Data were collected on the depth (yards) and duration (minutes) of the dives of

Question

Data were collected on the depth (yards) and duration (minutes) of the dives of penguins. The equation for the least-squares regression line for predicting depth,y from duration,x, was then determined to be y =0.015+2.915x with R^2=0.895 and r=0.946.

35. Which of the following is a valid interpretation of the correlation coefficient, r? a. 94.6% of the variation in the depth of the penguins dive is explained by the least- b. There is a weak positive linear relationship between the duration and the depth of a c. A relationship between duration and depth of a penguin's dive exists, but we are not d. There is a strong positive linear relationship between the duration and the depth of a e. None of the above. squares regression line. penguin's dive. given enough information to tell what type of relationship exists. penguin's dive. 36. If Penguin Joey dove for 5 minutes and the residual for his dive is -2, which of the following statements is an accurate interpretation of Joey's dive? accurate a. Joey's dive was 2 yards above average for a penguin who dives for 5 minutes b. Joey's dive was 2 yards below average for a penguin who dives for 5 minutes. c. Joey's dive was 5 minutes above average for a 2 yard dive. d. Joey's dive was 5 minutes below average for a 2 yard dive. e. None of the above.

Explanation / Answer

Question 35:

The coefficient of determination R2 signifies the percentage of variation in the dependent variable that is explained by the regression line. Therefore 89.4% of the variation in the depth of the penguins dive is explained by the least squares regression line. Therefore a) is false.

Now as the correlation coefficient is 0.946, there is a strong positive linear relationship between the duration and the depth of a penguin's dive.

Therefore d) is the correct answer here.

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