In a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. A regression analysis was completed and the value for r squared was 52 point 1 percent Which of the following is the correct interpretation of r squared ?
Answer
A
About 52 point 1 percent of the variation in handspan is accounted for by the linear relationship formed with the number of bite-sized pretzels grabbed with the dominant hand.
B
About 52 point 1 percent of the variation in number of bite-sized pretzels grabbed with the dominant hand is accounted for by the linear relationship formed with handspan.
C
About 72 point 1 percent of the variation in number of bite-sized pretzels grabbed with the dominant hand is accounted for by the linear relationship formed with handspan.
D
About 47 point 9 percent of the variation in handspan is accounted for by the linear relationship formed with the number of bite-sized pretzels grabbed with the dominant hand.
Explanation
The coefficient of determination, r², is the percentage of variation in the response variable explained by its linear relationship with the explanatory variable. Here, the number of pretzels grabbed is the response, and handspan is the explanatory variable. Since r² = 52.1%, about 52.1% of the variation in pretzels grabbed is accounted for by the linear relationship with handspan, which is choice D.
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