June 2022 Paper 2 Q15

OCR MEICurrent spec9 marksCorrelation & RegressionLarge Data Set

15 The pre-release material includes information on life expectancy at birth in countries of the world. Fig. 15.1 shows the data for Liberia, which is in Africa, together with a time series graph.

Time series graph “Life expectancy at birth – Liberia”: life expectancy at birth against year from 1960 to 2010, increasing from about 35 to about 60
196019701980199020002010
34.6739.2546.0047.1852.4259.63

Fig. 15.1

Sundip uses the LINEST function on a spreadsheet to model life expectancy as a function of calendar year by a straight line.

The equation of this line is \(L = 0.473y - 892\), where \(L\) is life expectancy at birth and \(y\) is calendar year.

(a) Use this model to find an estimate of the life expectancy at birth in Liberia in 1995. [1]

According to the model, the life expectancy at birth in Liberia in 2025 is estimated to be 65.83 years.

(b) Explain whether each of these two estimates is likely to be reliable. [2]
(c) Use your knowledge of the pre-release material to explain whether this model could be used to obtain a reliable estimate of the life expectancy at birth in other countries in 1995. [1]

Fig. 15.2 shows the life expectancy at birth between 1960 and 2010 for Italy and South Africa.

Fig. 15.2: “Life expectancy at birth – Italy and South Africa”, 1960 to 2010; Series 1 (solid line) rises from about 53 to about 62 in 1990 then falls to about 56; Series 2 (dashed line) rises steadily from about 69 to about 82
Fig. 15.2
(d) Use your knowledge of the pre-release material to
  • Explain whether series 1 or series 2 represents the data for Italy.
  • Explain how the data for South Africa differs from the data for most developed countries.
[2]

Sundip is investigating whether there is an association between the wealth of a country and life expectancy at birth in that country. As part of her analysis she draws a scatter diagram of GDP per capita in US$ and life expectancy at birth in 2010 for all the countries in Europe for which data is available. She accidentally includes the data for the Central African Republic. The diagram is shown in Fig. 15.3.

Fig. 15.3: scatter diagram of life expectancy at birth in 2010 (40 to 85) against GDP per capita in US dollars (0 to 160 000); most points between 70 and 82 for GDP up to about 75 000, two points near 80 at about 105 000 and 140 000, and one isolated point at about 47.5 near GDP 0
Fig. 15.3
(e) On the copy of Fig. 15.3 in the Printed Answer Booklet, use your knowledge of the pre-release material to circle the point representing the data for the Central African Republic. [1]

Sundip states that as GDP per capita increases, life expectancy at birth increases.

(f) Explain to what extent the information in Fig. 15.3 supports Sundip’s statement. [2]
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