3. (5.30) A study of king penguins looked for a relationship between how deep th

Question

3. (5.30) A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled The relation of dive duration (DD) to depth (D)." Duration DD is measured in minutes, and depth D is in meters. The report then says, "The regression equation for this bird is: DD = 2.62 + 0.02D." What is the slope of the regression line? (Round your answer to the nearest hundredth.) This means that on average, if the length of the dive increases by one meter, the diving duration increases by minutes. (Round your answer to the nearest hundredth.) According to the regression line, how long does a typical dive to a depth of 152 meters last? minutes. (Round your answer to the nearest tenth.) eBook odot module pdX bps7 09 a 4095a53dbaasta99aTbabsaeor on www.macr llanhighered.com launchpad/bps7e/7 14541 8#/startite

Explanation / Answer

Concept Base

In the regression equation, y = + x, represents the y-intercept ……………..(1a) and

represents the slope of the regression line ……………………………………..(1b)

Physically,

represents the value of dependent variable, y when the independent variable x is zero…(2a) and represents the change in y per unit change in x, negative means decrease and positive means increase ……………………………………………………………………..(2b)

Now, to work out the answers,

Q3 Part (1)

Vide (1b) above, the slope = 0.02 ANSWER

Q3 Part (2)

Vide (2b) above, ‘this means on average, if the length of dive increases by one meter, the diving duration increases by 0.02 minutes. ANSWER

Q3 Part (3)

According to the given regression equation, DD = 2.62 + 0.02D, when D = 152,

DD = 2.62 + (0.02 x 152)

= 2.62 + 3.04

= 5.64.

Thus, a typical dive of to a depth of 152 meters would last 5.64 minutes ANSWER

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