Question

Consider the following time series.

t	1	2	3	4	5
yt	5	10	10	15	14

(a)	Choose the correct time series plot.
	(i) (ii) (iii) (iv)
	- Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv)Item 1
	What type of pattern exists in the data?
	- Select your answer -Positive trend patternHorizontal stationary patternVertical stationary patternNegative trend patternItem 2
(b)	Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
	If required, round your answers to two decimal places.
	y-intercept, b0 =
	Slope, b1 =
	MSE =
(c)	What is the forecast for t = 6?
	If required, round your answer to one decimal place.

Answer 1

a) Time series plot:

Type of pattern : Positive trend pattern

b)

X	Y	XY	X²	Y²
1	5	5	1	25
2	10	20	4	100
3	10	30	9	100
4	15	60	16	225
5	14	70	25	196
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
15	54	185	55	646

Sample size, n =	5
x̅ = Ʃx/n = 15/5 =	3
y̅ = Ʃy/n = 54/5 =	10.8
SSxx = Ʃx² - (Ʃx)²/n = 55 - (15)²/5 =	10
SSyy = Ʃy² - (Ʃy)²/n = 646 - (54)²/5 =	62.8
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 185 - (15)(54)/5 =	23

Slope, b1 = SSxy/SSxx = 23/10 = 2.3

y-intercept, b0 = y̅ -b1* x̅ = 10.8 - (2.3)*3 = 3.9

Regression equation :

ŷ = 3.9 + (2.3) x

SSE = SSyy -SSxy²/SSxx = 62.8 - (23)²/10 = 9.9

MSE = SSE/(n-2) = 3.3

c)

Predicted value of y at x = 6

ŷ = 3.9 + (2.3) * 6 = 17.7