School Survey- Component Factor Analysis and Multi Linear Regression Model using R.

A survey was created to find relationships that exist and what were the main contributors to a student recommending the school to a friend. The aim of the end model is to predict which variables would make the students satisfied enough to recommend the school- our goal (independant variable).

14 questions were asked with a ranking scale out of 10. These are the questions:

What year level are you in?

How accessible is the location?

How have you achieved in your results?

How would you rate the overall teaching experience in your classes?

How friendly are the teachers?

How well are the facilities maintained?

Do you get additional assistance from teachers when requested?

How would you rate the behaviour of other students in your classes?

How do you rate the facilities (classrooms, fields) and equipment (AV, Networks) in the school?

How would you rate your effort and engagement in class?

Rate the influence your parents would have on your school results?

Rate the engagement of other students in your classes?

Do you get on well with your peers at school?

How would you rate your overall experience at school?

Would you tell a friend to come to the school?

The following correlations exist. From this graph it shows that Recommendation is strongly correlated with School Experience. There are some other correlations that exist.

Testing using the KMO brings a value of 0.8 which indicates a component factor analysis will be good for this data. It also recommends 3 factors. Although the following is an experiment with 4 factors below. It helps categorise but it does not help with creating a model that determines recommendation. Recommendation needs to be excluded from the Linear model later on.

THE RMSEA 0.084is seen as a good fit for the data but this includes recommendation which is the independant variable.

The data was tested using a factor analysis tool. The following questions were grouped into 4 factors of MR1, MR2, MR3 and MR4. The following groups are interpreted as:

MR1- Students view of personal effort correlates with achievement of results, but it is also linked to a teachers friendliness, additional time a teacher provides to students and accessibility to the school (perhaps being stuck in traffic effects students?).

MR2- School experience determines whether a student is likely to recommend the school to their friends.

MR3- Facilities and the maintenance of facilities is closely correlated but this seems to also effect the teaching experience. An example may be that AV is not working, or air conditioning it seems this effects a students learning experience. However the teaching experience seems to not fit in reality.

MR4- Engagement of other students is mainly effected by the behaviour and is also linked to peers getting along in class.

Running the data again twice it creates the best model with an RMSEA of 0.076 which is a good fit and it excludes the independant variable of recommendation (out ultimate goal). It also required that we use 3 factor analysis based on the KMO tool recommendation.

This model excludes some of the different factors as they are double loaded and it creates a better fit using RMSEA as an indicator. But this model does have an R2 of just over 0.5. This is low and does not have strong fit with the model. However, due to this being a survey of people (which are more unpredictable than machines) it is a more acceptable range.

Y= - 1.906+MR1*0.5645+MR2*0.7008+MR3*0.2544

The model suggests that recommendations for the school start at -1.906. If this model is accurate and my interpretation is correct then we have less recommendations in this data set and work needs to be done in certain areas.

Easy wins to improve student recommendations would be-

MR2 - 0.708

To ensure students have good peers and friendships at school (co curriculum and sport assist with this)

Other engagement- ensuring their friends are engaged in class (better behaviour/engaged classes?) and the experience of school is good. These last two factors are difficult to interpret consistently.

MR1- 0.56

Easiest win- improve facilities and maintenance of facilities at a school. However not always that easy to get more land?

MR3 - 0.25

Student Results, personal effort (motivating students), Accessibility of school and teacher additional help - this has less of an effect on the students recommendation in comparison to MR1 and MR2.

It is a start at real data and creating a model based on the data. Future blogs will use similar techniques to look at various other data sets that would help to provide a Regression model to explain the data.

Please see the source code below: