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business
business statistics in practice

Questions and Answers of Business Statistics In Practice

=+d) What other time series components (besides trend) are likely present in this series?45. E-commerce, part 2.
=+c) Use both models to forecast the quarterly values for Q4 2007 and Q1 2008. Which model produces better forecasts?
=+b) Fit an exponential trend model to this series but do not use the last two quarters.
=+a) Fit a linear trend model to this series but do not use the last two quarters (Q4 2007 and Q1 2008).
=+44. E-commerce. Quarterly e-commerce retail sales (in millions of dollars) in the United States are provided.(Source: U.S. Census Bureau; www.census.gov.) Use this time series to answer the
=+Alpha 0.5 1 20 40 60 80 100 Month (Jan 1990 = 1)Passengers 500,000 750,000 1,000,000 1,250,000 1,500,000 120 140 160 180 Accuracy Measures MAPE 8 MAD 69231 MSD 8705890030 Variable Actual Fits 95.0%
=+Exercise 41. Discuss how each deals with the outlier.20 80 Month (Jan 1990 = 1)Passengers 1,500,000 1 40 60 100 500,000 750,000 1,000,000 1,250,000 120 140 160 180 Accuracy Measures MAPE 8 MAD
=+43. Oakland outlier. The plot of residuals in Exercise 41 shows an outlier that wasn’t as evident in the data. The outlier is September 2001. Clearly, this wasn’t a typical month for air
=+c) In what month of the year are gas prices highest?
=+seasonal dummy variables for months.M19_SHAR8696_03_SE_C19.indd 715 14/07/14 7:37 AM 716 CHAPTER 19 Time Series Analysis Dependent variable is: Log price R squared = 92.0% R squared (adjusted) =
=+42. Monthly gas prices. We have seen that gas prices can fluctuate. But during some periods they have moved consistently. Here are the data extracted for one week of each month from January 2002
=+d) What components would you now say are in this series?
=+c) Which months have the lowest traffic at Oakland airport? (Hint: Consider all 12 months.)Here’s a plot of the residuals from the model fit to the Oakland airport passengers, created in Excel:
=+dummy variables.Dependent variable is: LogPassengers R squared = 92.4% R squared (adjusted) = 91.9%s = 0.0358 with 194 - 13 = 181 degrees of freedom Variable Coeff SE(Coeff) t-ratio P-value
=+d) Create the c chart for this two-week period.
=+41. Oakland passengers. The Port of Oakland airport reports the number of passengers passing through each month. At first glance, this is just simple growth, but by recognizing the series as a
=+d) Even though the R2 for this model is lower than the corresponding R2 for the model fit in Exercise 39 to domestic tourist visits, you might feel more comfortable predicting the number of
=+c) International tourists often visit Hawaii in January. How can you tell that from this model?
=+b) The R2 for this model is lower than for the model fit to domestic visitors in Exercise 39. Does that mean that an exponential trend model would do better?
=+28. Patient forms. The medical facility in Exercise 27 also keeps track of the number of errors found when transcribing information from patient forms. Last year the average number of errors was
=+M19_SHAR8696_03_SE_C19.indd 714 14/07/14 7:37 AM Exercises 715 Dependent variable is: International R squared = 59.9% R squared (adjusted) = 49.7%s = 13540 with 60 - 13 = 47 degrees of freedom
=+40. Hawaii tourism, pre-crisis part 2. In Exercise 39 we examined domestic tourists who visit Hawaii. Now, let’s consider international tourism. Here’s a time series plot of international
=+d) How many tourists would you predict for Hawaii in April 2007 (month 63 of this series)?
=+c) Do you find evidence of a seasonal effect? Explain.
=+b) You are planning to visit Hawaii and hope to avoid the crowds. A friend says that September and November have the fewest average visitors. Why might that not be correct?
=+Dependent variable is: Domestic Visitors R squared = 96.6% R squared (adjusted) = 95.8%s = 12870 with 60 - 13 = 47 degrees of freedom Variable Coeff SE(Coeff) t-ratio P-value Intercept 302,921.34
=+39. Hawaii tourism pre-crisis. Much of the public and private industry in Hawaii depends on tourism. The following time series plot shows the number of domestic visitors to Hawaii by air from the
=+e) What probably happened to earnings after the initial 17 days?
=+d) Predict what earnings probably were for Monday 12/3/01. What does this say about the model?
=+c) Interpret the coefficient of Saturday in this model.
