Question

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

x	22	24	26	30	35	40
y	12	20	34	36	39	37

(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 (C) 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 =

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

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

x	9	32	18	15	26
y	9	20	22	16	23

(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 =

(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 =

(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

using minitab>Stat>Regression

we have

Regression Analysis: y versus x

The regression equation is
y = - 7.53 + 1.261 x

S = 7.49205 R-Sq = 62.9% R-Sq(adj) = 53.6%

Analysis of Variance

Source DF SS MS F P
Regression 1 380.810 380.810 6.78 0.060
Error 4 224.523 56.131
Total 5 605.333

(a) an estimated regression equation for the data of the form

ŷ =- 7.5 + 1.261 x

(b) F= 6.78

p-value =0.060

using minitab>Stat>Regression

we have

Polynomial Regression Analysis: y versus x

The regression equation is
y = - 169.5 + 12.21 x - 0.1769 x^2

S = 3.87428 R-Sq = 92.6% R-Sq(adj) = 87.6%

Analysis of Variance

Source DF SS MS F P
Regression 2 560.303 280.152 18.66 0.020
Error 3 45.030 15.010
Total 5 605.333

(C) an estimated regression equation for the data is

ŷ =- 169.5 + 12.21 x - 0.1769 x^2

(D) the value of the test statistic(F)=18.66

p-value =0.020

when x = 25 , ŷ =- 169.5 + 12.21*25 - 0.1769*25*25 = 25.188

using minitab>stat>Regression

we have

Regression Analysis: y versus x

The regression equation is
y = 8.606 + 0.4697 x

S = 4.36642 R-Sq = 56.0% R-Sq(adj) = 41.3%

Analysis of Variance

Source DF SS MS F P
Regression 1 72.803 72.8030 3.82 0.146
Error 3 57.197 19.0657
Total 4 130.000

Ans a ) an estimated regression equation

ŷ = 8.61 + 0.470 x

Ans b ) using minitab>Stat>Regression

we have

Polynomial Regression Analysis: y versus x

The regression equation is
y = - 12.94 + 2.930 x - 0.05935 x^2

S = 1.57242 R-Sq = 96.2% R-Sq(adj) = 92.4%

Analysis of Variance

Source DF SS MS F P
Regression 2 125.055 62.5275 25.29 0.038
Error 2 4.945 2.4725
Total 4 130.000

(b) Develop an estimated regression equation for the data of the form

ŷ = - 12.94 + 2.930 x - 0.0594 x^2  

(c)the value of y when x = 20.

ŷ = - 12.94 + 2.930*20 - 0.0594*20*20 =21.90