Question

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

x	22	24	26	30	35	40
y	13	22	34	34	41	35

(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 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 =

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.

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 linear relationship may be appropriate.

No, the scatter diagram suggests that a curvilinear 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 α = 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.)

Answer 1

a
)Applying regression from excel: data -data analysis:

y^ =-3.7+1.138x

b)F =5.62

p value =0.077

No, the relationship is not significant.    

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

d)

y^ =-165.5+12.07x-0.1766x²

e)value of the test statistic =17.51

p-value =0.022

.

Yes, the relationship is significant.

f)

predicted value =-165.5+12.07*25-0.1766*25^2=25.875 (please try 25.887 if this comes wrong)