Which line is best?

Which line is best?

A model is a family member that fits the data best. When a scatter plot looks like a line, the family is the line family, y = mx + b, and the question is which member comes closest to the points. You could draw many lines through a cloud of points. Which one is best?

The line of best fit, also called the least squares regression line, is the line that makes the total error as small as possible. For each point, measure how far it is above or below the line. Square each of those distances, add them up, and find the line that makes that total the smallest.

You do not compute this line by hand. Regression means finding the best-fitting line or curve, and technology does it: the tool below, or a graphing calculator, gives the slope m, the y-intercept b, and r. Your jobs are to choose the family, read the numbers in the story, and judge the predictions.

First, try it by eye. A lab rat is weighed once a week. Slide the two ends of your dashed line until it runs through the middle of the points, then show the least squares line and compare.

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