Question

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

Answer 1

Answer:

The equation of trend line is $y = 0.500000x + 16.857143$.

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

$y=a+bx$             .... (1)

where, a is y-intercept and b is slope.

$b=\frac{\sum_{i=1}^nx_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^nx_i^2-n\overline{x}^2}$

$a=\overline{y}-b\overline{x}$

Using the graphing calculator we get

$a=16.857143$

$b=0.500000$

Substitute these values in equation (1).

$y = 0.500000x + 16.857143$

The equation of trend line is $y = 0.500000x + 16.857143$.

Substitute x=8 to find the linear trend forecast for period 8.

$y = 0.500000(8) + 16.857143$

$y =20.857143$

$y \approx 20.86$

Therefore the linear trend forecast for period 8 is about 20.86.