About 74% of the variation in the number of service calls is explained by the linear relationship between the number of service calls and the number of machines. Therefore, the correct answer is 74%.
The value r represents the correlation coefficient, which measures the strength and direction of a linear relationship between two variables.
The correlation coefficient ranges from -1 to 1, where 1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship.
In this case,
r=0.86, which indicates a strong positive linear relationship. The coefficient of determination r^2 represents the proportion of the variance in the dependent variable (number of service calls, y) that is predictable from the independent variable (number of copy machines, x).
r^2 =0.86^2 =0.7396
So, about 74% of the variation in the number of service calls is explained by the linear relationship between the number of service calls and the number of machines.
Therefore, the correct answer is:
74%
Question
A copy machine dealer has data on the number x of copy machines at each of 89 customer locations and the number y of service calls in a month at each location. r was found to be 0.86. About what percent of the variation in the number of service calls is explained by the linear relation between the number of service calls and number of machines? *
86%
93%
74%
43%