To see the effect on yield, trend analysis was done with yield as the dependent variable. Yield has a quadratic variation with fertilizer consumption as shown by

y = 470 + 221.7 x F - 24.94 F2

This means that larger inputs of fertilizer may not lead to desirable effect on yield. Very large value of F will, in fact, reduce the yield. A precise relationship should be established.

The relationship between yield (y) and fertilizer (F) consumption for the period 1955-56 to 1972-73 comes out to be linear as

y = 504.6 + 111.3 x F

Whereas the same relationship for the second period 1973-74 to 1988-89 is quadratic given by

y = 552.5 + 205.1 * F - 24.91 x F2

This again reinforces the previous conclusion. During the first period, fertilizer usage was very small and so we have a linear increase in yield. But additional use of fertilizer leads to the second relationship which states that there is an upper value for fertilizer usage for maximum yield.

A similar quadratic relationship between yield (y) and irrigation (I) results in

y = 433.7 + 65.61 x I - 1.196 x I2

If we devide the entire period into two periods 1955-56 to 1972-73 and 1972-73 to 1988-89 as before, the relationships are

y = 372.7 + 18.51 x I (linear) (period 1)

y = -165.8 + 100.3 I - 2.21 I2 (period 2)

This also suggests an upper bound for irrigation. But results are inconclusive. We need more data to confirm this and arrive at a meaningful conclusion.

A regression analysis to see the effect of irrigation and fertilizers on yield was made as follows: