Question

The following data is representative of that reported in an article with x = burner-area liberation rate (MBtu/hr-ft²) and y = NO_x emission rate (ppm):

x	100	125	125	150	150	200	200	250	250	300	300	350	400	400
y	160	140	190	210	190	320	280	390	420	440	400	590	620	670

(a) Does the simple linear regression model specify a significant relationship between the two rates? Use the appropriate test procedure to obtain information about the P-value, and then reach a conclusion at significance level 0.01.
State the appropriate null and alternative hypotheses.

H₀: β₁ ≠ 0
H_a: β₁ = 0H₀: β₁ = 0
H_a: β₁ > 0     H₀: β₁ = 0
H_a: β₁ < 0H₀: β₁ = 0
H_a: β₁ ≠ 0

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
P-value	=

State the conclusion in the problem context.

Fail to reject H₀. There is no evidence that the model is significant.Fail to reject H₀. There is evidence that the model is significant.     Reject H₀. There is no evidence that the model is significant.Reject H₀. There is evidence that the model is significant.

Answer 1

ΣX = 3300
ΣY = 5000
ΣX * Y = 1406500
ΣX2 = 913750
ΣY2 = 2181800
Sxx =Σ (Xi - X̅ )2 =    135892.857
Syy = Σ( Yi - Y̅ )2 =    396085.714
Sxy = Σ (Xi - X̅ ) * (Yi - Y̅) =    227928.571

Equation of regression line becomes Ŷ = -38.213 + 1.677 X

To Test :-
H0 :- ß1 = 0
H1 :- ß1 ≠ 0

Test Statistic :-
t = ( b - ß) / ( S / √(S(xx)))
t = ( 1.6773 - 0 ) / ( 33.8978 / √(135892.8572))
t = 18.24

Decision based on P value
P - value = P ( t > 18.24 ) = 0

Reject null hypothesis if P value < α level of significance
P - value = 0 < 0.01 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

Reject H0. There is evidence that the model is significant.