Lee and Jin are data scientists that provide consulting for various companies. This time, they have been hired to consult on the advertising strategy for a company named TEK. They will first try to fit the following model = 0 + 1 + 2 + ; where is the sales revenue in quarter , is the advertising budget in quarter , is the number of clicks that online ads for TEK have generated, and is the error term.

a) Lee and Jin fit their model using TEKs 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. [2 marks]

b) The test statistics (calculated as estimate divided by its standard error) of 0 and 1 are 1.11 and 0.76, respectively. Do you keep 0 and 1? Justify your answer. [2 marks]

c) State two limitations of this model. [2 marks] Lee and Jin decide to take a different approach. They now build a model, given by the formula = 0 + 11 + 22 + , where is the error term.

d) Lee thinks that they do not need the 2 term in this model, but Jin thinks that they may need a third 3 term as well as 2. What calculation/process should they perform to decide on the number of terms? Note: you do NOT need to perform any calculations for this part. [2 mark]

e) Lee has calculated the autocorrelations (ACF) for the past sales data. He has found that the first five autocorrelations are 0.05, 0.14, -0.06, 0.03, and -0.04. Lee 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 = 250. What do these autocorrelations suggest about the model they are using?