The length, x (in inches), and weight, y (in ounces), for a type of bass were measured for a random sample of 10 bass from a lake. These measurements were then analyzed and the value for r squared was determined to be 96% Which of the following is the best interpretation of this value?
Answer
A
96 percent of the variation in the bass’s length is determined by the variation in the bass’s weight.
B
4 percent of the variation in the bass’s length is determined by the variation in the bass’s weight.
C
98 percent of the variation in the bass’s weight is determined by the variation in the bass’s length.
D
96 percent of the variation in the bass’s weight is determined by the variation in the bass’s length.
Explanation
The coefficient of determination, r², tells us the percentage of variation in the response variable explained by its linear relationship with the explanatory variable. Here, bass weight (y) is the response and bass length (x) is the explanatory variable. Thus, r² = 96% means 96 percent of the variation in the bass’s weight is explained by variation in its length, which is choice D.
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