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 St = ao + 2 A+ + a20t; where St is the sales revenue in quarter t, At is the advertising budget in quarter t, and Ot is the number of clicks that online ads for TEK have generated. a) Lee and Jin fit their model using TEK's past data. They calculate both R2 and adjusted Rfor 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 a, and a are 1.38 and 0.91, respectively. Do you keep o and ? 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 St = b+ b St-1 + b St-2 + Zt d) Lee thinks that they do not need the St-2 term in this model, but Jin thinks that they may need a third St-3 term as well as St-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 0.02, -0.16, 0.05, -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 n = 300. What do these autocorrelations suggest about the model they are using? [2 marks] 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 St = ao + 2 A+ + a20t; where St is the sales revenue in quarter t, At is the advertising budget in quarter t, and Ot is the number of clicks that online ads for TEK have generated. a) Lee and Jin fit their model using TEK's past data. They calculate both R2 and adjusted Rfor 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 a, and a are 1.38 and 0.91, respectively. Do you keep o and ? 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 St = b+ b St-1 + b St-2 + Zt d) Lee thinks that they do not need the St-2 term in this model, but Jin thinks that they may need a third St-3 term as well as St-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 0.02, -0.16, 0.05, -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 n = 300. What do these autocorrelations suggest about the model they are using? [2 marks]
