Following table shows the all India infant mortality rates (per ’000) for years 1980 to 2010 :Year1980198519901995200020052010IMR10754310Fit the trend line to the above data by the method of least squares.

Answer: Trend line \(y = 4.2857 - 1.5714u\), where \(u = \dfrac{t - 1995}{5}\)

There are 7 years (odd), equally spaced 5 years apart, so take the origin at the middle year 1995 and \(u = \dfrac{t - 1995}{5}\).

Since \(\sum u = 0\), the normal equations give \(a = \dfrac{\sum y}{n} = \dfrac{30}{7} = 4.2857\) and \(b = \dfrac{\sum uy}{\sum u^2} = \dfrac{-44}{28} = -1.5714\).

The trend line is \(y = 4.2857 - 1.5714u\). The trend values in the last column are found by putting \(u = -3, -2, \dots, 3\). The negative slope shows that the infant mortality rate is falling.