Using this least squares regression line, we can answer questions like:įor a person who weighs 170 pounds, how tall would we expect them to be? How to Use the Least Squares Regression Line In this case, a one pound increase in weight is associated with a 0.2001 inch increase in height. This means that a one unit increase in x is associated with a 0.2001 unit increase in y. This means when the predictor variable weight is zero pounds, the predicted height is 32.7830 inches. Sometimes the value for b 0 can be useful to know, but in this specific example it doesn’t actually make sense to interpret b 0 since a person can’t weight zero pounds.ī 1 = 0.2001. How to Interpret a Least Squares Regression Line That’s because this least squares regression lines is the best fitting line for our data out of all the possible lines we could draw. Notice how our data points are scattered closely around this line.
If we zoom out on our scatterplot from earlier and added this line to the chart, here’s what it would look like: The calculator automatically finds the least squares regression line: Related: 4 Examples of Using Linear Regression in Real Life Finding the “Line of Best Fit”įor this example, we can simply plug our data into the Statology Linear Regression Calculator and hit Calculate: Where ŷ is the predicted value of the response variable, b 0 is the y-intercept, b 1 is the regression coefficient, and x is the value of the predictor variable. The formula for the line of best fit is written as: Usually you would use software like Microsoft Excel, SPSS, or a graphing calculator to actually find the equation for this line. This line is known as the least squares regression line and it can be used to help us understand the relationships between weight and height. Using linear regression, we can find the line that best “fits” our data. From the scatterplot we can clearly see that as weight increases, height tends to increase as well, but to actually quantify this relationship between weight and height, we need to use linear regression. Suppose we’re interested in understanding the relationship between weight and height.
If we graph these two variables using a scatterplot, with weight on the x-axis and height on the y-axis, here’s what it would look like: Let weight be the predictor variable and let height be the response variable. The other variable, y, is known as the response variable.įor example, suppose we have the following dataset with the weight and height of seven individuals: One variable, x, is known as the predictor variable. Simple linear regression is a statistical method you can use to understand the relationship between two variables, x and y.
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