contestada

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 = 2.69 + 0.0138D.
1. What is the slope of the regression line?
2. Explain in specfic language what this slope says about this penguin's dives.
A. If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.
B. If the depth of the dive is decreased by one meter, it adds 0.0138 minutes to the time spent under water.
C. If the depth of the dive is increased by 0.0138 meter, it adds one minute to the time spent under water.
3. According to the regression line, how long does a typical dive to a depth of 200 meters last?
4. According to the regression line, how long does a typical dive to a depth of 210 meters last?
5. According to the regression line, how long does a typical dive to a depth of 220 meters last?
6. According to the regression line, how long does a typical dive to a depth of 230 meters last?
7. According to the regression line, how long does a typical dive to a depth of 240 meters last?
8. According to the regression line, how long does a typical dive to a depth of 150 meters last?
9. According to the regression line, how long does a typical dive to a depth of 160 meters last?
10. According to the regression line, how long does a typical dive to a depth of 170 meters last?
11. According to the regression line, how long does a typical dive to a depth of 180 meters last?
12. According to the regression line, how long does a typical dive to a depth of 190 meters last?

Respuesta :

Answer:

(1)0.0138

(2)A. If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.

Nos 3-12: See Explanation

Step-by-step explanation:

Given the regression equation for the relation of dive duration (DD) to depth (D).

[tex]DD = 2.69 + 0.0138D\\$Where: Duration DD is measured in minutes\\epth D is in meters.[/tex]

(1)The slope of the regression lie =0.0138

(2)

When D=1, DD = 2.69 + 0.0138(1)=2.7038

When D=2, DD = 2.69 + 0.0138(2)=2.7176

2.7176-2.7038=0.0138

Therefore, If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.

(3) When depth, D =200 meters

DD = 2.69 + 0.0138(200)=5.45 Minutes

(4) When depth, D =210 meters

DD = 2.69 + 0.0138(210)=5.588 Minutes

(5) When depth, D =220 meters

DD = 2.69 + 0.0138(220)=5.726 Minutes

(6) When depth, D =230 meters

DD = 2.69 + 0.0138(230)=5.864 Minutes

(7) When depth, D =240 meters

DD = 2.69 + 0.0138(240)=6.002 Minutes

(8) When depth, D =150 meters

DD = 2.69 + 0.0138(150)=4.76 Minutes

(9) When depth, D =160 meters

DD = 2.69 + 0.0138(160)=4.898 Minutes

(10) When depth, D =170 meters

DD = 2.69 + 0.0138(170)=5.036 Minutes

(11) When depth, D =180 meters

DD = 2.69 + 0.0138(180)=5.174 Minutes

(12) When depth, D =190 meters

DD = 2.69 + 0.0138(190)=5.312 Minutes

A regression line is only a single line that fits the data the best. It tells how steep it is, whereas the intercept reveals where it intersects an axis.

Regression line:

For question 1):

By calculating the slope of the regression line we get the slope value that is [tex]= 0.0138[/tex]

For question 2):

Describe whatever this slope means about this penguin's dives in precise terms.

The time spent under liquid increases by 0.0138 minutes whenever the diving depth is raised by one meter, which is equal to "Option A".

For question 3):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times200 = 2.69+2.76 = 5.45\ minutes[/tex]

For question 4):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times210 = 2.69 + 2.898 = 5.588\ minutes[/tex]

For question 5):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 220 = 2.69 + 3.036 = 5.726\ minutes[/tex]

For question 6):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times230 = 2.69 + 3.174 = 5.864 \ minutes[/tex]

For question 7):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times240 = 2.69 + 3.312 = 6.002\ minutes[/tex]

For question 8):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 150 = 2.69 + 2.07 = 4.76\ minutes[/tex]

For question 9):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 160 = 2.69 + 2.208 = 4.898\ minutes[/tex]

For question 10):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 170 = 2.69 + 2.346 = 5.036\ minutes[/tex]

For question 11):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 180 = 2.69 + 2.484 = 5.174 \ minutes[/tex]

For question 12):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 190 = 2.69 + 2.622 = 5.312\ minutes[/tex]

Find out more about the regression line here:

brainly.com/question/7656407

Otras preguntas