Question

A statistical program is recommended.

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

x	22	24	26	30	35	40
y	13	20	33	35	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 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 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.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 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 on above data:

	df	SS	MS	F	p value
Regression	1	357.23	357.23	7.13	0.0557
Residual	4	200.27	50.07
Total	5	557.50
	Coeff	Std Error	t Stat	P-value
Constant	-6.528	13.794	-0.473	0.6607
x1	1.221	0.457	2.671	0.0557

y^ =-6.5+1.221*x

b)

F test statistic =7.13

p value =0.056

No, the relationship is not significant.    

c)

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

y^ =-163..6+11.84x-0.1715x²

value of the test statistic F =24.94

p-value = 0.014

Yes, the relationship is significant

predicted value =-163..6+11.84*25-0.1715*25^2 =25.213 (please try 25.144 if this comes wrong)