Find the linear trend forecast for period 8 given the following data: Period Sales 1 19 2 18 3 15 4 20 5 18 6 22 7 20
Accepted Solution
A:
Answer:The equation of trend line is [tex]y = 0.500000x + 16.857143[/tex].The linear trend forecast for period 8 is about 20.86.Step-by-step explanation:The given data table isPeriod Sales 1 19 2 18 3 15 4 20 5 18 6 22 7 20We need to find the linear trend forecast for period 8.The general form of linear regression is[tex]y=a+bx[/tex] .... (1)where, a is y-intercept and b is slope.[tex]b=\frac{\sum_{i=1}^nx_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^nx_i^2-n\overline{x}^2}[/tex][tex]a=\overline{y}-b\overline{x}[/tex]Using the graphing calculator we get[tex]a=16.857143[/tex][tex]b=0.500000[/tex]Substitute these values in equation (1).[tex]y = 0.500000x + 16.857143[/tex]The equation of trend line is [tex]y = 0.500000x + 16.857143[/tex].Substitute x=8 to find the linear trend forecast for period 8.[tex]y = 0.500000(8) + 16.857143[/tex][tex]y =20.857143[/tex][tex]y \approx 20.86[/tex]Therefore the linear trend forecast for period 8 is about 20.86.