Going to be the difference between what they actually The residual of a customer with a height of 155 centimeters who rents a bike with a 51 centimeter frame? So how do we think about this? Well, the residual is If I get a new person, I could take their height and put as x and figure out what frame This as a way of predicting, or either modeling the relationship or predicting that, hey,
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So our regression line, y-hat, is equal to 1/3 plus 1/3 x. It might look something, let me get my ruler tool, it might look something like, it might look something like this. And so the least squares regression, maybe it would look something like this, and this is just a rough estimate of it. To minimize the square of the distance between these points. And a least squares regression is trying to fit a line to this data. Of 100 centimeters in height who got a frame that was slightly larger, and she plotted it there. I don't know if that's reasonable or not, for you bicycle experts,īut let's just go with it. And so there might've been someone who measures 100 centimeters in height who gets a 25 centimeter frame. Something like this, where in the horizontalĪxis you have height measured in centimeters, and in the verticalĪxis you have frame size that's also measured in centimeters. The height of the customer, what size frame that person rented. So she had a bunch of customers, and she recorded, given
So before I even look at this question, let's just think about what she did. Squares regression equation for predicting bicycle frame size from the height of the customer. Was fairly linear, so she used the data to calculate the following least After plotting her results, Vera noticed that the relationship between the two variables She recorded the height, inĬentimeters, of each customer and the frame size, in centimeters, of the bicycle that customer rented.
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