Question

What is the quadratic regression equation for the data set?

Data set down below

x y

50 10
30 11
11 5
35 9
50 12
20 3
90 7


Answers down below

A. y=−0.004x^2−0.415x−0.546

B. y=0.004x^2+0.415x+0.546
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C. y=−0.004x^2−0.415x+0.546

D. y=−0.004x^2+0.415x−0.546

(Note: One of the answers is the listed EQUATIONS, not a pair from the data set.)

Answer 1

Option D -
`y=-0.004x^2+0.415x-0.546`

Explanation:

Given : Data set down below.

To find : What is the quadratic regression equation for the data set?

Solution :

x y

50 10

30 11

11 5

35 9

50 12

20 3

90 7

Using regression calculator we plot the points of the data and find the regression equation.

Refer the attached figure below showing the regression calculation.

With the help of the graph the regression equation form is
`y=-0.0037x^2+0.4148x-0.5458`

which is approximately
`y=-0.004x^2+0.415x-0.546`

Therefore, Option D is correct.

Answer 2

Option: D is the correct answer.

D.
`y=-0.004x^+0.415x-0.546`

Explanation:

We are given set of data points as:

x y

50 10

30 11

11 5

35 9

50 12

20 3

90 7

By plotting all these point in a scatter plot we see that the equation that best fits the data is a curve or a parabola that opens down and attains it's maximum value and the equation as is obtained on the regression calculator is:

`y=-0.004x^2+0.415x-0.546`