# Data Mining Project 1
Names: **Sam Behrens, Karl Molina**

Teaching Assistant Evaluation Data Set:
https://archive.ics.uci.edu/ml/datasets/Teaching+Assistant+Evaluation

## Introduction
The Teaching Assistant Evaluation Data Set from the UCI Machine Learning Repository was used in a machine learning paper about split selection methods for classification trees.(http://www3.stat.sinica.edu.tw/statistica/oldpdf/A7n41.pdf). The collector of the data was Wei-Yin Loh and the donor of the data set was Tjen-Sien Lim, both from the Department of Statistics at University of Wisconsin.

There are five attributes and 151 entities represented in the data. There is one numerical attribute and four categorical attributes. Two of the categorical attributes are binary so they do not need to be encoded. The other two categorical attributes should be one-hot encoded because if we were to look at the distance or similarity between the values, they all have the same similarity to each other.

This data set is interesting to us because we are both teaching assistants for CSCI 127 Joy and Beauty of Data at Montana State University and we are interested to see what factors contribute to a highly ranked teaching assistant and what can lead to low ratings.

We predict that the most descriptive attributes are the class size due to that affecting how much time a TA can dedicate to an individual in that class, and whether the TA was a native English speaker because that can limit a student's understanding of the TA's explanations in some cases.

## Analysis

The multivariate mean of the data set is

(1.80794702, 8.1589404   5.50993377, 1.84768212, 27.86754967, 2.01986755)

with label encoding all of the categorical variables. These variables are Course Instructor and Course.

The covariance matrix of our data is:

 [[  0.1562   0.3507   0.4453   0.0306  -0.7723  -0.0828]
 [  0.3507  40.1612  19.3117   0.7244   1.2145  -1.4765]
 [  0.4453  19.3117  37.5582   0.6849  -4.412   -0.8102]
 [  0.0306   0.7244   0.6849   0.13     1.253   -0.0836]
 [ -0.7723   1.2145  -4.412    1.253  166.249   -0.3774]
 [ -0.0828  -1.4765  -0.8102  -0.0836  -0.3774   0.6729]]

### English speaking vs summer/regular semester
English speaker and summer or regular semester may be related. We think that these attributes could be related because there may be more foreign exchange students over the summer than during a regular semester.


Since both English speaking and the summer/regular semester attributes are both binary, we can not really see anything from this scatter plot, other than that both English and non English speakers both teach during the summer and the regular semester.

### Course vs Course Instructor

Course and Course Instructor may be also be related. It makes sense that an instructor would teach the same course multiple times.


This scatter plot doesn't tell us much, but we can see that there are a few courses that taught by many different instructors, and there a few a courses that only have one instructor.

### Summer/regular semester vs class size

Two other attribute that may be related are the summer and regular semester and the class size because there will probably be less students taking classes during the summer.


The scatter plot shows us that there is a higher variation of class sizes during the regular semester and also a higher class sizes during the regular semester. During the summer there are a small amount of classes and the class size is lower.

### Course instructor vs summer/regular semester

The course instructor and summer or regular semester attributes may be related because there might be some instructors that only teach during the regular semester.


Examining the scatter plot, we can see that there are very few instructors that work during the summer.

### Course vs class size

The course and class size may be related because there will probably higher number of students attending some lower level courses.


Looking at the scatter plot we can see that there are some classes with a higher variation of class sizes but there don't seem to be courses that always have a higher number of students.

#### Correlation and Variance
There are no pairs of attributes that have a correlation greater than or equal to 0.5. There are seven pairs of attributes that have negative sample covariance. The total variance of the data is `244.927`. Because there are only five features on our data set, the total variance of features with the highest sample variance is also `244.927`