The correlation coefficient ranges from –1 to +1. The closer r is to +1, the closer the data points are to an increasing straight line indicating a positive linear relationship. The closer r is to –1, the closer the data points are to a decreasing straight line indicating a negative linear relationship. When r = 0, there is no linear relationship between x and y but not necessarily a lack of relationship.
Example: Rising Hills Manufacturing Inc. wishes to study the relationship between the number of workers, X, and the number of tables, Y, produced in its Redwood Falls plant. It has obtained a random samples of 10 hours of production. The following (x, y) combinations of points were obtained:
(12, 20) (30, 60) (15, 27) (24, 50) (14, 21)
(18, 30) (28, 61) (26, 54) (19, 32) (27, 57)
Compute the covariance and correlation coefficient. Discuss briefly the relationship between the number of workers and the number of tables produced per hour.
Solution: The computations are set out in the Table bellow.
We conclude that there is a strong positive relationship between number of workers and number of tables produced per hour.
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