3 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.
$$n = 6 \quad \sum x = 7000 \quad \sum x ^ { 2 } = 8700000 \quad \sum y = 456 \quad \sum y ^ { 2 } = 36262 \quad \sum x y = 509900$$
- Calculate the equation of the regression line of \(y\) on \(x\) for these 6 countries.
The original data were plotted on a scatter diagram and the regression line of \(y\) on \(x\) was drawn, as shown below.
\includegraphics[max width=\textwidth, alt={}, center]{13d8d940-fd63-4b62-bd7a-aa7174f6af4b-3_721_1246_680_408} - The GDP for another country, Tanzania, is 1300 dollars. Use the regression line in the diagram to estimate the IMR of Tanzania.
- 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.
- 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.
- 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).