Regression Line

You know that one friend in your group who never has a beef with anyone, who always remembers little details about everyone’s lives, who always has a kind word, and even volunteers to help you move?

A regression line is kinda like that for a set of linear-ish data, always trying to stay as close to every data point as possible, no matter how far away some data points try to get. In fact, it’s the one “line of best fit” that minimizes the distances between the data points and the line.

It’s important to remember that we only find regression lines for data that is probably linear. We say “probably,” because there’s no way to be sure that a data set must be linear...only a bunch of circumstantial evidence that it might be linear.

Polly, the CEO of the world-renowned plant distributor “Polly’s Pretty Plants,” sells vegetable plants she has grown in her vast network of greenhouses. Okay, you got us. She works out of her mom’s basement, and she’s 13. Still, Polly is a maven for experimentation and statistical data gathering. So much so that she's gathered data on the different amounts of her special fertilizer/water mixture given to several plants from the same packet of tomato plant seeds all planted in soil from the same spot in her mom’s backyard.

Polly would like to be able to predict the amount of growth a seed will experience based on how much fertilizer she puts in the water. The whole point of the regression line is to allow her to do this...at least to a certain degree of accuracy. Regression lines give predictions, not guarantees.

Regression lines are the best fit lines to a set of data with a linear pattern. In this case, the phrase “best fit” means the line reduces the vertical distance between the points and the best fit line to as small as possible. We can find the slope and intercept of the regression line using the formulas, or we can just use tech to do everything for us.

And we can use the regression equation to help us predict either x or y values, with the expectation that the real result will probably be close to the value predicted by the regression equation.

Now we just need some regression to help us figure out if we were Albert Einstein or Fred Astaire in a previous life.