Question

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

x	22	24	26	30	35	40
y	13	20	34	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 =

(c)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 =

(d)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.)

test statistic=?

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

p-value =

(e) Use the model from part (c) to predict the value of y when x = 25. (Round your answer to three decimal places.)

predicted value=?

Answer 1

Analysis is performed using Minitab

(a)

Develop an estimated regression equation

Regression Equation

y   =   -5.9 + 1.207 x

b)

Find the value of the test statistic.

F = 6.44

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

p-value = 0.064

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

(c)

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.)

Now define X2 as x*x that is x2 and then build the regression model

x	y	x2
22	13	484
24	20	576
26	34	676
30	35	900
35	40	1225
40	36	1600

Regression Equation

y   =   -165.8 + 12.01 x - 0.1746 x2

d)

Analysis of Variance
Source	DF	Adj SS	Adj MS	F-Value	P-Value
Regression	2	523.44	261.72	18.74	0.02
x	1	214.57	214.57	15.37	0.03
x2	1	174.71	174.71	12.51	0.038
Error	3	41.9	13.97
Total	5	565.33

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.)

test statistic=18.74

p-value =0.020

since p-value =0.020 <α = 0.05 so we reject the null hypothesis and conclude that relationship between x, x2,and y is not significant.

(e) Use the model from part (c) to predict the value of y when x = 25. (Round your answer to three decimal places.)

y   =   -165.8 + 12.01*25 - 0.1746*252

y = 25.325