Answered: Consider the following data for two…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Consider the following data for two variables, x and y.

x	22	24	26	30	35	40
y	11	20	32	36	40	36

(a)

Develop an estimated regression equation for the data of the form

ŷ = b₀ + b₁x.

(Round b₀ to one decimal place and b₁ to three decimal places.)

ŷ = ????

(b)

Use the results from part (a) to test for a significant relationship between x and y. Use ? = 0.05.

Find the value of the test statistic. (Round your answer to two decimal places.)

F = ??

Find the p-value. (Round your answer to three decimal places.)

p-value = ??

Is the relationship between x and y significant?

Yes, the relationship is significant.No, the relationship is not significant.

(c)

Develop a scatter diagram for the data.

-A scatter diagram has 6 points. The horizontal axis ranges from 20 to 45 and is labeled: x. The vertical axis ranges from 0 to 45 and is labeled: y. Moving from left to right, the leftmost point is at (22, 40), with the next 5 points extending downward in a diagonal direction.

-A scatter diagram has 6 points. The horizontal axis ranges from 20 to 45 and is labeled: x. The vertical axis -ranges from 0 to 45 and is labeled: y. Moving from left to right, the leftmost point is at (22, 7), with the next 4 points extending upward, the first two rising more steeply than the next two. The last point goes back down.

-A scatter diagram has 6 points. The horizontal axis ranges from 20 to 45 and is labeled: x. The vertical axis ranges from 0 to 45 and is labeled: y. Moving from left to right, the leftmost point is at (22, 36), with the next point extending upward. The last 4 points then continue downward in a diagonal direction.

-A scatter diagram has 6 points. The horizontal axis ranges from 20 to 45 and is labeled: x. The vertical axis ranges from 0 to 45 and is labeled: y. Moving from left to right, the leftmost point is at (22, 11), with the next 4 points extending upward, the first two rising more steeply than the next two. The last point goes back down.

Does the scatter diagram suggest an estimated regression equation of the form

ŷ = b₀ + b₁x + b₂x²?

Explain.

-Yes, the scatter diagram suggests that a linear relationship may be appropriate.

-Yes, the scatter diagram suggests that a curvilinear relationship may be appropriate.

- No, the scatter diagram suggests that a curvilinear relationship may be appropriate.

-No, the scatter diagram suggests that a linear relationship may be appropriate.

(d)

Develop an estimated regression equation for the data of the form

ŷ = b₀ + b₁x + b₂x².

(Round b₀ to one decimal place and b₁ to two decimal places and b₂ to four decimal places.)

ŷ = ??

(e)

Use the results from part (d) to test for a significant relationship between x, x², and y. Use ? = 0.05. Is the relationship between x, x², and y significant?

Find the value of the test statistic. (Round your answer to two decimal places.)

STATISTIC=??

Find the p-value. (Round your answer to three decimal places.)

p-value = ??

Is the relationship between x, x², and y significant?

Yes, the relationship is significant.

No, the relationship is not significant.

(f)Use the model from part (d) to predict the value of y when

x = 25. (Round your answer to three decimal places.)

???

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