A study of king penguins looked for a relationship between how deep the penguins

Question

A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay under water. For all but the shallowest dives, there is a linear relationship between depth of dive and length of time under water. The study report gives a scatterplot for a random sample of penguins. The dive duration is measured in minutes and depth (x value) is in meters. The depths are all positive numbers. The dives varied from 40 meters to 300 meters in depth. The report then says, "The regression equation for this bird is

(a) What is the y-intercept of the regression line? (Use 2 decimal places)

(c) What is the slope of the regression line? (Use 4 decimal places)

(d) What is the correct interpretation of the slope?

1- For every increase of 1 meter in depth, the mean dive duration increases by exactly 0.0127 minutes.

2- For every increase of 1 meter in depth, the mean dive duration decreases by exactly 0.0127 minutes.    

3- For every increase of 1 meter in depth, the mean dive duration increases by approximately 0.0127 minutes.

4- For every increase of 1 meter in depth, the mean dive duration decreases by approximately 0.0127 minutes.

(e) Based on the slope in (c), the correlation for this data is

1-Zero

2-Positive    

3-Negative

Explanation / Answer

a) y-intercept of the regression line =2.73

c)slope of the regression line=0.0127

d)3- For every increase of 1 meter in depth, the mean dive duration increases by approximately 0.0127 minutes.

e) correlation for this data is 2-Positive

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