The line of least fit is a line from which the sum of the deviations of various points is zero. This is the best method for obtaining the trend values.
(i) The straight line trend is represented by
 Y = a + b X ...(1)
where Y is the actual value and X is time
(ii)  The constants 'a' and 'b' are estimated by solving the following two normal Equations
 \(\sum\) Y = n a + b \(\sum\) X
\(\sum\) XY = a\(\sum\) X + b  \(\sum\) X²   where n is the number of years given in the data.
(iii) By substituting the values of 'a' and 'b' in the trend equation (1), we get the line of best fit.

Computation of four- yearly moving averages.

Since the number of years is odd(seven), we will leave the middle year’s production value and obtain the averages of first three years and last three years.

\(\overset { = }{ X } =\frac { \sum { \bar { X } } }{ 10 } =\frac { 442 }{ 10 } =44.2\)
\(\bar { R } =\frac { \sum { R } }{ n } =\frac { 58 }{ 10 } =5.8\)
\(UCL=\overset { = }{ X } +{ A }_{ 2 }\bar { R } \)
= 44.2 + 0.483(5.8) = 47.00
\(CL=\overset { = }{ X } =44.2\)
\(LCL=\overset { = }{ X } -{ A }_{ 2 }\bar { R } =44.2-0.483(5.8)=41.39\)
The above diagram shows all the three control lines with the data points plotted, since four points falls out of the control limits, we can say that the process is out of control.