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23. The table below shows the altitude of a plane once it begins its descent to a runway.
a) Write an equation to model the data using linear regression.
Time
(minutes)
0
1
Altitude
(feet)
28,500
26,378
24,105
21,774
19,452
17,991
b) Find the height of the plane after 8 minutes.
2
3
4
5
c) How long will it take the plane to land?
Gina Wilson (All Things Algebra), 2015

Respuesta :

fichoh
  • The regression equation to model the data is Ŷ = 28437.191 - 2161.543X

  • The altitude of the plane after 8 minutes is 11144.847 feets

  • The landing time of the plane is approximately 13 minutes

The table :

Time (x)_____ Altitude (y)

0 _______28500

1 _______ 26378

2 _______24105

3 _______ 21774

4 _______ 19452

5 _______ 17991

Using a linear regression calculator or excel, we could obtain the regression equation :.

The regression equation obtained is :

Ŷ = 28437.191 - 2161.543X

Where :

Ŷ = Predicted value

Intercept = 28437.191

Slope = - 2161.543

  • Height of the plane after 8 minutes

X = 8

Ŷ = 28437.191 - 2161.543(8) = 11144.847 feets

  • Time it will take for the plane to land.

Altitude at landing = 0, Ŷ = 0

We solve for X in the equation :

0 = 28437.191 - 2161.543X

0 - 28437.191 = - 2161.543X

- 28437.191 = - 2161.543X

Divide both sides by - 2161.543

- 28437.191 / - 2161.543 = X

X = 13.156

Hence, the land will land in approximately 13 minutes.

Learn more : https://brainly.com/question/4997238?referrer=searchResults

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