51015202530352468SO tCARE MUST BE TAKEN WHEN EXTRAPOLATING
We need to be careful when extrapolating.For example, in the 30 years prior to the 1968 Mexico City
Olympic Games, there was a steady, regular increase in the
long jump world record. However, due to the high altitude and
a perfect jump, the USA competitor Bob Beamon shattered
the record by a huge amount, not in keeping with previous
increases.Example 2 Self Tutor
The table below shows the sales for Yong’s Computer supplies established in late 2001.Year 2002 2003 2004 2005 2007 2008
Sales($10 000s) 6 : 1 7 : 6 17 : 3 19 : 7 20 : 6 30 : 9a Draw a scatter diagram to illustrate this data.
b Find the equation of the line of best fit using a graphics calculator. Give your answers correct to
4 significant figures.
c Predict the sales figures for 2006 , giving your answer to the nearest$1000.
Comment on whether this prediction is reasonable.
d Predict the sales figures for 2010 , giving your answer to the nearest$1000.
Comment on whether this prediction is reasonable.a Lettbe the time in years from 2001
andSbe the sales in$10 000s.t S
1 6 : 1
2 7 : 6
3 17 : 3
4 19 : 7
6 20 : 6
7 30 : 9b The line of best fit is S¼ 3 : 732 t+2: 729 ffrom a graphics calculatorg
c In 2006 , t=5 ) S¼ 3 : 732 £5+2: 729 ¼ 21 : 4
So, we the estimate the sales for 2006 to be $214 000.
The scatter diagram suggests that the linear relationship between sales and the year is strong and
positive. Since the prediction is interpolation between the poles, this estimate is reasonable.
d In 2010 , t=9 ) S¼ 3 : 732 £9+2: 729 ¼ 36 : 3
So, we estimate the sales for 2010 to be $363 000.
Since this prediction is an extrapolation, it will only be reasonable if the trend evident from 2002
to 2008 continues to the year 2010. This may or may not occur.464 Two variable analysis (Chapter 22)IGCSE01
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Y:\HAESE\IGCSE01\IG01_22\464IGCSE01_22.CDR Monday, 27 October 2008 2:15:01 PM PETER