Simple linear regression models

Linear regression models can be built to obtain preliminary insight about the trend and seasonal impact on the time series variable. The trend and seasonal components are specified as independent variables while the time series, visitors count here, is the dependent variable. We make the following assumptions while building the linear regression model:

1. The time series is linear in the trend and seasonal variables.
2. The trend and seasonal components are independent of each other.
3. The observations, time series values, are independent of each other.
4. The error associated with the observation follows normal distribution.

Let Y_t 1 < t < T, denote the time series which observations at the time points 1, 2, ..., T. For example, in our overseas visitors data, we have T = 228. In the simplistic regression model, the trend variable is the vector 1, 2, ..., T, that is, X^Tr = (1, 2, ..., T). We know that for monthly data, we have the month name as the seasonal indicator...