Question

8. Shoreline Park in Mountain View, California, has kept close tabs on the number of patrons using the park since its opening in January 1993. For the first six months of 2013, the following figures were recorded: Month Number of Patrons Number of Patrons 133 285 Month January February March May June 640 ,876 2,550 a. Draw a graph of these six data points. Assume that January period 1, February period 2, and so on. Using a ruler, "eyeball" the best straight-line fit of the data. Estimate the slope and intercept from your graph. b Compute the exact values of the intercept a and the slope b from the regression equations regression equation determined in part (b)? would you be about the accuracy of the forecasts that you obtained? C. What are the forecasts obtained for July through December 2013 from the d. Comment on the results you obtained in part (c). Specifically, how confident 29·The Mountain View Department of Parks and Recreation must project the total use of Shoreline Park for calendar year 2014. a. Determine the forecast for the total number of people using the park in 2014 based on the regression equation b. Determine the forecast for the same quantity using a six-month moving average. c. Draw a graph of the most likely shape of the curve describing the park's usage by month during the calendar year, and predict the same quantity using your graph. Is your prediction closer to the answer you obtained for part (a) or part (b) Discuss your results. 0. For the data in Problem 28, use the results of the regression equation to estimate the slope and intercept of the series at the end of June. Use these numbers as the initial values of slope and intercept required in Holt's method. Assume that α = . 15, β·10 for all calculations. a. Suppose that the actual number of visitors using the park in July was 2,150 and the number in August was 2,660. Use Holt's method to update the estimates of the slope and intercept based on these observations. b. What are the one-step-ahead and two-step-ahead forecasts that Holt's method gives for the number of park visitors in September and October? C. What is the forecast made at the end of July for the number of park attendees in Note:

Answer 1

28)

a.

3000 T 2500 2000 1500 S 1000 500 0 1 2 34 5 Month

estimated slope =500 and intercept = -500

b.

Solution For regression Month Jan Feb Mar t. D 133 183 285 640 1876 133 366 855 2560 9380 255015300 5667 28594 16 25 36 91 pr Jun Total 21 y=a+bx Dt-a + bt 21). (5667 28594 500,54 SStf 212 91 5667 ー-(500.54).-=-80 7,39

Then a So_-807,39 b G,-500,54 α-0,15 β-0,10

Therefore , Y = 500.54.X – 807.4

Slope = 500.54

Intercept = -807.4

c. 247= july, 248=August, 249=September and so on.

Forecast for July = -807.4 + (500.54 X 7) = 2696.38

Predicted values for: Number of patrons
		95% Confidence Intervals		95% Prediction Intervals
Month	Predicted	lower	upper	lower	upper	Leverage
247	122,826.686	49,345.830	196,307.541	49,334.988	196,318.384	3388.295
248	123,327.229	49,544.619	197,109.839	49,533.820	197,120.637	3416.181
249	123,827.771	49,743.407	197,912.136	49,732.653	197,922.890	3444.181
250	124,328.314	49,942.195	198,714.434	49,931.484	198,725.144	3472.295
251	124,828.857	50,140.983	199,516.731	50,130.316	199,527.399	3500.524
252	125,329.400	50,339.771	200,319.029	50,329.147	200,329.653	3528.867

d.We are not much confident about this prediction because this year 2013 is 20 year from the data given.