In example 6 6, we noted that the quartic roots (y t y t 25 ) of the hotel room averages seemed to produce a transformed series with constant variation Figure 6 37 (page 322) presents the SAS output of an analysis of the quartic roots using the model y t 0 1 t 2 M 1 3 M 2 12 M 11 1 where y t y t 25 a Do all the variable seem important in the model Justify your answer b Find and report 169 and 170 , the point estimates of y 169 and y 170 c Using the least squares estimates in Figure 6 37, write the prediction equation for the model and compute 169 and 170 d Compute the point forecast 169 ( 25 169 ) 4 and 95 prediction interval (5 2913) 4 , (5 4065) 4 for y 169 , the hotel room average in January of next year e Compute the point forecast 170 and 95 prediction intervalfor y 170 , the hotel room average in February of next year f Test for positive autocorrelation by using the Durbin Watson statistic with 0 05 322 Chapter 6 Time Series Regression FIGURE 6 37 (for Exercise 6 5) SAS dummy variable regression of the quartit looks of the flotel room avery Parameter Estimates Parameter Standard Variable Error t Value DF Estimate Pr It 568 07 Intercept 4 80732 0 00846 79 01

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In example 6.6, we noted that the quartic roots (y t * = y t .25 ) of the hotel room averages seemed to produce

In example 6.6, we noted that the quartic roots (y_t^*= y_t^.25) of the hotel room averages seemed to produce a transformed series with constant variation. Figure 6.37 (page 322) presents the SAS output of an analysis of the quartic roots using the model

y_t^*=_{0 +1}t +₂M₁+₃M₂+ . . . +₁₂M₁₁+₁

where

y_t^*= y_t^.25

a. Do all the variable seem important in the model? Justify your answer.

b. Find and report^*_{169 and}^*₁₇₀, the point estimates of y^*₁₆₉and y^*_170.

c. Using the least squares estimates in Figure 6.37, write the prediction equation for the model and compute^*_{169 and}^*_170.

d. Compute the point forecast^*₁₆₉= (^.25₁₆₉)⁴and 95% prediction interval [(5.2913)⁴, (5.4065)⁴] for y₁₆₉, the hotel room average in January of next year.

e.Compute the point forecast^*₁₇₀and 95% prediction intervalfor y₁₇₀, the hotel room average in February of next year.

f. Test for positive autocorrelation by using the Durbin-Watson statistic with= 0.05.

322 Chapter 6 Time Series Regression FIGURE 6.37 (for Exercise 6.5) SAS dummy variable regression of the quartit looks of the flotel room avery Parameter Estimates Parameter Standard Variable Error t Value DF Estimate Pr > It! 568.07 Intercept 4. 80732 0. 00846 79.01 <.0001 time . m1 m2 m3 m4 ms m6 m7 mb m9 m10 durbin-watson d dep var predicted std error obs qtrooty value mean predict cl table exercise number of reported cases a new disease over the last months month>