Consider the following data for two variables, x and y. x 22 24 26 30 35 40 y 11 21 34 36 39 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, 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, 39), 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, 11), 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. Does the scatter diagram suggest an estimated regression equation of the form ŷ = b0 + b1x + b2x2? Explain. No, 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.Yes, 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.) 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.)

Consider the following data for two variables, x and y. x 22 24 26 30 35 40 y 11 21 34 36 39 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, 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, 39), 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, 11), 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. Does the scatter diagram suggest an estimated regression equation of the form ŷ = b0 + b1x + b2x2? Explain. No, 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.Yes, 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.) 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.)

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	21	34	36	39	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, 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, 39), 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, 11), 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.

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

ŷ = b₀ + b₁x + b₂x²?

Explain.

No, 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.Yes, 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.)

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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