Explain the difference between dependent and independent var

Explain the difference between dependent and independent variables? Why is this distinction not made in correlation? Why is it important in regression? •

How is a line fit through the data? In other words, what is minimized to fit the equation of a line? •

What is the coefficient of determination? Why is it important to report this value with a regression? •

How can plotting residuals help find outliers and nonlinear patterns in the data? •

What is the danger of including extreme values in a regression?

Solution

Explain the difference between dependent and independent variables?

Why is this distinction not made in correlation?

The best way to think about this is to imagine a scatterplot of points with y on the vertical axis and xrepresented by the horizontal axis. Given this framework, you see a cloud of points, which may be vaguely circular, or may be elongated into an ellipse. What you are trying to do in regression is find what might be called the \'line of best fit\'. However, while this seems straightforward, we need to figure out what we mean by \'best\', and that means we must define what it would be for a line to be good, or for one line to be better than another, etc. Specifically, we must stipulate a loss function. A loss function gives us a way to say how \'bad\' something is, and thus, when we minimize that, we make our line as \'good\' as possible, or find the \'best\' line.

Why is it important in regression? •

First, some similarities:

Second, some differences: