Using the semi-average method, determine the trend line equation for the following sales data (in tonnes) for the year 1979: Jan: 280, Feb: 300, Mar: 280, Apr: 280, May: 270, Jun: 240, Jul: 230, Aug:

There are 12 data points (months from January to December 1979).
First half (Months 1-6): 280, 300, 280, 280, 270, 240
Second half (Months 7-12): 230, 230, 220, 200, 210, 200

First semi-average ($S_1$):

This average corresponds to the mid-point of the first half. The months are 1, 2, 3, 4, 5, 6. The mid-point is between month 3 and month 4, which is $T_1 = 3.5$.

Second semi-average ($S_2$):

This average corresponds to the mid-point of the second half. The months are 7, 8, 9, 10, 11, 12. The mid-point is between month 9 and month 10, which is $T_2 = 9.5$.

We have two points $(T_1, S_1) = (3.5, 275)$ and $(T_2, S_2) = (9.5, 215)$.

Calculate the slope ($b$):

Calculate the y-intercept ($a$) using one of the points, for example $(3.5, 275)$:

The trend line equation is $Y_t = a + bT$.

where $Y_t$ is the sales in tonnes and $T$ is the month number (e.g., $T=1$ for January, $T=2$ for February, etc.).