![]() ![]() Our teacher already knows there is a positive relationship between how much time was spent on an essay and the grade the essay gets, but we’re going to need some data to demonstrate this properly. Sure, there are other factors at play like how good the student is at that particular class, but we’re going to ignore confounding factors like this for now and work through a simple example. ![]() If a teacher is asked to work out how time spent writing an essay affects essay grades, it’s easy to look at a graph of time spent writing essays and essay grades say “Hey, people who spend more time on their essays are getting better grades.” What is much harder (and realistically, pretty impossible) to do by eye is to try and predict what score someone will get in an essay based on how long they spent on it. Often the questions we ask require us to make accurate predictions on how one factor affects an outcome. The line of best fit is described by the equation bX + a, where b is the slope of the line and a is the intercept (i.e., the value of Y when X 0). How to find a least squares regression line It’s the bread and butter of the market analyst who realizes Tesla’s stock bombs every time Elon Musk appears on a comedy podcast, as well as the scientist calculating exactly how much rocket fuel is needed to propel a car into space. ![]() Being able to make conclusions about data trends is one of the most important steps in both business and science. ![]()
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