (group 3).

1. First let's import the data set using the `read.csv()` function.

```{r}

library(caret) # load the caret package

admData <- read.csv('admission.csv') # change the path to the file if needed ```

2. Now, let's create 10 folds to be used by our models. This is done so that all the models are fit and tested on the same two sets of data points.

```{r}

set.seed(123)

# for reproducibility of results - don't remove this line

testInd <- createFolds(admData$Group,k=10)

```

For example,

```

{r}

testInd[[1]]

# 9 11 14 46 51 59 75 83

```

stores the indices of the test points of the 1st fold.

a. Using the `train()` function of the `caret` package, fit `Multinomial Logistic Regression` 10 times where each time you exclude the data points from the $k$-th fold during model training. Set your `method` argument to "multinom". Since the response variable `Group` is coded as numeric (with values 1,2 and 3), convert it into a factor variable using the `as.factor()` function during model fitting. Compute an estimate for the test `Accuracy` (i.e. the accuracy on the test set) using 10-fold cross validation.

b Repeat part (a) for `LDA` setting the `method` argument to "lda".

c. Repeat part (a) for `QDA` setting the `method` argument to "qda".

d. Repeat part (a) for `Naive Bayes` setting the `method` argument to "nb".

e. Repeat part (a) for `KNN` with $K=1,2,\ldots,10$ and setting the `method` argument to "knn". In this case, standardize your data prior to fitting the `KNN` model. Choose the optimal value of $K$ using 5-fold cross validation (_hint_: set `trControl=trainControl(method='cv',number = 5)` within the `train()` function).

f. In a single table report the **cross validation based** estimates of the test `Accuracy` for each model. Based on the results which model would you recommend?

admissions.csv

GPA	GMAT	Group
2.96	596	1
3.14	473	1
3.22	482	1
3.29	527	1
3.69	505	1
3.46	693	1
3.03	626	1
3.19	663	1
3.63	447	1
3.59	588	1
3.3	563	1
3.4	553	1
3.5	572	1
3.78	591	1
3.44	692	1
3.48	528	1
3.47	552	1
3.35	520	1
3.39	543	1
3.28	523	1
3.21	530	1
3.58	564	1
3.33	565	1
3.4	431	1
3.38	605	1
3.26	664	1
3.6	609	1
3.37	559	1
3.8	521	1
3.76	646	1
3.24	467	1
2.54	446	2
2.43	425	2
2.2	474	2
2.36	531	2
2.57	542	2
2.35	406	2
2.51	412	2
2.51	458	2
2.36	399	2
2.36	482	2
2.66	420	2
2.68	414	2
2.48	533	2
2.46	509	2
2.63	504	2
2.44	336	2
2.13	408	2
2.41	469	2
2.55	538	2
2.31	505	2
2.41	489	2
2.19	411	2
2.35	321	2
2.6	394	2
2.55	528	2
2.72	399	2
2.85	381	2
2.9	384	2
2.86	494	3
2.85	496	3
3.14	419	3
3.28	371	3
2.89	447	3
3.15	313	3
3.5	402	3
2.89	485	3
2.8	444	3
3.13	416	3
3.01	471	3
2.79	490	3
2.89	431	3
2.91	446	3
2.75	546	3
2.73	467	3
3.12	463	3
3.08	440	3
3.03	419	3
3	509	3
3.03	438	3
3.05	399	3
2.85	483	3
3.01	453	3
3.03	414	3
3.04	446	3