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Hi Ken,
In the question, what does a,b and r indicate?In b i, how is the percentage calculated?
“Although Noble Pets’ share of this market remains the same (30%), this is
a reduction in real terms of 18,000 tonnes of production (from 111,000 to 93,000 tonnes). “,I didn’t understand this line. Please tell me where did 111000 and 93000 tones came from?The linear regression line is of the form
y = a + bx
where y = volume and x = years.
When x = 0, volume started off at a, 369.57. For every year, volume decreases by b ie a decrease of 9.86. r is the coefficient of correlation. As this is close to -1, there is a good negativeassociation between time and volume.
a and b have been calculated from the historical data.
Noble Pets has 30% of the market so would have started with 30% x 369.97 = 111
The last market data given is for 2013 and 30% x 310 = 93
291 = 369.57 – 8 x 9.86 = 291 [8 – the year after year 7, which represents 2013
Other figures are 9.86 less each year.
Sir in b ii, how did the examiner came up with 300000 tonnes for the next three years?
It is explained in the answer. Using the regression figures would give:
2014 = 291 (as above)
2015 = 291 – 9.86 = 281.14
2016 = 281.14 – 9.86 = 271.28
Total = 843 (rounded)
1/3 of this would be (for moist) 281
However, teh answer argues that the trend is not linear so fitting a linear regression line might be wrong. Recent sales do not seem to be falling off as steeply as old sales so 281 is perhaps too low. An estimated figure of 300 might be better – but 95 or 105 might be just as good an estimate)
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