Question

The following data is representative of that reported in an article with x = burner-area liberation rate (MBtu/hr-ft2) and y = NOx emission rate (ppm): x 100 125 125 150 150 200 200 250 250 300 300 350 400 400 y 150 140 170 210 180 320 280 400 420 440 400 590 620 680 (a) Does the simple linear regression model specify a useful 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 Ha: β1 > 0 H0: β1 = 0 Ha: β1 < 0 H0: β1 = 0 Ha: β1 ≠ 0 H0: β1 ≠ 0 Ha: β1 = 0 Correct: Your answer is correct. 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. Reject H0. There is evidence that the model is useful. Reject H0. There is no evidence that the model is useful. Fail to reject H0. There is no evidence that the model is useful. Fail to reject H0. There is evidence that the model is useful. (b) Compute a 95% CI for the expected change in emission rate associated with a 10 MBtu/hr-ft2 increase in liberation rate. (Round your answers to two decimal places.) , ppm You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

(a) H0: β1 = 0 Ha: β1 ≠ 0

t=b/SE(b)=1.745/0.091=19.16 with error df=12

p-value=0.000

Reject H0. There is evidence that the model is useful

(b) the simple linear regression model is y=-54.258+1.745x

for x=10, y=-54.258+1.745*10=-36.81

95% confidence interval=-36.81t(0.05/2,12)*33.58*sqrt(1/14+(10-235.71)/135893)=

=-36.812.18*33.58*sqrt(1/14+(10-235.71)/135893)=-36.8119.34=(-56.15,-17.47)

following information has been generated using ms-excel

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.984048109
R Square	0.96835068
Adjusted R Square	0.965713237
Standard Error	33.57781021
Observations	14
ANOVA
	df	SS	MS	F	Significance F
Regression	1	413956.0822	413956.1	367.1551	2.3E-10
Residual	12	13529.63206	1127.469
Total	13	427485.7143
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-54.25755585	23.27039377	-2.33161	0.037959	-104.959	-3.55572
X Variable 1	1.745335085	0.091086509	19.16129	2.3E-10	1.546875	1.943796

y=-54.258+1.745x