A trend forecast equation is being developed to describe sal

A trend forecast equation is being developed to describe sales over time. The analyst has completed the tabulation using the raw data and is about to develop the forecast equation with the least squares equations. Use the calculated trend information tabled below to calculate the simple linear regression equation (hint: for Y = a + bX, find the values of a and b). Number of periods, n = 5 ybar = 5 xbar = 3 Sum ( x2 ) = 55 Sum ( xy ) = 80 The calculated linear regression equation is:

Solution

Let Y = a + bX be the required linear regression equation.

Then the normal equations are given by

Y = na + bX

XY = aX + bX²

we are given by n = 5 , Y = 5 , X = 3 , X² = 55 and XY = 80

Substitute these values in the above normal equations , we get

5 = 5a + 3b

80 = 3a + 55b

Solving these equations , we get

a = 0.131578947   and b = 1.447368421

Hence , the required linear regression equation is   Y = 0.131578947 + (1.447368421)X