Data Description

Bike sharing systems using apps have become popular in many cities. They provide economical transportation in an environmentally friendly manner. A number of companies are now into the bike-sharing business.

Assume you are working for Lime, a bike-sharing company, and plan to enter a new market with bike sharing. You have collected data on bike sharing rentals in a major U.S. city on the east coast of the U.S. for two years (The data is actual bike-sharing rental data from one city). The fields are as follows:

- ID: record ID

- season : season (1:spring, 2:summer, 3:fall, 4:winter)

- mnth : month ( 1 to 12)

- day day of the month ( 1 to 28 or 29 or 30 or 31)

- hr : hour (0 to 23)

- holiday : whether day is holiday or not

- weekday : day of the week

- workingday : if day is neither weekend nor holiday is 1, otherwise is 0.

+ weathersit :

- 1: Clear, Few clouds, Partly cloudy, Partly cloudy

- 2: Mist + Cloudy, Mist + Broken clouds, Mist + Few clouds, Mist

- 3: Light Snow, Light Rain + Thunderstorm + Scattered clouds, Light Rain + Scattered clouds

- 4: Heavy Rain + Ice Pallets + Thunderstorm + Mist, Snow + Fog

- temp : Normalized temperature in Celsius. The values are divided to 41 (max)

- atemp: Normalized feeling temperature in Celsius. The values are divided to 50 (max)

- hum: Normalized humidity (varies from 0 to 1. Actual humidity was divided by 100)

- windspeed: Normalized wind speed (varies from 0 to 1. The actual windspeed values were divided by the maximum observed windspeed of 67)

- casual: count of casual users

- registered: count of registered users

- cnt: count of total rental bikes including both casual and registered

Dataset: - https://1drv.ms/x/s!Ag_k1mIrF-BshDqE4ysR6zKlj9UY?e=4YfLVh

STEP 1: Instead of looking at data on an hourly basis, we will look at the data on a six hour basis. You have to bin the data (put into buckets) into the following groups.

For each day you have to create the buckets

EM (early morning) = Hr 0,1,2,3,4,5

MN (morning to noon) = Hr 6,7 8,9,10,11

AN (afternoon) = Hr 12,13,14,15, 16,17,

EN (evening/night) = Hr 18,19,20,21,22,23

You will have to add the casual, registered and cnt values for the six hours in each bucket, but you have to take the average of temp, atemp, hum and windspeed for the six hours. For weathersit take the average and use the Round() function to round up/down the number.

STEP 2: From the aggregated dataset from step 1 take a sample of 65% of records and put them into training dataset. Put the remaining records into test dataset. You will submit your training and test data sets (in CSV form) with your assignment. (5 marks) For the next steps use these training and test datasets.

STEP 3: MLR Model

Develop a MLR model for predicting total rental bikes (cnt) as a function of the independent variables using the training data set. Use Regsubsets with Malloys Cp as the selection criteria to select the best model.

1. What is the RMSE of your model on the training data set?
2. Now run the MLR model on the test data set. What is the RMSE of the MLR model on the test dataset?

STEP 4: Knn Model

Develop a knn model for predicting total rental bikes (cnt) as a function of the independent variables using the training data set. Use k=10

1. Copy/paste the knn model here

(show the R command you have used for the knn model)

2. What is the RMSE of your model on the training data set?

2. Now run the knn model on the test data set. What is the RMSE on the test dataset.

STEP 5: Which model (MLR or KNN) would you chose for implementation? Why?

STEP 6: Principal Components

Consider the variables weathersit, temp, atemp, hum and windspeed in the training data set for aggregated data. Treat weathersit as a numeric variable. Extract the Principal components based on these variables. List the equations for the top two Principal Components.