1.10 Consider again the following estimated model: Y = Bo+B+Bzxzi+B3x3i+ẞ4x4i + U₁ Given below is part of the regression output with and without robust standard errors: Coefficient SE P-value Robust SE P-value Constant 5.00 1.20 0.001 1.30 0.002 2.50 0.80 0.003 1.10 0.023 X21 -1.80 0.90 0.045 1.20 0.080 X31 6.65 1.65 0.001 1.76 0.001 X4i 3.50 0.50 0.001 0.66 0.001 Suppose you are writing your final report to a manager who cares only about results that pass all the relevant diagnostic tests. Which results should you focus on? Interpret the coefficients ẞ₁ and ẞ2 at the 5% level of significance. [5]

Estimate the double-log (log linear) time trend model for log cruise ship arrivals against log time. Estimate a linear time trend model of cruise ship arrivals against time. Calculate the root mean square error between the predicted and actual value of cruise ship arrivals. Is the root mean square error greater for the double log non-linear time trend model or for the linear time trend model?

Savings-Mart (a chain of discount department stores) sells patio and lawn furniture. Sales are seasonal, with higher sales during the spring and summer quarters and lower sales during the fall and winter quarters. The company developed the following quarterly sales forecasting model: Y t=8.25+0.125t2.75D1t+3.50D3t where Y t=predictedsales(million)inquartert 8.25=quarterlysales(million)whent=0 t=timeperiod(quarter)wherethefourthquarterof2002=0,firstquarterof2003=1,secondquarterof2003=2,... D1t={1forfirst-quarterobservations0otherwiseD2t={1forsecond-quarterobservations0otherwiseD3t={1forthird-quarterobservations0otherwise Forecast Savings-Marts sales of patio and lawn furniture for each quarter of 2010.

In attempting to formulate a model of the passenger arrival data on cruise ships over time would a nonlinear (perhaps a multiplicative exponential) model be preferable to a linear model of cruise ship arrivals against time? What about in the case of the passenger arrivals by ferry against time?

Metropolitan Hospital has estimated its average monthly bed needs as N=1,000+9X where X=timeperiod(months);January2002=0 N=monthlybedneeds Assume that no new hospital additions are expected in the area in the foreseeable future. The following monthly seasonal adjustment factors have been estimated, using data from the past five years: Forecast Metropolitans bed demand for January, April, July, November, and December 2007. If the following actual and forecast values for June bed demands have been recorded, what seasonal adjustment factor would you recommend be used in making future June forecasts?

Bell Greenhouses has estimated its monthly demand for potting soil to be the following: N=400+4X where N=monthlydemandforbagsofpottingsoil X=timeperiodsinmonths(March2006=0) Assume this trend factor is expected to remain stable in the foreseeable future. The following table contains the monthly seasonal adjustment factors, which have been estimated using actual sales data from the past five years: Forecast Bell Greenhouses demand for potting soil in March, June, August, and December 2007. If the following table shows the forecasted and actual potting soil sales by Bell Greenhouses for April in five different years, determine the seasonal adjustment factor to be used in making an April 2008 forecast.

Plot the logarithm of arrivals for each transportation mode against time, all on the same graph. Which now appears to be growing the fastest?

A firm experienced the demand shown in the following table. *Unkown future value to be forecast Fill in the table by preparing forecasts based on a five-year moving average, a three-year moving average, and exponential smoothing (with a w=0.9 and a w=0.3). Note The exponential smoothing forecasts may be begun by assuming Y t+1=Yt. Using the forecasts from 2005 through 2009, compare the accuracy of each of the forecasting methods based on the RMSE criterion. Which forecast would you have used for 2010? Why?