Question

We have been given the history of shipping costs below. You have been asked to calculate a linear trend line for this data.

What is the intermediate solution for the value of b? (Your answer should be an integer)

Week	Costs
1	466965
2	433500
3	548436
4	557338

Answer 1

Solution:

The linear trend line for cost forecast is represented by the following equation

y = a + b *x

Where y​= Dependent Variable (cost) and x​= Independent Variable (week)

And a is the y-intercept of the line and b is the slope of the line.

Formula to calculate the a and b are following

Slop b = (n * Σxy – Σx * Σy) / {n * Σ(x^2) - (Σx) ^2}

Intercept a = (Σy – b * Σx) / n

Where,

n is number of period = 4

Σy is the sum of total costs

Σx is the sum of weeks

Σxy is the sum of total costs * weeks

Σx^2 is the sum of squares of weeks

	x	y	xy	x^2
	1	466965	466965	1
	2	433500	867000	4
	3	548436	1645308	9
	4	557338	2229352	16
Sum =	10	2006239	5208625	30

n =	4
Slop b = (n * Σxy – Σx * Σy) / {n * Σ(x^2) - (Σx)^2} =	38605.5
Intercept a = (Σy – b * Σx) / n =	405046

The linear trend line is Y = 405046 + 38605.5X

The intermediate solution for the value of b

Slop b = (n * Σxy – Σx * Σy) / {n * Σ(x^2) - (Σx) ^2}

= (4 * 5208625 – 10 * 2006239) / {4 * 30 - (10) ^2}

= 38605.5