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-ft^2) and y = NO_x 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 NO_x emission rate when burner area liberation rate equals 210? ppm (c) Estimate the amount by which you expect NO_x emission rate to change when burner area liberation rate is decreased by 40. ppm

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -34.645204 + 1.6712221 x
Sample size: 14
R (correlation coefficient) = 0.97325508
R-sq = 0.94722545
Estimate of error standard deviation: 41.978552

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

a) Regression equation:

y = -34.6452 + 1.6712 x

b) For x = 210,

y = -34.6452 + 1.6712(210)

y = 316.31

c) Slope = 1.6712,

So if we decrease the burner area liberation rate by 40 then NOx emission rate will decrease by:

1.6712(40) = 66.85 ppm

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -34.645204 29.092351 0 12 -1.1908698 0.2567 Slope 1.6712221 0.1138752 0 12 14.675909 <0.0001

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