Project 1: Developing a multiple regression model

For this analysis, you will need to build a multiple regression model using profit as the dependent variable. You should follow the model building process introduced in the lecture and tutorial. To select variables to include in the model, start with transforming categorical variables into dummy variables. When transforming location into dummy variables, consider Central as the baseline variable (category). Then, create scatter diagrams, and calculate correlation coefficients. Afterwards, assess the model for overall significance (F test with alpha set at 0.05). In the next step, if the overall model is found to be significant, remove variables that are not contributing to any significant change in the dependent variable one at a time (if there are any), by conducting a series of t-tests with alpha set at 0.05.

In particular, you should at least consider the following questions:

a) Which independent variable has the strongest linear relationship with profit?

b) Are there any potential multicollinearity problems? If so, which variables are they? (Note: if there are collinearity problems between the independent measures, you should firstly remove the variable that has the “least correlation” with the dependent measure, then run the model and assess again).

c) Is your multiple regression model significant?

d) If so, which variables do not help you in modelling the dependent variable?

e) How well does the model explain profit? (Use R2 and adjusted R2 in your explanation.)

f) What would be the profit for a dealership with 20 staff, advertising budget of $50,000, located in the Eastern suburbs, and 1000 square metres in size? [Note, only use the values that you have found to be significant (α set at 0.05) contributors to the behaviour of the dependent measure].

g) Build a 95% prediction interval also a 95% confidence interval for the estimated profit in the previous question.

Project 2: Time series analysis

For this study, you need to consider several forecasting models and evaluate model performance in terms of forecasting accuracy and model fit.

You should consider the following questions:

a) Is there a trend and if so what type of trend is it?

b) What do the errors say about the usefulness of the forecasting model?

c) What are the R2 values of the models?

d) What would be the forecasted profit for the next time period?

Project 3: Confidence interval and hypothesis testing

Produce the necessary descriptive and graphical summary information. Then, build a confidence interval for the parameter of interest. Test the claim made by Aussie Cars management to determine if it could, in fact, be true.

Project 4: Payoff table

Construct a payoff table for all of the possible profit outcomes. Consider the following when structuring your decision criteria: Maximin criterion, Maximax criterion, and long term averaged outcomes.