Question

Company has expanded their operations to the world of amusement parks. Their new Park is currently being designed to open in 2020. They have the following data for another park and they also have another forecast:

Year Audiance Alternate Forecast

2013 60,109 70,151

2014 64,305 75,321

2015 59,935 80,321

2016 62,795 82,123

2017 62,673 83,157

2018 66,675 88,101

Please assume 2019 will add 10% in actual attendance.

a. Plot these data, develop a hypothesis of an appropriate model, estimate the model’s parameters, and forecast passengers for 2020-20222.

b. Illustrate an exponential smoothing model using an alpha of .1 and then an alpha of .5.

Answer 1

Below is the chart. from chart, it is clear that it has linear trend. So, we will calculate Slope & Intercept to find the linear regression equation -

Below is the formula for Slope & Intercept -

Below the result of Slope & Intercept -

Below will be the regression equation -

Y = 57522.29 + 1684.95X

For 2020, X will be 8, For 2021, X will be 9 and For 2022, X will be 10.

Putting the value of X in regression equation -

Forecast for 2020 = 57522.29 + 1684.95*8 = 71001.89

Forecast for 2021 = 57522.29 + 1684.95*9 = 72686.84

Forecast for 2022 = 57522.29 + 1684.95*10 = 74371.79

b)

Formula for Exponential Smoothing is -

F_t = F_t-1 + Alpha*(A_t-1 - F_t-1)

Below is the screenshot of formula applied in Excel

Below will be the result obtained -