The following data is representative of that reported in an article on nitrogen

Question

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

(a) Assuming that the simple linear regression model is valid, obtain the least squares estimate of the true regression line. (Round all numerical values to four decimal places.)
y =

(b) What is the estimate of expected NOx emission rate when burner area liberation rate equals 200? (Round your answer to two decimal places.)
___________ppm

(c) Estimate the amount by which you expect NOx emission rate to change when burner area liberation rate is decreased by 50. (Round your answer to two decimal places.)
__________ ppm

x 100 125 125 150 150 200 200 250 250 300 300 350 400 400 y 140 140 170 200 180 310 270 400 440 430 390 590 610 680

Explanation / Answer

We run regression analysis in excel and we get the output as below :

a) Here we get intercept coefficient = a = -58.3246

slope coefficient = b = 1.7474

Hence the regression equation is given by

y = a+ b * x

y = - 58.3246+ 1.7474 * x

b) burner area liberation rate = x= 200

y = - 58.3246+ 1.7474 * 200

= 291.16 PPM

c) Burner area liberation rate is decreased by 50

y = - 58.3246+ 1.7474 * ( -50)

y = -146.70 ppm

SUMMARY OUTPUT Regression Statistics Multiple R 0.979481 R Square 0.959384 Adjusted R Square 0.955999 Standard Error 38.26161 Observations 14 ANOVA df SS MS F Significance F Regression 1 414954 414954 283.448 1.03E-09 Residual 12 17567.41 1463.951 Total 13 432521.4 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -58.3246 26.5164 -2.19957 0.048174 -116.099 -0.55029 x 1.747438 0.103792 16.83592 1.03E-09 1.521294 1.973581

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