Regression Model - Multicollinearity - Assessment Answer

Assignment Task:

Problem 1. 
Use the data set canadian_gas data set. Use library(fpp3) and data(canadian_gas); Build a time series object using canadian_gas["Volume"]; Plot the time series; Build a seasonal naïve model and forecast for next 12 months level; Build a trend and season regression model for the Volume using them function; Are the trend and seasonality coefficients significant? Predict the 12-month gas volume and the 95% confidence intervals using the trend and season. Hint: You may need to use forecast:: forecast to access the forecast function. 

Problem 2. 

In R FPP package, there is a credit data set. Use data(credit) command to get access to it. Does the following information come from the command? credit.
Description
A random sample of 500 observations of customers applying for personal loans at an Australian bank. All customers were 25 years old or
under.
Usage
data(credit)

Format
A data frame with 500 observations on the following 7 variables.
Score a numeric vector giving the credit scores calculated by the bank on a scale from 0 to 100.
Savings a numeric vector giving the total personal savings of each customer (in thousands of $).
Income a numeric vector giving the total net income of each customer (in thousands of $).
Fte TRUE if the customer has full-time employment, and FALSE otherwise.
Single TRUE if the customer is single, and FALSE otherwise.
time. address a numeric vector giving the number of months each customer has lived at their current address.
time. employed a numeric vector giving the number of months each customer has been with their current employer.
(a) Build a regression model to predict the credit score;
(b) Assess the model to report by:
Report the value of adjusted R squared after you try to optimize the model;
Check for normality of residuals, the autocorrelation of residuals, check for the existence of
heteroscedasticity using the check residuals command, and describe what you observe;
Check for multicollinearity using if command in-car package and also describe what you
observe. Is there a serious problem?
(c) Extra 5 points. You can try to add nonlinear transformations of predictor variables. How much did you improve the Adjusted R squared metric? Hint: use log(variable + 1) and variable^2 as possible transformations.

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