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Aloiza [94]
3 years ago
12

use a graphing calculator or other technology to answer the question which quadratic regression equation best fits the data set

?​

Mathematics
1 answer:
Greeley [361]3 years ago
3 0

Answer:

Option C is the correct option.

In other words, the quadratic regression y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\: best fits the data set, as it gets very much close to the data values given in the data table.

The graph of the equation  y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:  is also attached.

Step-by-step explanation:

x                 y

3                470

4                416

5                403

Analyzing Option A:

Considering the equation

y=32.86\:\left(x\right)^2+379.14\left(x\right)-1369.14\:

From (3, 470), putting x = 3

y=32.86\:\left(3\right)^2+379.14\left(3\right)-1369.14\:

y=64.02

From (4, 470), putting x = 4

y=32.86\:\left(4\right)^2+379.14\left(4\right)-1369.14\:\:

y=673.18

From (5, 403), putting x = 5

y=32.86\:\left(5\right)^2+379.14\left(5\right)-1369.14\:

y=1348.06

Analyzing Option B:

y=32.86\:\left(x\right)^2-379.14\left(x\right)

From (3, 470), putting x = 3

y=32.86\:\left(3\right)^2-379.14\left(3\right)

y=-841.68

From (4, 470), putting x = 4

y=32.86\:\left(4\right)^2-379.14\left(4\right)

\:y=-990.8

From (5, 403), putting x = 5

y=32.86\:\left(5\right)^2-379.14\left(5\right)

\:y=-1074.2

Analyzing Option C:

Considering the equation

y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:

From (3, 470), putting x = 3

y=32.86\:\left(3\right)^2-379.14\left(3\right)+1369.14\:

y=527.46

So, the approximately result is (3, 527)

From (4, 470), putting x = 4

y=32.86\:\left(4\right)^2-379.14\left(4\right)+1369.14\:

y=378.34

So, the approximately result is (4, 378)

From (5, 403), putting x = 5

y=32.86\:\left(5\right)^2-379.14\left(5\right)+1369.14\:\:\:

y=294.94

So, the approximately result is (5, 295)

Analyzing Option D:

Considering the equation

y=-1369.14\:\left(x\right)^2-379.14\left(x\right)+32.86

From (3, 470), putting x = 3

y=-1369.14\:\left(3\right)^2-379.14\left(3\right)+32.86\:\:

y=-13426.82

From (4, 470), putting x = 4

y=-1369.14\:\left(4\right)^2-379.14\left(4\right)+32.86

y=-23389.94

From (5, 403), putting x = 5

y=-1369.14\:\left(5\right)^2-379.14\left(5\right)+32.86\:\:

y=-36091.34

Therefore, from the above calculations and analysis, we conclude that Option C is the correct option.

In other words, the quadratic regression y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\: best fits the data set, as it gets very much close to the data values given in the data table.

The graph of the equation  y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:  is also attached.

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