Regression Analysis
In many of the recent
blog posts, along with several discussions in class, we have touched upon the
topic of regression analysis. In this
post, I will elaborate on the basics of regression analysis
Regression analysis is
a method of statistical analysis which estimates the relationship among
variables. This method focuses in the relationship between a dependent variable
(y) and one or more independent variables (the variables that affect the thing
you want to calculate). Usually, this method estimates something called “conditional
expectation,” which refers to the average value of the dependent variable (the
variable you want to calculate) when the other variables are fixed.
Regression analysis is
mostly used for prediction and forecasting. When discussing many of the
relationships in class, we mentioned that we could make equations to predict
certain outcomes. A regression model is presented as an equation, which solves
for a dependent variable (y) given the known values of the X variables.
Y= K + AX1+BX2
·
Being
A and B coefficients
·
K is
a constant ( similar to a y-intercept)
·
X1
and X2 being variables
When we predict within the range of values
that we have in our data set, we are interpolating our data. When we are
predicting values outside of our range, we are extrapolating.
Usually, it is easier
to trust the interpolation of our data as we have something to back it up. On
the other hand, the extrapolation can be misguiding. When we are predicting
something outside of our range, we assume that the conditions are the same and
this might not be the case. A rule of thumb is that the farther away we
extrapolate our data, the more likely we are to make a mistake in our
predictions.
I remember you mentioning this in class and I was curious about what you meant by this. Thanks for explaining this to us in a blog post. I didn't really understand the different between interpolation and extrapolation, and the impact it had on data.
ReplyDeleteA picture would easily clarify the difference between interpolation and extrapolation (but I can't put pictures in comments). Xavi, you could also explain this in terms of the example that brought it up in class in the first place.
ReplyDelete