Consider the following regression model with the dependent variable y_t and the linear trend:
where u_t is a random variable and betas are parameters of the model.
How would you decide whether the linear trend is significant?

Question

Consider the following regression model with the dependent variable y_t and the linear trend:

where u_t is a random variable and betas are parameters of the model.

How would you decide whether the linear trend is significant?

Accepted Answer

The t-test for
individual significance is appropriate for testing the linear trend.

Answer

The trend is significant if the estimated value of beta_1 is not zero.

Answer

The model cannot be used to test the linear trend since the time series
should be detrended first.

Answer

The coefficient of determination is appropriate for testing the linear
trend.

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