=+Dependent variable is: Earnings R squared = 96.9% R squared (adjusted) = 94.6%s = 2.365 with 17 - 8 = 9 degrees of freedom Variable Coeff SE(Coeff) t-ratio P-value Intercept 21.0000 2.090 10.0
=+a) Without plotting the data, what components can you see in this series? Be specific.For some series, a “seasonal” effect repeats weekly rather than annually. Here’s a regression model fit
=+38. Harry Potter revenue. The movie Harry Potter and the Sorcerer’s Stone opened as a great success. But every movie sees declining revenue over time. Here are the daily revenues for the movie
=+e) What does it mean that the coefficient for Oct is the only negative coefficient in the model?
=+d) What revenue would you predict for Walmart in February 2007 (the 40th month in this series)?M19_SHAR8696_03_SE_C19.indd 713 14/07/14 7:37 AM 714 CHAPTER 19 Time Series Analysis
=+Dependent variable is: WM Rev R squared = 94.3% R squared (adjusted) = 91.6%s = 1.121 with 39 - 13 = 26 degrees of freedom Variable Coeff SE(Coeff) t-ratio P-value Intercept 12.0322 0.6562 18.3
=+a) What components of a time series do you see in this timeplot?Here’s a regression model fit using dummy variables for months and a Time variable that counts from 1 for the first data value in
=+37. Walmart revenue. Walmart grew rapidly in the years leading up to the financial crisis. Here is the monthly revenue ($Billion) for Walmart from November 2003 to January 2007.10 15 30 25 20 Nov
=+d) Interpret the coefficient of the dummy variable named Q3.
=+c) What is the quarter that on average has the highest profits over the time frame of the series?
=+b) What is the quarter that on average has the lowest profits over the time frame of the series?
=+a) What are the profits for the second quarter of the time series?
=+36. Another seasonal model. Use the following model to forecast quarterly profits ($000) of a company (where time is rescaled to begin at zero and Q2, Q3, and Q4 are dummy variables for the
=+35. Seasonal model. Use the following model to forecast quarterly sales ($Million) for a company (where time is rescaled to begin at zero and Q2, Q3, and Q4 are dummy variables for the indicated
=+29. Baseball circumferences. Baseballs used in the major leagues in the United States must adhere to strict standards. One such standard is that the circumference must be between 9 and 9.25
=+b) Does this model show that there is a (possibly unsuspected) 13-week seasonal cycle in interest rates? Explain.
=+Dependent variable is: Rate 44 total cases of which 13 are missing R squared = 17.2% R squared (adjusted) = 14.4%s = 3.164 with 31 - 2 = 29 degrees of freedom Variable Coefficient SE(Coeff) t-ratio
=+a) What components do you see in this series?Here’s an autoregressive model with a 13-week lag fit to these data.
=+34. Interest rates 2009. Average annual interest rates (banks prime lending) in the United States from 1966 through 2009 are shown in the following time series graph.4 812 16 1970 1980 1990 2000
=+c) Would you use this model to predict future gas prices?Explain.
=+b) Does this model show that there is a (possibly unsuspected) 14-week seasonal cycle in gas prices? Explain.
=+a) What components can you see in this plot?Here’s an AR(14) model fit to these data.Dependent variable is: Gas Price 130 total cases of which 14 are missing R squared = 31.0% R squared
=+33. Gas prices 2013, part 2. In Exercise 30 we looked at the weekly average retail price (cents per gallon) of regular gas nationwide from 2011 through June 2013. Here’s the time series plot
=+c) A regression model fit to the same data from 2009 on has the equation of 201.8 + 0.419t. Which model would you prefer to use to predict the CPI for June 2013? Explain.
=+b) Is this model appropriate for this series? Explain.
=+a) What does the intercept 206 represent in this trend line?What does the slope represent?
=+32. Consumer price index 2013. The most common use of the CPI is as an economic indicator to forecast inflation and evaluate the effectiveness of government policies.Following is the time series
=+a) Create a run chart for the baseballs’ circumferences.
=+b) Find the predicted value for the year 2012. Is it realistic?
=+a) The R2 for this trend line is 94%. A student decided to use this linear model to obtain a forecast for the percent who will respond “yes” in 2012. What value should the student use for Year?
=+Here is a time series plot of the percentage answering “yes” versus the year of the (20th) century. The least squares trend line is given by: ynt = 5.58 + 0.999Year, where Year = 37, 45, c 99
=+31. Gallup poll. The Gallup organization periodically asks the following question:If your party nominated a generally well-qualified person for president who happened to be a woman, would you vote
=+b) Is the process for making baseballs in terms of their circumference in control?
=+Dependent variable is: gas 130 total cases of which 3 are missing R squared = 95.5% R squared (adjusted) = 95.4%s = 0.0440 with 127 - 4 = 123 degrees of freedom Variable Coefficient SE(Coeff)
=+30. Gas prices 2013. We have data on the weekly average retail price (cents per gallon) of regular gas nationwide from 2011 through June 2013. Here’s a time series plot.Time 30 60 90 120 Gas
=+c) Find a prediction based on a 2-point moving average.How does it compare with the AR model?
