Chapter 10.4: Multiple Linear Regression: Controlling for Variables - An Introduction 

It is my favorite chapter of the whole book and I do hope it inspires you to take that second or third course in statistics. Understanding cause and effect is what we are all trying to do as a large community of people fumbling around in the dark. Right?

Usually, there's some degree of collinearity between predictor variables. In this case, there is. If you want to predict who will win the election, you could probably get by with just the approval rating. If you want to know the effect of campaign spending on the election result, you definitely want both variables. It depends on the question you are trying to answer.

Hi Goodlife Always. It doesn't always work out that way but it does sometimes. If the predictor variables are not collinear then you have found two independent predictor variables (that's really good). Quite often though, the predictor variables are correlated and you have collinearity. There's nothing wrong with that but if they are strongly correlated, you may only need one of them to make accurate predictions and avoid over-fitting the model.

Hello Wasia. I didn't select these values. They were determined from multiple linear regression software applied to this data (which I didn't provide). If you are wondering, there is no way for you to determine these slopes from the video presentation. It is meant to be a demonstration of how simple (one variable) linear regression can be misleading and how multi-variable linear regression can make sense of it.

Indeed. You're right. I say spending is not as important as the approval rating but that is an overstatement. If you're an incumbent looking at re-election with a lot of money and a low approval rating, spending is a lot more important than the approval rating.