I changed the numbers in the number of bedroom variable.
The new correlation table looks like this:
The data table is as follows:
The regression output is as follows:
The coefficient table shows that square feet is not related to rent, where as number of bedrooms is related to rent. We can see that the correlation between number of bedrooms and square feet is very high i.e. .857 (much higher than .70). This explains that when we have two highly correlated x variables in the model at the same time, that means that one of them becomes significantly related to the y variable and other one becomes un-related – even though they may each be related to y variable when the other one is not present in the model. This is happenening because they share such high correlation that when one x variable gets to explain the y, then the other highly correlated x variable does not have any thing else left to explailn the y.
Now interesting we see that number of bedrooms is related to rent and not the square feet. In other example else where in this blog we see that square is related to rent and not the number of bedrooms. Here in this example as I mentioned above I massaged some number of bedrooms so that I got a different correlation matrix this time (see above). Since this time Rent shares higher correlation with number of bedrooms (.946) as opposed to square feet (.876) thats why number of bedrooms gets to explain the y (rent) first, and becomes significantly related to rent, and square feet goes second, and has no new story to tell (since number of bedrooms already explained the story), and hence square feet is left un-related to rent (with p value higher than alpha i.e. .05).