Questions: The accompanying scatterplot shows the number of passengers departing from an airport month by month since the start of 1997 to May of 2006. Time is shown as years since 1990, with fractional years used to represent each month. (Thus, June of 1997 is 7.5 -halfway through the 7th year after 1990.) The regression and the residuals plot are also given in the accompanying display. Complete parts a) through g). d) Would you use this model to predict the numbers of passengers in 2010 (YearsSince1990=20)? Explain. A. No, because that would extrapolate too far from the years that were observed. B. Yes, because the year 2010 is close enough to the last observed value to be a safe estimate. C. Yes, because the value of R^2 is large enough to safely predict the number of passengers. D. No, because air traffic is too random to predict for any time period. e) There's a point near the middle of this time span with a large negative residual. Can you explain this outlier? A. The negative residual is September 2001. Air traffic was artificially low following the attacks on 9/11. B. The negative residual is January 1998. The extremely high ticket prices that year caused air traffic to decline. C. The negative residual is July 1999. There is no apparent cause for the decline in air traffic. D. The negative residual is March 2004. A boom in the economy was causing higher than normal air traffic as more people were traveling abroad. f) The data has been updated through 2016 and plotted on a new scatterplot, shown to the right. If the model for the data through 2006 had been used to predict the number of passengers in 2010, how well would it have worked? Why?

The accompanying scatterplot shows the number of passengers departing from an airport month by month since the start of 1997 to May of 2006. Time is shown as years since 1990, with fractional years used to represent each month. (Thus, June of 1997 is 7.5 -halfway through the 7th year after 1990.) The regression and the residuals plot are also given in the accompanying display. Complete parts a) through g). d) Would you use this model to predict the numbers of passengers in 2010 (YearsSince1990=20)? Explain. A. No, because that would extrapolate too far from the years that were observed. B. Yes, because the year 2010 is close enough to the last observed value to be a safe estimate. C. Yes, because the value of R^2 is large enough to safely predict the number of passengers. D. No, because air traffic is too random to predict for any time period. e) There's a point near the middle of this time span with a large negative residual. Can you explain this outlier? A. The negative residual is September 2001. Air traffic was artificially low following the attacks on 9/11. B. The negative residual is January 1998. The extremely high ticket prices that year caused air traffic to decline. C. The negative residual is July 1999. There is no apparent cause for the decline in air traffic. D. The negative residual is March 2004. A boom in the economy was causing higher than normal air traffic as more people were traveling abroad. f) The data has been updated through 2016 and plotted on a new scatterplot, shown to the right. If the model for the data through 2006 had been used to predict the number of passengers in 2010, how well would it have worked? Why?
Transcript text: The accompanying scatterplot shows the number of passengers departing from an airport month by month since the start of 1997 to May of 2006. Time is shown as years since 1990, with fractional years used to represent each month. (Thus, June of 1997 is 7.5 -halfway through the 7th year after 1990.) The regression and the residuals plot are also given in the accompanying display. Complete parts a) through g). d) Would you use this model to predict the numbers of passengers in 2010 (YearsSince1990=20)? Explain. A. No, because that would extrapolate too far from the years that were observed. B. Yes, because the year 2010 is close enough to the last observed value to be a safe estimate. C. Yes, because the value of $R^{2}$ is large enough to safely predict the number of passengers. D. No, because air traffic is too random to predict for any time period. e) There's a point near the middle of this time span with a large negative residual. Can you explain this outlier? A. The negative residual is September 2001. Air traffic was artificially low following the attacks on 9/11. B. The negative residual is January 1998. The extremely high ticket prices that year caused air traffic to decline. C. The negative residual is July 1999. There is no apparent cause for the decline in air traffic. D. The negative residual is March 2004. A boom in the economy was causing higher than normal air traffic as more people were traveling abroad. f) The data has been updated through 2016 and plotted on a new scatterplot, shown to the right. If the model for the data through 2006 had been used to predict the number of passengers in 2010, how well would it have worked? Why?
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Solution

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Solution Steps

Step 1: Analyzing the Model for Predicting 2010 Passenger Numbers
  • Question (d): Would you use this model to predict the numbers of passengers in 2010 (YearsSince1990 = 20)? Explain.
  • Answer:
    • Option A: No, because that would extrapolate too far from the years that were observed.
    • Explanation: The data only goes up to 2006, and predicting for 2010 would require extrapolation beyond the observed data range, which can lead to unreliable predictions.
Step 2: Identifying the Outlier with a Large Negative Residual
  • Question (e): There’s a point near the middle of this time span with a large negative residual. Can you explain this outlier?
  • Answer:
    • Option A: The negative residual is September 2001. Air traffic was artificially low following the attacks on 9/11.
    • Explanation: The significant drop in air traffic in September 2001 is well-documented due to the impact of the 9/11 terrorist attacks, which caused a sharp decline in air travel.
Step 3: Evaluating the Model's Performance for Data Through 2006
  • Question (f): If the model for the data through 2006 had been used to predict the number of passengers in 2010, how well would it have worked? Why?
  • Answer:
    • Option B: The model would not have worked well because the data shows a clear change in the pattern after 2006.
    • Explanation: The scatterplot indicates a change in the trend after 2006, suggesting that the model based on data up to 2006 would not accurately predict future values due to the shift in the pattern.

Final Answer

  1. Step 1: No, because that would extrapolate too far from the years that were observed.
  2. Step 2: The negative residual is September 2001. Air traffic was artificially low following the attacks on 9/11.
  3. Step 3: The model would not have worked well because the data shows a clear change in the pattern after 2006.
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