Michael and Franklin 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 Merryweather. They will first try to fit the following model Se = do + 0, A2 + a20 + where S is the sales revenue in quarter t, A, is the advertising budget in quarter t, O, is the number of clicks that online ads for Merryweather have generated, and & is the error term. a) Michael and Franklin fit their model using Merryweather's past data. They calculate both R2 and adjusted R2 for their model. Give a brief explanation of the difference between these two values in terms of what they represent. [2 marks) b) For the fitted model, R2 is calculated to be 90%. Explain what this suggests in terms of the usefulness of the fitted model. [2 marks) c) State two limitations of this model. [2 marks] Michael and Franklin decide to take a different approach. They now build a model, given by the formula Se = bo + b2 St-1 + b2S3-2 + Z. where Ze is the error term. d) Franklin thinks that they do not need the S-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. [2 mark] e) Michael has calculated the autocorrelations (ACF) for the past sales data. He has found that the first five autocorrelations are 0.05, -0.15, 0.02 -0.01, and 0.005. Michael 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 = 200. What do these autocorrelations suggest about the model they are using? Michael and Franklin 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 Merryweather. They will first try to fit the following model Se = do + 0, A2 + a20 + where S is the sales revenue in quarter t, A, is the advertising budget in quarter t, O, is the number of clicks that online ads for Merryweather have generated, and & is the error term. a) Michael and Franklin fit their model using Merryweather's past data. They calculate both R2 and adjusted R2 for their model. Give a brief explanation of the difference between these two values in terms of what they represent. [2 marks) b) For the fitted model, R2 is calculated to be 90%. Explain what this suggests in terms of the usefulness of the fitted model. [2 marks) c) State two limitations of this model. [2 marks] Michael and Franklin decide to take a different approach. They now build a model, given by the formula Se = bo + b2 St-1 + b2S3-2 + Z. where Ze is the error term. d) Franklin thinks that they do not need the S-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. [2 mark] e) Michael has calculated the autocorrelations (ACF) for the past sales data. He has found that the first five autocorrelations are 0.05, -0.15, 0.02 -0.01, and 0.005. Michael 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 = 200. What do these autocorrelations suggest about the model they are using
