A retail company collects sales data at its stores on a daily basis. The shops open 7 days per week. They have found by plotting the data that sale figures on Saturday and Sunday are higher than other days of the week. If they would like to fit a time series regression model with trend and seasonality components, how many seasonal dummies do they need to create? [Answer as an integer]
Question
A retail company collects sales data at its stores on a daily basis. The shops open 7 days per week. They have found by plotting the data that sale figures on Saturday and Sunday are higher than other days of the week. If they would like to fit a time series regression model with trend and seasonality components, how many seasonal dummies do they need to create? [Answer as an integer]
Solution
The company needs to create 6 seasonal dummy variables.
Here's why:
In time series analysis, a dummy variable is created for each level of the categorical variable, minus one. The "minus one" is because the last category is captured in the intercept term of the regression model.
In this case, the categorical variable is the day of the week, which has 7 categories (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday). Therefore, the company needs to create 7 - 1 = 6 dummy variables.
Each dummy variable will represent one day of the week. For example, the first dummy variable could be 1 if the day is Monday and 0 otherwise, the second could be 1 if the day is Tuesday and 0 otherwise, and so on. The day not represented by a dummy variable (in this case, it could be Sunday) is the reference category, and its effect is included in the intercept of the regression model.
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