Linear Regression

Right now, my son is learning in junior high.  I’ve told him that in my opinion, the two deepest insights that he will learn from algebra are this and the quadratic equation.

My son was not convinced.  He said it was obvious to him that the quadratic equation was deep because the equation was complicated but in his view, graphing a line was pretty straight since is the slope (whether the line goes up or down) and is the -intercept (the intersection on the axis when ).

I asked him if he knew the difference between causality and a correlation.  He said he did and not to repeat my anecdote about ice cream sales and drowning rates (as ice cream sales increase, more people drown.  This a non-causal correlation where both data points have a common cause– warmer weather: more people buy ice cream and more people go swimming.  Details here).

I told him that one of the most powerful ways to analyze correlation is through a linear regression.  When he looked unclear, I added: using .

There are many types of correlation.  But sometimes, if there a strong enough relationship between two variables, a prediction can be made.  Of course, this assumes two assumptions that people often skip.

• The scatter plot forms a roughly linear pattern
• The correlation is strong enough (I wanted to tell him about the Pearson correlation coefficient but I held off)

He was quite impressed.  I realized after we had finished talking that I forgot to mention how to figure out which line best matches a scatter plot.  But I guess I had already used up my 15 minutes quota of his attention.