Question

In a trendline based on four observations, if he average of Y is 80 and the slope of the line is 24 then the intercept is :

A. 20

B. 30

C.40

D. None of the above.

Answer 1

Solution:-(A) 20

Here the time points are 1,2,3,4

The trend line equation is

$Y = a+b*t$ ...(*)

where a : intercept

b : slope

Taking average on all 4 consecutive points,we get

$\sum_{t=1}^{4}Y_{t} = 4a+b\sum_{t=1}^{4}t$

$\Rightarrow \frac{1}{4}\sum_{t=1}^{4}Y_{t} = \frac{4a}{4}+b*\frac{1}{4}\sum_{t=1}^{4}t$

$\Rightarrow \bar{Y} =a+b*\frac{1}{4}\sum_{t=1}^{4}t$

$\Rightarrow \bar{Y} =a+b*2.50$

$\Rightarrow \bar{Y} =a+2.5b$

$\Rightarrow 80 =a+2.5*24$

$\Rightarrow a=80-(2.5*24)=80-60$

$\Rightarrow a= 20$