Question

The production of wheat in Punjab in metric tons in a certain locality are given below. Fit a logarithmetic trend of the type y = ab^x and estimate the production for the year 2006.

Answer 1

The exponential / logarithmic equation is 

y = ab^x by taking logarithms

We get log y = log a + x log b

The normal equations are:- 

n log a + log b Σx = Σ logy.......(1) 

log a Σx + log b . 

Σx² = Σx log y .......(2) 

Using deviation method Σx = 0 

Let x and y be the year and production of wheat.

From equation (1); since Sx = 0

Similarly from (2)

The fitted legarithmic / Exponential trend equation is; logy = log a + x log b. 

i.e., logy= 1.0725 + x(0.0093)

Estimation for the year 2006; x = 6

logy = 1.0725 + 0.0093(6)

= 1.0725 + 0

logy =1.0725

and y = Anti log (log y)

= A.L (1.0725)

y = 11.82 metric tons.