3)A new course in Data Mining is being offered and the number of students registered in the course is monitored. Supposed the academic year is divided into four quarters: Q₁, Q₂ Q₃ and Q_4. The number of students registered in the course for the last 4 years is recorded in the table below.

2014:

Q1 42

Q2: 58

Q3: 51

Q4: 58

2015:

Q1: 45

Q2: 60

Q3: 53

Q4: 60

2016:

Q1: 48

Q2: 68

Q3: 57

Q4:68

2017:

Q1: 52

Q2: 70

Q3: 60

Q4:72

a)Plot the course registration over time and identify the patterns

b)Derive a linear model to predict Registration. Describe the model. Predict Registration for the four quarters of 2018. Calculate the corresponding Mean Absolute Deviation.

c)Derive a linear model to predict Registration using linear trend and seasonality using dummy variables. Use = 0.05. Calculate the corresponding Mean Absolute Deviation. Predict Registration for the four quarters of 2018.

d)Consider a Three-Period Weighted Moving Average Forecasting model, where the highest weight (3) is given to the most recent data and the smallest weight (1) is given to the oldest data and (2) to the intermediate data:

Calculate the corresponding Mean Absolute Deviation. Predict Registration for the four quarters of 2018.

e)Consider the Exponential Smoothing approach with optimal . Predict Registration for the four quarters of 2018. Calculate the corresponding Mean Absolute Deviation.

f)Which of the above models is better using MAD?