The numbers of mobile phone subscriptions in Singapore, \(y\) million, for certain years from 2004 are given in the following table. The variable \(x\) is the number of years after a base year of 2000. Ling thinks that the number of mobile phone subscriptions in Singapore can be modelled by one of the formulae \(y=ax+b\), \(e^y=cx+d\), where \(a\), \(b\), \(c\) and \(d\) are constants. Find, correct to 4 decimal places, the value of the product moment correlation coefficient between \(x\) and \(y\), between \(x\) and \(e^y\). Explain which of Ling’s models, \(y=ax+b\) or \(e^y=cx+d\), gives a better fit to the data and find the equation of the regression line for this model. Use the equation of the regression line to estimate the number of mobile phone subscriptions in 2024. Explain whether your estimate is reliable.

The numbers of mobile phone subscriptions in Singapore, \(y\) million, for certain years from 2004 are given in the following table. The variable \(x\) is the number of years after a base year of 2000.

Ling thinks that the number of mobile phone subscriptions in Singapore can be modelled by one of the formulae \(y=ax+b\), \(e^y=cx+d\), where \(a\), \(b\), \(c\) and \(d\) are constants.

Find, correct to 4 decimal places, the value of the product moment correlation coefficient

Explain which of Ling’s models, \(y=ax+b\) or \(e^y=cx+d\), gives a better fit to the data and find the equation of the regression line for this model.

Use the equation of the regression line to estimate the number of mobile phone subscriptions in 2024. Explain whether your estimate is reliable.

Year	\(2004\)	\(2006\)	\(2008\)	\(2010\)	\(2012\)	\(2014\)	\(2016\)	\(2018\)
Number of years after base year, \(x\)	\(4\)	\(6\)	\(8\)	\(10\)	\(12\)	\(14\)	\(16\)	\(18\)
Number of subscriptions, \(y\) million	\(3.99\)	\(4.79\)	\(6.41\)	\(7.38\)	\(8.07\)	\(8.10\)	\(8.46\)	\(8.39\)

N2023 P2 Q7

N2023 P2 Q7