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.)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
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Chapter5: A Survey Of Other Common Functions
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Problem 1TU: The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t=...
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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.)Expert Solution
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