=+b) The next value in the series was, in fact, 138.90. Compute the APE.
=+a) Here are the last several values of the series: 88.48, 134.45, 135.85, and 136.10. What price does this model predict for the next value in the series?
=+29. Coffee prices 2013. Coffee is the world’s second largest legal export commodity (after oil) and is the second largest source of foreign exchange for developing nations. The United States
=+b) How would you determine which of your lagged variables should remain in the model? Explain.
=+a) What lagged variables would you try in a regression to forecast sales? Explain.
=+Q4 sales were $3.4B. Compare the APE for this forecast to that in parta. Compare the appropriateness of the different models.28. Another autoregressive model. Suppose an autoregressive model is
=+c) Assuming these quarterly sales have a seasonal component of length 4, use the following model to compute a forecast for Q4 of 2014: yt = 0.410 + 1.35 yt - 4. In fact,
=+b) Compare this forecast to the actual value ($2.9B) by computing the absolute percentage error (APE). Did you over-forecast or under-forecast?
=+a) If a first-order autoregressive model is developed with estimated parameters of b0 = 0.100 and b1 = 1.12, compute the forecast for Q1 of 2014.
=+27. Autoregressive model. Suppose an autoregressive model is used for data in which quarterly sales in 2013 were: 1.9, 1.7, 2.2, and 2.3 ($Billion).
=+c) How many baseballs produced were out of spec?
=+Why does the exponential smoother with the higher coefficient fit the series better? What about this series is important for this result? What does this suggest about using exponential smoothers
=+26. Women’s weekly earnings 2013. The following graph shows the quarterly median weekly earnings for U.S.women 25 years of age or older (U.S. Bureau of Labor Statistics; www.bls.gov). Data are
=+Identify which plot is the 2-quarter moving average and which is the 8-quarter moving average. Explain why the better-fitting model fits better.
=+d) When should the quality team have investigated the production process?Sample Circumference Deviation Sample Circumference Deviation 1 8.998 -0.127 26 9.121 -0.004 2 9.181 0.056 27 9.111 -0.014 3
=+25. Men’s weekly earnings 2013. This graph shows the quarterly median weekly earnings from the first quarter of 2003 through the first quarter of 2013 for men, 25 years of age or older, in the
=+b) In which graph is a larger value of a used?
=+a) Which time series components are evident?Single exponential smoothing (SES) models were found for these data. Examine the following time series graphs showing two different smoothing
=+24. Google stock price. The following time series graph shows daily closing stock prices (adjusted for splits and dividends) for Google, Inc. from January 1, 2008, through June 21, 2013 (Source:
=+b) In which application is a larger length used?
=+a) Which time series components seem to be present?The method of moving averages was applied to these data. Here are time series graphs showing moving average results using two different lengths.60
=+23. Toyota stock prices 2013. The following time series graph shows daily closing stock prices for Toyota Motor Manufacturing from April 1, 2008, through June 21, 2013(Source: Yahoo! Finance).71 91
=+c) Earnings per share in 2007 were, in fact, $3.18. Compute the absolute percentage error for each prediction.
=+b) Find a prediction for 2007 based on an exponential smoothing model with a = 0.8.
=+a) Find a prediction for 2007 based on a 3-year moving average and one for a 4-year moving average.
=+22. Target earnings. Target Corp. operates “big box” stores that sell everyday essentials and fashionable differentiated merchandise. It also operates an online business at target.com.
=+c) The actual price of sugar in 2013 was 0.21 $/pound (you can find current prices at www.imf.org/external/np/res/commod/table3.pdf.) Compute the absolute percentage error for each prediction.
=+b) Find a prediction for 2013 with an exponential smoothing model with a = 0.5.
=+21. Sugar prices. The price of sugar fluctuates on the United States market. Here are the prices ($/pound) for the years 2008–2012.2008 2009 2010 2011 2012 0.39 0.37 0.29 0.21 0.20a) Find a
=+a) Use a 4-year moving average to predict profits for 2014.b) Predict the profits for 2014 using a single exponential smooth with smoothing parameter a = 0.5.c) Think about the exponential
=+20. Baking profits. A supermarket is currently studying the possibility of closing its bakery division as it has registered losses for the past two years. They would like to predict the annual
=+b) Predict the value for 2015 using a single exponential smooth with smoothing parameter a = 0.2.
=+30. Baseball weights. Baseballs used in the major leagues in the United States must adhere to strict standards. One such standard is that the weight must be between 5 and
=+a) Use a 3-year moving average to predict what the number of claims would be in 2015.

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