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 is
Period Sales
1 19
2 18
3 15
4 20
5 18
6 22
7 20
We 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.
