Question

Please answer the following questions with actual average sales prices of existing single family homes in the United States over a number of years. (10pts)

Year	Avg Price
1	$114,400
2	$115,300
3	$124,700
4	$126,600
5	$129,300
6	$133,500
7	$135,800
8	$141,800
9	$150,500
10	$159,100
11	$168,300
12	$176,200
13	$185,300

Prepare a line graph of these data. Do the data appear to be stationary or non-stationary?

Create a (double) moving average model (with k=2) for the data set.

Prepare a line graph comparing the double moving average predictions against the original data.

What are the forecasts for the next two years using this technique?

Use Holt’s method to create a model that minimizes the MSE for the data set. Use solver to determine the optimal values of alpha and beta.

What are the optimal values of alpha and beta?

Prepare a line graph comparing the predictions from Holt’s method versus the original data.

What are the forecasts for the next two years using this technique?

Use regression analysis to answer the following questions.

Fit a linear trend model to the data set. What is the estimated regression function?

Prepare a line graph comparing the linear trend predictions against the original data.

Answer 1

a) Line graph

The data is stationary since the variance is less.

Double Moving Average
Year	Avg Price	M1(t)	M2(t)	F(t)	Error
1	$114,400
2	$115,300	$114,850
3	$124,700	$120,000	$117,425
4	$126,600	$125,650	$122,825	$115,708.33	$10,892
5	$129,300	$127,950	$126,800	$120,941.67	$8,358
6	$133,500	$131,400	$129,675	$126,033.33	$7,467
7	$135,800	$134,650	$133,025	$128,525.00	$7,275
8	$141,800	$138,800	$136,725	$131,941.67	$9,858
9	$150,500	$146,150	$142,475	$135,341.67	$15,158
10	$159,100	$154,800	$150,475	$140,025.00	$19,075
11	$168,300	$163,700	$159,250	$147,591.67	$20,708
12	$176,200	$172,250	$167,975	$156,283.33	$19,917
13	$185,300	$180,750	$176,500	$165,125.00	$20,175
				$173,666.67	($173,667)
				$60,250.00	($60,250)

Regression
Year	Avg Price	Predicted Y
1	$114,400	$108,441
2	$115,300	$114,224
3	$124,700	$120,007
4	$126,600	$125,790
5	$129,300	$131,573
6	$133,500	$137,355
7	$135,800	$143,138
8	$141,800	$148,921
9	$150,500	$154,704
10	$159,100	$160,487
11	$168,300	$166,270
12	$176,200	$172,053
13	$185,300	$177,836
Regression fuunction
Ypred=102657.69+5782.96*Avg.Price