Two variables Covariance and Correlation. On this one golf hole over several days I noticed my first shot was not the same distance from the tee. As I.

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Presentation transcript:

Two variables Covariance and Correlation

On this one golf hole over several days I noticed my first shot was not the same distance from the tee. As I thought more about it I noticed the wind was at my back and I was able to measure the speed of the wind. Say the distance of each shot, starting with the 5 MPH wind was the following: 235, 245, 260, 280, and 310. What is the covariance of these two variables? What is the correlation? What do the numbers mean? The tee (the place where one hits the first shot) Wind speed 40 mph 30 mph 20 mph 10 mph 5 mph

Wind Speed in MPH Distance from the tee XY(X - X bar)(Y - Y bar)(X - X bar)(Y - Y bar) sum of these means1695 of Xof Yto get Covariance 21266divide this sum by called5-1=4 X bar hereY bar hereto get 1695/4 = Here I have put together the information needed to calculate the covariance. The main point is that the number is positive and so we see that the wind speed and the distance the ball travels are positively related.

Wind Speed in MPH Distance from the tee XY(X - X bar)(Y - Y bar)(X - X bar)(Y - Y bar) sum of these means1695 of Xof Yto get Covariance 21266divide this sum by called5-1=4 X bar hereY bar hereto get 1695/4 = (X - X bar)^2(Y - Y bar)^ sum divide by these are variance values take squareroot these are standard deviations CorrelationCoefficient iscovariance divided by product of standard deviations Here the correlation coefficient has been calculated. Note that the standard deviation of each variable had to be calculated. The correlation coefficient of.99 is positive. This means the two variables are positively related. We saw this with the covariance as well. The other point about the correlation coefficient is that when positive the value can range from 0 to 1. A.99 value is almost 1 and this means the relationship is very strong. What this really means is that the distance the tee shot travels is very much influenced by the wind speed occurring during the shot. While not the case here in this example, note that if negative the correlation coefficient will fall between -1 and 0, and closer to -1 means the stronger the relationship.