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Now that we have looked upon both the models, we have to decide which of them explains the changes in the demand for coffee better. To compare them we would use the MWD-test and test the following hypotheses:
H0: y is a linear function of x, z, and trend
H1: ln(y) is a linear function of ln(x), ln(z), and trend
This would imply that there are two possible functions of the relationship and the test would tell which is better.
According to Gujarati (p 265) the MWD-test involves 6 steps, which can be summarized in the following. First, one has to estimate both y and ln(y). Then new variables have to be created, by subtracting the estimated ln(y) from the logarithm of the estimated y or the estimated y form the antilog of the estimated ln(y). Lastly, one has to run new regressions including the newly obtained variables in them – the linear into the log-linear model and the logarithmic – into the linear. The H1 can be rejected if the coefficient of the new linear variable is significant by the usual t-test.

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