# Fit an equation of the form Y = a+bX + cX 2 to the data given below:

Question: Fit an equation of the form Y = a+bX + cX2 to the data given below:

Years 1991 1992 1993 1994 1995
Consumption of wheat (in Qtls.) 25 28 33 39 46

Solution
Calculations for Second Degree Trend

The first step in fitting a second degree equation is translate the independent variable (time) into a coded time variable X. Not that the coded variable X is listed in one year intervals because there is an odd number of elements in our time series. Now find values of a, b and c by solving the three equations meant for the purpose.

Three equations are

By substituting the given values in the above equations, we get :

Now we shall find a and c by solving equations 1(a) and 2(a). 1. Multiply equation 1(a) by 2 and subtract equation 2(a) from equation 1(a)

In general, the exponential trend is applicable, where growth in the time series data is nearly at a constant rate per unit of time (expressed in percentage). When the aggregate variable related to national product, population, or production in the country as a whole or in a region are given we normally use exponential trend.

In general, the exponential trend is applicable, where growth in the time series data is nearly at a constant rate per unit of time (expressed in percentage). When the aggregate variable related to national product, population, or production in the country as a whole or in a region are given we normally use exponential trend.

Taking logarithm of both sides of Eq. (5), we get
Log Y = Log a + X log b ……….. (6)

When plotted on a semi logarithmic graph, the curve gives a straight line. However, on an arithmetic chart the curve gives a non-linear trend.

To obtain the values of the two constants, a and b, we need to solve simultaneously the two normal equations :

The rate of growth implicit in a semilogarithmic trend is often of interest. It is derived by solving the equation for compound interest – log (1+r) = b 1

Here b1 is the slope and r is the rate of growth.