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>