Question

A statistical program is recommended.

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

x	9	32	18	15	26
y	11	20	22	17	22

(a) Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x. (Round b₀ to two decimal places and b₁ to three decimal places.)

ŷ =

Comment on the adequacy of this equation for predicting y. (Use α = 0.05.)

The high p-value and low coefficient of determination indicate that the equation is inadequate.The high p-value and high coefficient of determination indicate that the equation is adequate.    The low p-value and low coefficient of determination indicate that the equation is inadequate.The low p-value and high coefficient of determination indicate that the equation is adequate.

(b) Develop an estimated regression equation for the data of the form ŷ = b₀ + b₁x + b₂x². (Round b₀ to two decimal places and b₁ to three decimal places and b₂ to four decimal places.)

ŷ =

Comment on the adequacy of this equation for predicting y. (Use α = 0.05.)

The high p-value and low coefficient of determination indicate that the equation is inadequate.The high p-value and high coefficient of determination indicate that the equation is adequate.    The low p-value and low coefficient of determination indicate that the equation is inadequate.The low p-value and high coefficient of determination indicate that the equation is adequate.

(c)

Use the model from part (b) to predict the value of y when x = 20. (Round your answer to two decimal places.)

Answer 1

Applying regression from excel: data-data analysis:

	Coeff	Std Error	t Stat	P-value
Constant	-68.079	136.035	-0.500	0.6664
x1	0.816	1.402	0.582	0.6196
x2	0.491	0.309	1.590	0.253
	df	SS	MS	F	p value
Regression	1	45.10	45.10	3.37	0.1635
Residual	3	40.10	13.37
Total	4	85.20

a)

y^ =11.01+0.370x

p value =0.1635

Coefficient of determination =SSR/SST =0.5294

The high p-value and low coefficient of determination indicate that the equation is inadequate.

b)

y^ =-6.94+2.419x-0.0494x²

The low p-value and high coefficient of determination indicate that the equation is adequate.

c)

predicted value =-6.94+2.419*20-0.0494*20^2 =21.68

(please try 21.66 if above comes wrong)