Question

Question 1.

A realtor working in a large city wants to identify the secular trend in the weekly number of single-family houses sold by her firm. For the past 15 weeks she has collected data on her firm’s home sales, as shown in the table.

Week t	Homes sold yt	Week t	Homes sold yt	Week t	Homes sold yt
1	59	6	137	11	88
2	73	7	106	12	75
3	70	8	122	13	62
4	82	9	93	14	44
5	115	10	86	15	45

1. Plot the time series. What are the appearing components?
2. The realtor hypothesize the model y_t= b₀+ b₁t + b₂t²+ efor the secular trend of the weekly time series. Fit the model to the data and give the estimated equation.
3. Show the plot the model in part (b) and the observed data in the same graph. How well does the quadratic model describe the trend?
4. Use the model to forecast home sales in weeks 16 to 19 with a 90% prediction interval.
5. Calculate Durbin-Watson statistic and use it to test for autocorrelation.
6. Suppose that we have positive autocorrelation of order 1. Given S=13.09 and φ=0.14, find the forecast of weeks 16 to 19 with a 90% prediction interval.

Attach appropriate Minitab project and Excel file and outputs used to answer those questions.

Answer 1

A)

DATA

week	sales
1	59
2	73
3	70
4	82
5	115
6	137
7	106
8	122
9	93
10	86
11	88
12	75
13	62
14	44
15	45

it looks like inverted parabola

there should quadratic term in t to capture this

b)

sales	t	t^2
59	1	1
73	2	4
70	3	9
82	4	16
115	5	25
137	6	36
106	7	49
122	8	64
93	9	81
86	10	100
88	11	121
75	12	144
62	13	169
44	14	196
45	15	225

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.884645571
R Square	0.782597786
Adjusted R Square	0.746364084
Standard Error	13.74649061
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	2	8162.807951	4081.403975	21.59861503	0.000105581
Residual	12	2267.592049	188.9660041
Total	14	10430.4
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	39.48791209	12.24446298	3.224960716	0.007287108	12.80951906
t	19.13031674	3.52154451	5.432365454	0.000151924	11.45753038
t^2	-1.315287654	0.214023921	-6.145517033	4.97998E-05	-1.781605719

y^= 39.4879 + 19.1303 -1.3153 t^2

c)

the model fits the data well except at few instance

Please post rest parts again