Question

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

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

Week Costs

week 1. 497430

week 2. 500072

week 3. 535584

week 4. 514058

Answer 1

Let’s assume that the linear trend equation for shipping costs is represented by the following equation

y = a + b *t…………………….. (1)

Where 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 * Σty – Σt * Σy) / {n * Σ (t^2) - (Σt) ^2}

Intercept a = (Σy – b * Σt) / n

Where,

n is number of period = 4 (number of weeks)

Σy is the sum of total costs

Σt is the sum of weeks

Σty is the sum of total costs * weeks

Σt^2 is the sum of squares of weeks

	Week (t)	Cost (y)	y*t	t^2
	1	497430	497430	1
	2	500072	1000144	4
	3	535584	1606752	9
	4	514058	2056232	16
Sum	10	2047144	5160558	30

Now,   Slop b = (n * Σty – Σt * Σy) / {n * Σ (t^2) - (Σt) ^2}

= (4 * 5160558 – 10 * 2047144) / (4 * 30 – 10^2) =8540

Therefore value of b is 8540

And Intercept a = (Σy – b * Σt) / n = (2047144 – 8540 * 10)/4 = 490437

Now putting the value of a & b in equation (1), we get linear trend equation

Y = 490437 + 8540 * t