Question

 

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

x	22	24	26	30	35	40
y	11	20	33	34	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 =

−8.3+1.259x

  

(b)

Use the results from part (a) to test for a significant relationship between x and y. Use α = 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 = 0.057

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, 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.

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.

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 =

Answer 1

Analysis is performed using Minitab

(a)

Develop an estimated regression equation

Regression Equation

y   =   -8.3 + 1.259 x

b)

Find the value of the test statistic.

F = 7.05

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

p-value = 0.057

No, the relationship is not significant. because p-value = 0.057> 0.05 level of significance.

(c)

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.

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

ŷ = b0 + b1x + b2x2?

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

d)

Regression Equation

y   =   -166.8 + 11.97 x - 0.1731 x2

.