Question 6 (10 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 Se = do + A + a20 + Eti where S is the sales revenue in quarter t, A is the advertising budget in quarter t, 0, is the number of clicks that online ads for TEK have generated, and t is the error term. a) Lee and Jin fit their model using TEK'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) The test statistics (calculated as estimate divided by its standard error) of d, and a are 1.11 and 0.76, respectively. Do you keep , 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 Se = bo + b St-1 + b2St-2 +Zt, where 2 is the error term. 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 0.05, 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 n = 250. What do these autocorrelations suggest about the model they are using? [2 marks] Question 6 (10 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 Se = do + A + a20 + Eti where S is the sales revenue in quarter t, A is the advertising budget in quarter t, 0, is the number of clicks that online ads for TEK have generated, and t is the error term. a) Lee and Jin fit their model using TEK'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) The test statistics (calculated as estimate divided by its standard error) of d, and a are 1.11 and 0.76, respectively. Do you keep , 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 Se = bo + b St-1 + b2St-2 +Zt, where 2 is the error term. 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 0.05, 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 n = 250. What do these autocorrelations suggest about the model they are using? [2 marks]
