Despite the growth in digital entertainment the nations 400

Despite the growth in digital entertainment, the nation’s 400 amusement parks have managed to hold on to visitors, as the following data show:

For estimation, let the variable t assume values 1, 2,…, 8.

Estimate a linear trend model and an exponential trend model for the sample. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)

Calculate the MSE for both trends. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

By comparing MSE, which of the above methods perform better?

Given the model of best fit, make a forecast for visitors to amusement parks in 2008. (Round your intermediate calculations to 4 decimal places. Enter your answer in millions rounded to 1 decimal place.)

Given the model of best fit, make a forecast for visitors to amusement parks in 2009. (Round your intermediate calculations to 4 decimal places. Enter your answer in millions rounded to 1 decimal place.)

Solution

b-1)

b-2)

b-3) on comparinfg,the linear trend performs better because its MSE is less than the other

C-1) the forecast for visitors to amusement parks in 2008 is given by 322.1429 + 3.107143(9) = 350.11 millions

C-2) the forecast for visitors to amusement parks in 2009 is given by 322.1429 + 3.107143(9) = 353.21 millions