The following data represent the time between eruptions and the length of eruption for 8 randomly selected geyser eruptions. The coefficient of determination is found to be 78.3%. Interpret this result.

Time, x Length, y Time, x Length, y

12.05 1.80 11.46 1.64

11.73 1.80 11.58 1.67

12.06 1.81 12.19 1.90

12.21 1.88 11.52 1.76

Choose the best interpretation below.

A. 78.3% of the variation in time between eruptions is explained by the least-squares regression equation.

B. 78.3% of the variation in time between eruptions is not explained by the least-squares regression equation.

C. 78.3% of the variation in length of eruption is explained by the least-squares regression equation.

D. 78.3% of the variation in length of eruption is not explained by the least-squares regression equation.

Question

Ayanna Arellano

Mathematics

8 June, 11:26

The following data represent the time between eruptions and the length of eruption for 8 randomly selected geyser eruptions. The coefficient of determination is found to be 78.3%. Interpret this result.

Time, x Length, y Time, x Length, y

12.05 1.80 11.46 1.64

11.73 1.80 11.58 1.67

12.06 1.81 12.19 1.90

12.21 1.88 11.52 1.76

Choose the best interpretation below.

A. 78.3% of the variation in time between eruptions is explained by the least-squares regression equation.

B. 78.3% of the variation in time between eruptions is not explained by the least-squares regression equation.

C. 78.3% of the variation in length of eruption is explained by the least-squares regression equation.

D. 78.3% of the variation in length of eruption is not explained by the least-squares regression equation.

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Answers (1)

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Laura York · Answer 1

C. 78.3% of the variation in length of eruption is explained by the least-squares regression equation.

Step-by-step explanation:

The coefficient of determination R-square is used to determine the explained variation in dependent variable explained by the least square regression line.

We know that independent variable in the given scenario is time of eruptions (x) and dependent variable is length of eruptions (y). We are given that coefficient of determination is 78.3%.

Thus, the 78.3% of variation in length of eruption is explained by the least square regression equation.