Hi k9queen!
Here are the answers to your questions.
a) The direction of causation is not clear in this case, as in most
supply/demand situations. For instance, it would be possible to argue
that the direction of causation is from avg. room rate to occupancy
rate. A plausible argument would be that a higher room rate makes
tourists want to travel to somewhere cheaper, so that a higher room
rate causes a lower occupancy rate. On the other hand, it's also be
possible to argue that the direction of causation is from occupancy
rate to room rate. In this case, the idea could be: that room rates
are high *because* occupancy rate is high. Since the supply of
available rooms is small (when occupancy rate is high), one would
expect that room prices should go up. Therefore, the direction of
causation is not clear. Moreover, it's not clear wether these
variables should be positively correlated (higher occupancy rates go
in hand with higher room rates) or negatively correlated (higher
occupancy rates go in hand with lower room rates).
b,c and d) Here I ran a regression in Excel using the occupancy rate
as a dependent variable and the room rate as an independent variable.
The R-squared I got was 0.62. The R-squared is a measure that compares
the variance of the errors of the regression with the variance of the
dependent variable (Y). In this case, it's telling us that the
variance of the errors is 38% of the variance of Y, so that the
regression model accounts for the other 62% of the variance of Y.
However, this has nothing to do with causation. Therefore, since the
R-squared measure is independent of the direction of causation, it's
exactly the same if we decide that the dependent variable is the
occupancy rate or that the dependent variable is the avg. room rate.
In other words, R-squared is also another way to measure the
correlation between both variables. Recall that correlation between 2
variables has nothing to do with causation: it's possible that A
causes B, or that B causes A, or that A and B are both caused by C.
Since causation doesn't matter to R-squared, it doesn't matter wether
we consider the room rate or the occupancy rate to be the "exogenous"
variable; the R-squared will be exactly the same.
In order to verify this, I ran a regression using the room rate as the
dependent variable and the occupancy rate as the independent (or
exogenous) variable. I got that the R-squared is 0.62, exactly the
same as before.
I hope this helps! If you have any questions regarding my answer,
please don't hesitate to request a clarification before rating it.
Otherwise I await your rating and final comments.
Best wishes!
elmarto |
