Mandy and Frank are data scientists that provide consulting for various companies. This time, they have been hired to consult for a company named BCB. They will first try to fit the following model

t = 0 + 1t + 2t ;

where t is the sales revenue in year , t is the advertising budget in year , and t is the number of clicks that online ads for BCB has generated.

a) Mandy and Frank fit their model using BCBs past data. They calculate both ^2 and adjusted ^2 for their model. Give a brief explanation of the difference between these two values in terms of what they represent.

b) For the fitted model, ^2 is calculated to be 20%. Explain what this suggests in terms of the usefulness of the fitted model.

c) State two limitations of this model.

Mandy and Frank decide to take a different approach. They now build a model, given by the formula t = 0 + 1t-1 + 2t-2 + t

d) Frank thinks that they do not need the t-2 term in this model. What calculation/process can he perform to justify this assertion? Note: you do NOT need to perform any calculations for this part.

e) Mandy has calculated the autocorrelations (ACF) for the past sales data. She has found that the first five autocorrelations are 0.05, -0.08, 0.12, -0.2, and 0.005. Mandy has performed further investigation, and believes that all further partial autocorrelations will lie between -0.01 and 0.01. Suppose that the sample size was = 400. What do these autocorrelations suggest about the model they are using?