Question

In a regression analysis involving 30 observations, the following estimated regression equation was obtained.

ŷ = 17.6 + 3.8x₁ − 2.3x₂ + 7.6x₃ + 2.7x₄

For this estimated regression equation, SST = 1,835 and SSR = 1,800.

(a)At α = 0.05, test the significance of the relationship among the variables.State the null and alternative hypotheses.

-H₀: One or more of the parameters is not equal to zero.
H_a: β₀ = β₁ = β₂ = β₃ = β₄ = 0

-H₀: β₀ = β₁ = β₂ = β₃ = β₄ = 0
H_a: One or more of the parameters is not equal to zero.    

-H₀: β₁ = β₂ = β₃ = β₄ = 0
H_a: One or more of the parameters is not equal to zero.

-H₀: One or more of the parameters is not equal to zero.
H_a: β₁ = β₂ = β₃ = β₄ = 0

(b)Find the value of the test statistic. (Round your answer to two decimal places.)

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

(d)State your conclusion.

-Reject H₀. We conclude that the overall relationship is significant.

-Do not reject H₀. We conclude that the overall relationship is significant.

-Do not reject H₀. We conclude that the overall relationship is not significant.

-Reject H₀. We conclude that the overall relationship is not significant.

Suppose variables x₁ and x₄ are dropped from the model and the following estimated regression equation is obtained. ŷ = 11.1 − 3.6x₂ + 8.1x₃

For this model, SST = 1,835 and SSR = 1,745.

(e)Compute SSE(x₁, x₂, x₃, x₄).

SSE(x₁, x₂, x₃, x₄)= _____

(f)Compute SSE(x₂, x₃).

SSE(x₂, x₃)=____

(g)Use an F test and a 0.05 level of significance to determine whether x₁ and x₄ contribute significantly to the model.State the null and alternative hypotheses.

(h)Find the value of the test statistic. (Round your answer to two decimal places.)

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

(j)State your conclusion.

-Reject H₀. We conclude that x₁ and x₄ do not contribute significantly to the model.

-Do not reject H₀. We conclude that x₁ and x₄ do not contribute significantly to the model.

-Reject H₀. We conclude that x₁ and x₄ contribute significantly to the model.

-Do not reject H₀. We conclude that x₁ and x₄ contribute significantly to the model.

Answer 1

a)

H₀: β₀ = β₁ = β₂ = β₃ = β₄ = 0
H_a: One or more of the parameters is not equal to zero.  

k=independent variables =			4
n=sample size =			30
SST=	1835	SSR =	1800
SSE =SST-SSR=		35.0
MSR=SSR/k=		450.0
MSE=SSE/(n-k-1)=		1.4
b)F =MSR/MSE =		321.43
c)p value =0.000

d)

-Reject H₀. We conclude that the overall relationship is significant.

e)

SSE(x1,x2,x,3,x4) =

35

f)

SSE(x2x3) =

90

g)

Ho: ß1 =ß4 =0

Ha: at least one of the variable is not zero

h)

F =	((90-35)/2)/(35/25)=		19.64
i)p value =0.000

j)

-Reject H₀. We conclude that x₁ and x₄ contribute significantly to the model.