1.    1.The dataset JohnsonJohnson is built into R.  Itcontains quarterly earnings per share for J&J from 1960 to 1980. (20 Pointstotal, see breakdown by parts)

a.    Plot thedata in a time plot.  What features ofthe plot suggest that the data should be transformed? (3 Points)

b.    Transformthe data by taking the log and then plot it again.  What is different? (3 Points)

c.    Calculateforecasts for the transformed data for each of the last 10 quarters using theNaïve Forecast 1. (3 Points)

d.    Computethe forecast errors and calculate the MSE, MAPE, MAD, MPE, ME and Theil’s U forthe out of sample forecast. (4 Points)

e.    Repeatpart d using Naïve Forecast 2.  Whichmodel performs better out of sample? (7 Points)

2.    Use thedataset from the fma library in R called “motel”. The dataset contains “Totalroom nights occupied and total monthly takings from accommodation at hotel,motel and guest house in Victoria, Australia: Jan 1980 - June 1995.” We areinterested in Roomnights. (15 Points total, see breakdown by parts)

a.    Find theweights of a 5 x 7 MA filter.  Using thisfilter, smooth the Roomnights variable. Make a plot of the data and add thesmoothed plot to it. (5 Points)

b.    Is therea better choice of a MA filter for this dataset?  Try a few and add them to the plot.  Which is better and why? (5 Points)

c.    Using thedecompose() function in R (or something like it STL etc.) on the Roomnightsdata, what can you say about the trend, seasonality and errors? (5 Points)

3.  The pull strength of a wire bond is an importantcharacteristic.  The data found here givesinformation on pull strength (y), die height (x1), post height (x2),loop height (x3), wire length (x4), bond width on the die(x5), and bond width on the post (x6). (20 Points, seebreakdown by parts)

  
• Analyze this data to find      which linear model is the best fit for this data (give details on how you      decided which model is best, including things like the Durbin Watson      test). (3 Points)
  

  
• Report the amount of      variation explained by the model you chose in part a). (2 Points)
  

  
• Report your estimate of s. (2 Points)
  

  
• Find a 97% Confidence      interval for each of the bj’s      in your model, and interpret. (5 Points)
  

  
• Holding all else fixed,      how does a unit change in x4 change the average value of y? (3      Points)
  

  
• For a specimen with x1      = 5.5, x2 = 19.3, x3 = 30.2, x4 = 90, x5      = 2, and x6 =1.85 find a 95% prediction interval for y      (hint: you may not need all of these values). (5 Points)