The following data is representative of that reported in an article with x = bur

Question

The following data is representative of that reported in an article with x = burner-area liberation rate (MBtu/hr-ft^2) and y = NO_x emission rate (ppm): (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. 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 H_0. There is no evidence that the model is useful. Reject H_0. There is no evidence that the model is useful. Fail to reject H_0. There is evidence that the model is useful. Reject H_0. 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-ft^2 increase in liberation rate. (Round your answers to two decimal places.) (, ) ppm

Explanation / Answer

(Sol:

in R i found correlation coeff between x and y is

x y
x 1.0000000 0.9744186
y 0.9744186 1.0000000

r=0.9744

t=15.02

p=0.000

REJECT H0

rcode for confidence interval:

predict(mod1, newdata, interval="confidence")
fit lwr upr
88.01445 42.18254 133.8464

(42.18,133.85)

we are 95% confident that the true emission rate lies in between 42.18 and 133.85

SUMMARY OUTPUT Regression Statistics Multiple R 0.974419 R Square 0.949492 Adjusted R Square 0.945282 Standard Error 42.0827 Observations 14 ANOVA df SS MS F Significance F Regression 1 399498.6 399498.6 225.5838 3.83E-09 Residual 12 21251.45 1770.954 Total 13 420750 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -49.1524 29.16453 -1.68535 0.117727 -112.696 14.39162 x 1.714586 0.114158 15.01945 3.83E-09 1.465858 1.963314

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