With a Grand Slam approaching, let’s talk tennis! If we were to predict a tennis pro’s weight based on his height, where would we begin? How will our understanding of the best-fit line and spreadsheets help us make this prediction?
We’ve collected the heights and weights of tennis pros including Federer, Djokovic, Nadal, Murray, Azarenka, Sharapova, and Williams, along with another 192 top players. Let’s investigate how to 1) calculate the correlation of weights and heights, and 2) draw a best fit-line and scatter plot in Google spreadsheets to extrapolate or make predictions!
Correlation between Weight & Height
The correlation coefficient r is a measure that describes how strong the linear relationship is between two items – which in our case is the height and the weight. Recall that r will always take on a value between -1 and 1. The closer r is to 1 (or -1), the closer the two variables are to achieving a perfect positive (or negative) linear relationship.
We’ll also calculate the r-squared, also called the coefficient of determination, to understand how much of the difference in one variable (y) can be accounted for or explained by the difference in another variable (x).
What do we find? The correlation between heights and weights of the top 100 male pros and top 100 female pros is approximately 71% with an r-squared greater than 50%. There is indeed a fairly strong positive correlation between the heights and weights! Do you know how to calculate the correlation and r-squared in spreadsheets? For a refresher, view our video tutorial here: Correlation and R-Squared
Line of Best Fit
The best-fit line, also known as the line of best fit or the least squares regression line, is a line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible. Why is it useful? It allows us to predict or extrapolate information!
For example, the best-fit line based on the data of the 200 tennis pro’s heights (x) and weights (y) is as follows: y = 5.6x – 235.7. (Learn how to calculate this line in a spreadsheet in the video below!) Note that the height (x) is measured in inches, and the weight (y) is measured in pounds (lbs).
So, based on this line, what would we expect a pro’s weight to be if his or her height is 6 feet or 72 inches? We can apply the height (x = 72 inches) to the best-fit equation, which results in 5.6 x 72 – 235.7 or 164 lbs.
For a 5-video on the Scatter Plot and Best-Fit Line, see below:
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