Question

Tabulate the trend values of the years and compute the expected sales trend for the year 2002.

Hint:

To calculate trend values for future years, extend the coded time variable \( t \) and substitute into the trend equation.

Answer 1

Step 1: Utilize the trend equation \( y = 5.93 + 1.18t \).

Step 2: Calculate the trend values for \( t = -2, -1, 0, 1, 2, 3 \):

\[ \begin{array}{|c|c|c|} \hline \textbf{Year} & t & \textbf{Trend Value (y)} \\ \hline 1996 & -2 & 5.93 + 1.18(-2) = 3.57 \\ 1997 & -1 & 5.93 + 1.18(-1) = 4.75 \\ 1998 & 0 & 5.93 + 1.18(0) = 5.93 \\ 1999 & 1 & 5.93 + 1.18(1) = 7.11 \\ 2000 & 2 & 5.93 + 1.18(2) = 8.29 \\ 2001 & 3 & 5.93 + 1.18(3) = 9.47 \\ \hline \end{array} \]

Step 3: Determine the trend value for the year 2002, where \( t = 4 \):

\[ y = 5.93 + 1.18(4) = 10.65. \]

Final Answer:

• The trend values for the years 1996 through 2001 are \( 3.57, 4.75, 5.93, 7.11, 8.29, \) and \( 9.47 \), respectively.
• The projected trend for sales in 2002 is \( 10.65 \) lakh ₹.