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A ski resort has come up with a model to predict the number of guests (given in hundreds) checking in throughout the year. The time series model contains both a trend and a seasonal component and is given by the following:

y_t = 0.2 \times \text{Time}_t + 10.5 + 3.0 \times D_{2t} + 2.1 \times D_{3t} + 2.8 \times D_{4t}

The trend component is reflected in variable $\text{TIME}_{(t)}$ , where $(t) = \text{month}$ .

Seasons are defined as follows:

Season	Months	Dummy
Winter	December, January and February	-
Spring	March, April and May	$D_{(2t)}$
Summer	June, July and August	$D_{(3t)}$
Fall	September, October and November	$D_{(4t)}$

The model starts in April 2019, i.e., $y_{(T+1)}$ refers to May 2019. How many more guests are expected in April 2020 than in July of the same year?

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NNikitesh

Last updated: February 2, 2026 at 10:22

A

10

B

30

C

9

D

15

Explanation:

The model is given as:

y_t = 0.2 \times \text{Time}_t + 10.5 + 3.0 \times D_{2t} + 2.1 \times D_{3t} + 2.8 \times D_{4t}

Since we have three dummies and an intercept, quarterly seasonality is reflected by the intercept (10.5) plus the three seasonal dummy variables ( $D_2, D_3$ and $D_4$ ).

If $y_{(T+1)} = \text{May 2019}$ , then April 2020 = $y_{(T+12)}$ and July 2020 = $y_{(T+15)}$ .

Finally, note that April falls under $D_{(2t)}$ , while July falls under $D_{(3t)}$ .

Step-by-step calculation:

April 2020 (y_{T+12}):
- Time_t = 12 (since it's the 12th month from the start)
- April is in Spring season, so D_{2t} = 1, D_{3t} = 0, D_{4t} = 0
- y_{April2020} = 0.2 × 12 + 10.5 + 3.0 × 1 + 2.1 × 0 + 2.8 × 0
- y_{April2020} = 2.4 + 10.5 + 3.0 = 15.9 (in hundreds)
July 2020 (y_{T+15}):
- Time_t = 15 (since it's the 15th month from the start)
- July is in Summer season, so D_{2t} = 0, D_{3t} = 1, D_{4t} = 0
- y_{July2020} = 0.2 × 15 + 10.5 + 3.0 × 0 + 2.1 × 1 + 2.8 × 0
- y_{July2020} = 3.0 + 10.5 + 2.1 = 15.6 (in hundreds)
Difference:
- Difference = y_{April2020} - y_{July2020} = 15.9 - 15.6 = 0.3 (in hundreds)
- Since the answer is in actual number of guests (not hundreds), multiply by 100: 0.3 × 100 = 30 guests

Therefore, April 2020 is expected to have 30 more guests than July 2020.

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