Consider the following time series. t 1 2 3 4 5 6 7 Yt 83 61...

Consider the following time series.

t	1	2	3	4	5	6	7
Y_t	83	61	45	36	29	28	36

b. Develop the quadratic trend equation for the time series. Enter negative value as negative number.(to 3 decimals)

T_t = ______ + _______t + ________ t²

c. What is the forecast for t = 8?

Solutions

Expert Solution

Following is the Quardratic model:

Regression Analysis

	R²	0.999
	Adjusted R²	0.998	n	7
	R	0.999	k	2
	Std. Error	0.838	Dep. Var.	Yt

ANOVA table
Source	SS	df	MS	F	p-value
Regression	2,338.0476	2	1,169.0238	1664.37	1.44E-06
Residual	2.8095	4	0.7024
Total	2,340.8571	6


Regression output					confidence interval
variables	coefficients	std. error	t (df=4)	p-value	95% lower	95% upper
Intercept	107.4286
t	-28.1310	0.7485	-37.584	2.99E-06	-30.2091	-26.0528
t²	2.5119	0.0914	27.470	1.04E-05	2.2580	2.7658

Predicted values for: Yt
			95% Confidence Interval		95% Prediction Interval
t	t²	Predicted	lower	upper	lower	upper	Leverage
8	64	43.1	39.5	46.8	38.8	47.5	2.429

The required model is:

The forecasted value is

orchestra answered 1 year ago

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