The Gross Domestic Product per Capita (GDP), $x$ dollars, and the Infant Mortality Rate per thousand (IMR), $y$, of 6 African countries were recorded and summarised as follows.

$n = 6$ \quad $\sum x = 7000$ \quad $\sum x^2 = 8700000$ \quad $\sum y = 456$ \quad $\sum y^2 = 36262$ \quad $\sum xy = 509900$

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\item Calculate the equation of the regression line of $y$ on $x$ for these 6 countries. [4]
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The original data were plotted on a scatter diagram and the regression line of $y$ on $x$ was drawn, as shown below.

\includegraphics{figure_3}

\begin{enumerate}[label=(\roman*)]
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\item The GDP for another country, Tanzania, is 1300 dollars. Use the regression line in the diagram to estimate the IMR of Tanzania. [1]

\item The GDP for Nigeria is 2400 dollars. Give two reasons why the regression line is unlikely to give a reliable estimate for the IMR for Nigeria. [2]

\item The actual value of the IMR for Tanzania is 96. The data for Tanzania ($x = 1300, y = 96$) is now included with the original 6 countries. Calculate the value of the product moment correlation coefficient, $r$, for all 7 countries. [4]

\item The IMR is now redefined as the infant mortality rate per hundred instead of per thousand, and the value of $r$ is recalculated for all 7 countries. Without calculation state what effect, if any, this would have on the value of $r$ found in part (iv). [1]
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\hfill \mbox{\textit{OCR S1 2013 Q3 [12]}}