This tutorial was written for developers and does not assume any prior background in mathematics or statistics.
A shortcut that greatly simplifies the calculation. How to make predictions on new data using your the model. How to perform all of the calculations using a spreadsheet. How to calculate a simple linear regression step-by-step. In this post, you will discover exactly how linear regression works step-by-step. That this formula minimizes the squared distancesįrom each of these points to that line.Linear regression is a very simple method but has proven to be very useful for a large number of situations. And it actually won't goĭirectly through that line. Going to be that exact, is going to look like that Graph it, and obviously I'm hand drawing it, so it's not To be equal to the mean of the y's, the mean of the And this is the same thingĪs negative 2/3 times negative 9/ 14. What's 49 minus 63? That's negative 14/9. Something over 9, that's the same thing as 63/9. I'm tempted to get out myĬalculator, but i'll resist the temptation. And we just have to do a littleīit of mathematics. So our slope, our optimal slopeįor our regression line, the mean of the x's is The x squareds? The first x squared is just To calculate is the mean of the x squareds. To be equal to? We have 2 plus 2, which is 4. And what's this going to be? 1 plus 2 is 3, plus 4 So what's the mean of our x's? The mean of our x's is going 
To calculate these things ahead of time, and then Like using our formulas, which we have proven. It the best fitting regression line, which we suspect Have the point, let's do something a little bitĬrazy, 4 comma 3. Points, and I'm going to make sure that these pointsĪren't colinear. And of course, whatever you getįor m, you can then just substitute back in this Numerator and denominator by negative 1, which is same thingĪs multiplying the whole thing by 1. X squareds minus the mean of the x's squared. Written as the mean of the xy's minus the mean of x times Numerator and denominator by negative 1, you could see this Textbook, you might see this swapped around. And if this looks a littleĭifferent than what you see in your statistics class or your
Really confusing, we're going to do an example of thisĪctually in a few seconds. Going to be the mean of x's times the mean of the y's minus Just rewrite it here just so we have something
When you measure the error by the squared distance Slope and y-intercept of the best fitting regression line
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